%% v20.2 (August 22, 2026): THE TWENTY-TWO-PAPER DISCLOSURE.
%%   Every reference to a companion paper now carries that companion's own
%%   permanent page -- e.g. https://preprints.arisaka-gg.org/a3-bi6/ -- in place
%%   of the single program address every reference used to share.  Papers that
%%   are not cohort members keep their own locators: the 1985 Kamiokande paper,
%%   the three PsyArXiv works, and the CKM paper still in preparation are
%%   untouched.
%%   Sixty-four companion references carried no locator at all and now carry
%%   one, in this paper's own format.
%%   A11-Origin is posted with the rest, so the twenty-one papers that called it
%%   "in preparation" no longer do, and fifteen printed statements about its
%%   status -- footnotes, table rows, captions and the staged-submission
%%   paragraph -- were corrected to match.  The author's own reservation about
%%   its upper layers is kept verbatim; only its posting status changed.
%%   Two malformed sentences were repaired: A3's "UCLA preprint,." and P2's
%%   title running into the identifier.
%%   No claim, value, figure, table or grade differs from the previous version.
%% ===================================================================
%% ===================================================================
%% v15.7 (August 18, 2026) -- BT-1: THE BIBLIOGRAPHY TITLE PASS.
%%
%% EVERY COMPANION IS NOW CITED BY THE TITLE PRINTED ON ITS OWN COVER.
%%
%% 10 of this paper's 21 cohort bibitems named a companion by a title
%% that companion does not carry.  Measured, not recalled: the truth is
%% each paper's printed cover, read from its deployed PDF; the markup is
%% each paper's own \GGTitlePage arguments, so the title sets in the same
%% faces the cover does.  Cohort-wide the pass touched 233 sites in 23
%% papers, and afterwards all 477 companion bibitems agree with their
%% covers.
%%
%% TWO CLASSES, and the difference is worth recording.
%%   RENAME PROPAGATION -- a paper was retitled and its citers were never
%%   updated.  The signature is the same wrong string in many papers:
%%   A6-GRIP's retired subtitle "Gi-4 Pillars (TGG, CCI, GFF, and GRIP) as
%%   the Geometric Backbone of GDOS" stood in seventeen papers, and
%%   C2-Hubble's retired "Two Hubble Constants as the Two Ends of One
%%   Six-Dimensional Geometric Corridor" in seventeen more.  W1-Symmetry,
%%   W2-Holonomy, P5-CPT and P6-Proton were all renamed and none of their
%%   citers followed.
%%   HOUSE SHORTHAND -- P5-CPT, W1-Symmetry and W2-Holonomy each wrote
%%   their own descriptive short form for every companion ("GDOS: the
%%   Boundary Law", "The Kaxion", "The Cosmological Inventory of the
%%   Descent").  Readable in prose and useless in a reference list,
%%   because none of those strings finds the paper.
%%
%% ONLY TITLE TEXT CHANGED.  Author blocks, years, availability lines,
%% Relevance notes, keys, labels and \emph/\textit wrappers are asserted
%% unchanged in count; the changelog comments are asserted BYTE-IDENTICAL.
%% ====================================================================
%% ===================================================================
%% v15.6 (August 18, 2026) -- FP-5: THE DISCLOSURE-PREP PASS.
%%
%% The cohort is posted as TWENTY-ONE papers with A11-Origin held back.
%%
%% (1) THE A11 BIBLIOGRAPHY ENTRY PROMISED A PAPER THAT WILL NOT BE
%%     THERE.  It read "Preprint, available at https://arisaka-gg.org/",
%%     which becomes false the day the homepage goes up carrying
%%     twenty-one papers.  It now reads "In preparation.  To be posted
%%     ... on completion; no result of the present paper depends on it."
%% (2) TWO SITES DESCRIBED A11'S CASCADE WITH THE WRONG LAYER COUNT: a
%%     figure caption ("the seventeen-layer deployment is A11") and a
%%     Discussion sentence ("A11's cascade generalizes through sixteen
%%     layers").  Measured from A11 v15.14 and not recalled -- its
%%     GRIPout longtable runs 1->2 through 17->18 -- the canonical counts
%%     are EIGHTEEN LAYERS and SEVENTEEN GRIPout TRANSITIONS.  Both
%%     corrected to eighteen.
%% (3) THE ROADMAP HEADING SAID NINE PARTS OVER A FIGURE SHOWING TEN.
%%     P3 has ten Parts; the subsection heading read "Roadmap of the nine
%%     Parts" while the figure caption directly below it read "Roadmap of
%%     the ten Parts" and the figure drew ten boxes.  Heading corrected.
%%     PROTECTED in the same screen: "organized into nine further Parts"
%%     is spoken inside Part I and counts the nine that follow it.  It is
%%     right, and it is left alone.
%%
%% P3 has no printed catalogue debt.
%%
%% NO OTHER CONTENT CHANGED.
%% ===================================================================
%% ===================================================================
% v15.5 (August 17, 2026) -- MIGRATED TO STYLE FILE v11.5.
%%
%% FOUR MACROS THAT LIVED IN THE PAPERS COME HOME, AND NOT ONE PAGE
%% MOVES.  This paper's part in that:
%%
%% * \GGShowcaseHead removed; this paper prints the sans form with \bigskip -- the style file default,
%%   and needs no setup line.
%%
%% The style file is v11.5 (2026/08/17).  Every one of the twenty-four
%% MANIFEST.sha256 files covers it, so changing it meant rebuilding and
%% repackaging all twenty-four -- which is why this was deferred five
%% times and is why it was done in one pass.
%%
%% ASSERTED, NOT ASSUMED: this paper's printed text is line for line
% what v15.4 printed, except for the lines named above.
%% ===================================================================
%% ===================================================================
%% v15.4 (August 17, 2026) -- THE -ise FAMILY.
%%
%% geometriser -> geometrizer (1); minimiser -> minimizer (1).  Charter 1.1's pair list names these forms; spelling_audit.py's
%% PAIRS list did not carry them, so this paper has reported MIXED
%% PAIRS 0 and ALWAYS-BRITISH 0 at every gate while printing them.  The
%% cohort sweep of August 17, 2026 found sixty-one across twelve of the
%% twenty-four live papers; Report 406 section 6 has the inventory and
%% spelling_audit.py now carries the family as a RULE rather than a list.
%%
%% Substitution is on PRINTED TEXT ONLY.  Changelog comments are the
%% historical record, \label/\ref/\cite arguments are keys, and published
%% titles are quoted rather than written -- all three are masked, and every
%% frozen title is asserted present and unchanged after the edit.
%% NOTHING ELSE IN THIS PAPER CHANGES: no claim, no number, no float, no
%% label, and no page.
%% ===================================================================
%% ===================================================================
%% v15.3 (August 17, 2026) -- THE RIDER: WHAT THIS PAPER SAID ABOUT P6,
%% AND A SYMBOL THAT MEANT TWO SCALES.
%%
%% (1) \S sec:stability-cite-p6 said P6-Proton "argues that the proton
%% never decays because baryon number is gauged and its anomaly
%% canceled", and that the two papers' absolute-stability claims "would
%% fall together".  P6 says neither.  Its protection is a WINDING and not
%% a symmetry -- "a symmetry can be broken ... A winding has nothing to
%% break" -- the surviving anomalies are ABSORBED by the BI-6
%% Green-Schwarz inflow rather than canceled, and P6 calls its own
%% protection "of a stronger kind", which is not two claims that fall
%% together.  Rewritten from P6's own words, including its one-line
%% summary of the pair.  Found during the P6 ship (Report 398); the
%% author's decision was a P3 rider rather than a change inside a P6
%% ship.
%%
%% (2) E_GUT MEANT TWO SCALES IN THIS PAPER, and one figure was
%% arithmetically impossible because of it.  fig:lepton-descent defines
%% E_GUT = M_Pl/2 outright; the seesaw floor's printed 8.6 meV requires
%% the cohort's 2.28e16; and fig:bulk-cross-section printed 2.28e16 at
%% r = 0 while putting the lock at r = K = 35 -- but 2.28e16 * e^{-35} is
%% 14 GeV, not the 3.85 TeV the same figure prints at that point.
%%
%% The author's decision, the same one taken on P6-Proton v15.1: rename
%% the DESCENT-AXIS sites to E_seam = M_Pl/2, where no number moves, and
%% correct the single wrong value -- fig:bulk-cross-section's r = 0 label
%% -- to what that figure's own K = 35 already requires.  THE SEESAW
%% FORMULA IS NOT TOUCHED: with the axis renamed, its E_GUT means only
%% the cohort's 2.28e16, which is the value its 8.6 meV was computed
%% from, so it becomes correct without a character changing.  Six sites
%% move; the footnote in Part I and the seesaw stay.
%%
%% ONE NUMBER CHANGES IN THIS SHIP, and it is a wrong one becoming right.
%% ===================================================================
%% ------------------------------------------------------------
%% v15.1 -> v15.2, August 16, 2026.  THE SHOWCASE PAGE REBUILT ON
%% FIGURES 6 AND 7, AT THE AUTHOR'S REQUEST.
%%   v15.1 showcased Table 4, the six questions with their grades.
%%   Honest, and dull: a reader arriving from the homepage met a
%%   grid of status tags.  Figures 6 and 7 are the paper's own
%%   picture of the same result -- the charged-lepton GFF landscape
%%   as a one-dimensional Morse cut, and the same chain as a
%%   three-node cascade -- and the paper's prose already pairs them:
%%   'Figure 6 draws the whole story in one picture; Figure 7 states
%%   the same chain as a Morse diagram.'  On the body pages they sit
%%   one page apart; here they are one above the other.
%%   Table 4 is back to being an ordinary body table, in the same
%%   place with the same caption.  Nothing is lost.
%%   THE LAYOUT IS MEASURED.  Natural boxed sizes: Fig 6 is
%%   432.889 x 292.390 pt (aspect 1.481), Fig 7 is 401.014 x 326.910
%%   (aspect 1.227); \textheight is 650.43 pt.  Stacked at their body
%%   widths the plates alone are 491.4 pt and the page does not
%%   close.  Side by side the widest legible pair is about 0.52 and
%%   0.44, which renders Fig 6's \scriptsize annotations at 71 per
%%   cent of a size already small on the body page -- rejected on
%%   legibility, not on taste.  0.66 and 0.61 stacked is 443.0 pt
%%   and closes with about 35 pt to spare.
%%   THE BOXES HOLD THE UNSCALED PICTURE; the \resizebox stays at
%%   each use site, so the body copies are still exactly 0.733 and
%%   0.676 \textwidth and the showcase copies are the same drawings
%%   at ninety per cent.  Scaling DOWN is the safe direction:
%%   rendered rule weights shrink, so the showcase copy cannot cross
%%   the house 0.956 pt ceiling.  A5's failure ran the other way.
%%   Filled at \setstretch{1}, probed inside both figure
%%   environments -- which matters more for a tikzpicture than for a
%%   table, because both plates carry multi-line nodes whose
%%   internal leading \baselinestretch sets.
%% NEW PROSE IN THIS SHIP: one headline and one showcase caption,
%% both on the rebuilt page.  Nothing in the body is rewritten, and
%% no figure or table is altered, moved or renumbered.
%% ------------------------------------------------------------
%% ------------------------------------------------------------
%% v15.0 -> v15.1, August 16, 2026.  THE SHOWCASE PAGE, AND ONE
%% MARGIN OVERRUN.  Seventeenth of the twenty-four.
%%   THE PAGE.  P3 had no showcase page: cover, Executive Summary,
%%   Keywords, then straight into the four lists.  The subtitle is
%%   'The Six Oldest Questions about the Electron, Closed and
%%   Fenced', and Table 2 is those six with one sentence of answer
%%   each and the grade that answer is held at -- written, in the
%%   author's own words, 'to be read before the derivations rather
%%   than after them', which is what a showcase page is for.
%%   Unnumbered, so Tables 1-11 keep their numbers.
%%   THE OVERRUN, FOUND AT STAGE 0 AND NOT LOOKED FOR.  P3's
%%   roadmap plate on page 18 sits in a \begin{minipage}{\textwidth}
%%   with no \noindent, so the box is set at \parindent +
%%   \textwidth and hangs one indent into the right margin.
%%   Measured, not assumed: \parindent is 16.33182 pt and the log
%%   carries exactly one overfull \hbox of 16.33182 pt.  On the
%%   artifact the phase-sidebar labels reach x = 558.2 against a
%%   text block ending at 541.75.  This is A11's defect, and C1's,
%%   and C2's -- P3 is the fourth paper to carry it, and the fourth
%%   time the showcase pass found it rather than a gate tool.
%%   THE SPACING, PROBED INSIDE THE ENVIRONMENT.  tab:solutions
%%   runs BSTR 1, AS 1.3, \tabcolsep 6 pt.  There is NO house value
%%   to fall back on -- tab:status runs AS 1.25 and tab:cascade
%%   runs 1, in this same paper -- so the 1.3 the box carries is
%%   measured at the use site and nothing else.
%%   STAGE 0, ALL SIX CHECKS: one \includegraphics, present, zero
%%   'not found'; the baseline reproduces the deployed PDF at 0 of
%%   125 pages compared PAGE BY PAGE; zero pre-existing saveboxes;
%%   one \begin{minipage}{\textwidth} and it was bare; no digit in
%%   the savebox name; every macro in the new prose defined here.
%% NEW PROSE IN THIS SHIP: one headline and one showcase caption,
%% both on the new page.  Nothing in the body is rewritten; the
%% \noindent changes no word.
%% ------------------------------------------------------------
% ===================================================================
%  P3-Electron v14.14 (August 12, 2026) -- cohort-wide sweep, two defects.
%
%  (1) GU-5 IS A THREE-PLUS-TWO PARTITION, exactly as OGN-5 is
%      (M,N,L;J,K).  The separator before k_B is a SEMICOLON:
%      {c, G_N, hbar; k_B, Q_B}.  0 site(s) corrected here.
%      NOT touched, by design: the four-constant Planck unit system
%      {c, G_N, hbar, k_B}, which is a different object and takes a
%      comma; a semicolon there would be wrong.
%
%  (2) Internal affairs -- companion versions, dates, page counts and
%      build status -- do not belong in a preprint.
%%      Nothing of this class was found in this paper.
%
%  No physics changes; no parameter, theorem or falsifier is touched.
% ===================================================================
%% ===================================================================
%%  P3-Electron v14.13  (August 6, 2026)  -- the cohort-wide figure-size sweep.
%%  5 figures re-placed so their node text lands at the house size,
%%  7.79pt: what GG-P3-Electron Figure 3 renders (\footnotesize at
%%  0.865 of natural size).  For a picture of measured width W drawn
%%  at a base font of B points the target is f = (7.79/B) * W / 159.2
%%  of \textwidth, W being measured by compiling each picture
%%  standalone and reading its ink bounding box.  Nothing inside any
%%  picture changes: no font command, no dimension, no text, no
%%  relative position.  The cohort map and the central-claim funnel
%%  are excluded, both being at the house size already.
%%  Per-figure table and recipe: [v13-support]/allsweep.py and
%%  [v13-support]/figure_census.json.
%% ===================================================================
%% ===================================================================
%%  Arisaka-GG-P3-Electron  v14.12  (August 5, 2026)
%%  -----------------------------------------------------------------
%%  CHANGELOG (v14.11 -> v14.12), author-directed: Figure 1's boxes
%%  closed up on its type.
%%    * v14.11 bought its small type by growing the source geometry
%%      4/3 while the node text stayed put, so a 138.7mm box held
%%      about 104mm of text -- some 15mm of empty padding a side,
%%      where Figure 3's boxes are filled nearly edge to edge.
%%    * Type and box size are locked together by the \resizebox, so
%%      snug boxes at Figure 3's type means a narrower plate.  The
%%      geometry comes back near its pre-v14.11 values (node distance
%%      19mm, box 115 x 12mm, arrowhead 3.4mm) and the target with it,
%%      0.757 -> 0.627\textwidth -- again computed, not chosen: the
%%      picture measures 115.4mm wide compiled standalone, and
%%      0.93 x 115.4 / 171.1 = 0.627 holds the type at Figure 3's.
%%    * Net vs v14.11: boxes 17% smaller, type unchanged.  Vs v14.10:
%%      boxes 37% smaller, type 43% smaller.  No font command, no
%%      text and no relative position touched.
%%  Script: [v13-support]/p3_v1412_fig1.py.
%% ===================================================================
%% ===================================================================
%%  Arisaka-GG-P3-Electron  v14.11  (August 5, 2026)
%%  -----------------------------------------------------------------
%%  CHANGELOG (v14.10 -> v14.11), author-directed: Figure 1 brought
%%  down to the size of Figures 3 and 4.
%%    * Measured at 105 dpi on v14.10, a \footnotesize character in
%%      Figure 1 ran about 8.2 px against about 5.0 px in Figure 3 --
%%      1.65x, and the cause is the \resizebox rather than any font
%%      setting: Figure 1's boxes are 104mm wide where Figure 3's are
%%      120-150mm, so the same \footnotesize arrives half as large
%%      again.
%%    * Two changes, because the two faults are separable.  The SOURCE
%%      geometry grows by 4/3 (node distance 17 -> 22.7mm, box
%%      104 -> 138.7mm wide and 11 -> 14.7mm tall, arrowhead 3 -> 4mm),
%%      which shrinks the type relative to the boxes and nothing else;
%%      and the plate target moves from \textwidth to
%%      0.757\textwidth, which sets the absolute size.  The 0.757 is
%%      computed, not chosen: compiled standalone, Figure 1's picture
%%      measures 104.4mm wide and Figure 3's 171.1mm, and Figure 3 sits
%%      at 0.93\textwidth, so 0.93 x 139.2 / 171.1 = 0.757 puts the two
%%      figures at exactly the same type size.
%%    * Net on the page: boxes 24% smaller (the author's 20-30%), type
%%      43% smaller -- the type being the part that was out of
%%      proportion.  No font command, no text and no relative position
%%      is touched.
%%  Script: [v13-support]/p3_v1411_fig1.py.
%% ===================================================================
%% ===================================================================
%%  Arisaka-GG-P3-Electron  v14.10  (August 5, 2026)
%%  -----------------------------------------------------------------
%%  CHANGELOG (v14.9 -> v14.10), author-directed: the one-line page 19.
%%  Part II's closing paragraph spilled a single line past the page
%%  break \GGPart opens for Part III, leaving page 19 with one line on
%%  it.  About fourteen words -- one printed line -- trimmed from the
%%  two paragraphs that close the Part: "we do not duplicate it here"
%%  (the sentence has already said where the Dictionary lives) and the
%%  closing sentence's second statement of its own image.  The
%%  grep-verified clause on the inheritance ledger, every citation and
%%  every cross-reference are untouched, and Part III is not touched
%%  at all.
%%  Script: [v13-support]/p3_v1410_p19.py.
%% ===================================================================
%% ===================================================================
%%  Arisaka-GG-P3-Electron  v14.9  (August 5, 2026)
%%  -----------------------------------------------------------------
%%  CHANGELOG (v14.8 -> v14.9), author-directed: the roadmap figure
%%  (Figure 3) re-cut to the format of A1-Constitution Figure 4.
%%    * Plate 0.64 -> 0.93\textwidth: at 0.64 the 12mm boxes landed
%%      about 7.7mm tall against A1's 11mm, with a third of the page
%%      left white beneath the caption.
%%    * Row pitch 13 -> 16mm on 12mm boxes (the gap was 1mm; A1's is
%%      4mm), 18.5mm around the taller highlighted box.
%%    * Phase labels 67 -> 74mm.  Four of the ten boxes carry a
%%      ~100-character subtitle, which drives the node past the 120mm
%%      the style asks for and through the label column; invisible at
%%      the old scale, plain at the new one.
%%    * Plate vertically centred between \vfill's, as A1 does.
%%  No text of the figure or its caption changes.
%%  Script: [v13-support]/p3_v149_fig3.py.
%% ===================================================================
%% ===================================================================
%%  P3-Electron v14.8  (August 5, 2026)  -- the twenty-two-paper cohort sweep.
%%  The cohort map becomes the twenty-two-paper map: GG-P6-Proton on
%%  the Predictions row with a second sister-import arrow, and the
%%  White-Paper Branch (GG-W1-Symmetry above GG-W2-Holonomy) as a
%%  right-flank column at the mirror positions of the Foundations
%%  column -- the left flank feeds the spine, the right reads it.
%%  GG-P7-Inflow does not appear: it is Appendix H of GG-P2-N3.
%%  The plate is also enlarged for reading: boxes and the type inside
%%  them x1.15, every word outside a box x1.20, and the long
%%  A10 -> C-frame edge redrawn as a polyline, which returns 24mm of
%%  bounding box that was Bezier control points rather than ink.
%%  Prose: every count site, the series breakdown, and the canonical
%%  Suffix list, which was missing Proton, Symmetry and Holonomy.
%%  Recipe and variant analysis: [v13-support]/sweep22.py.
%% ===================================================================
%% ===================================================================
%%  P3-Electron v14.4  (July 30, 2026) -- L-INT vocabulary conformance
%%  to P2 v14.2 canon + P7-Inflow status update.  ~14 sites:
%%  "integrality lemma L-INT" -> "integrality theorem L-INT (residue
%%  R-INT)"; the stale verbatim P2 quote ("the single statement...
%%  that remains open") replaced by P2 v14.2's actual words on R-INT
%%  ("topological bookkeeping... not a conceptual gap"); status tags
%%  CONJ -> THM for the L-INT import (legend's THM = theorem with
%%  grep-verified upstream location, which now holds); the D-P3-2
%%  fence recast (benchmark case closed by the kappa-bridge of the
%%  inflow member UCLA/Arisaka-GG-P7-Inflow; open items = its warped
%%  and relative refinements); O-P3-4 response updated.  NO physics
%%  touched; the import remains conditional and says so.
%% ===================================================================
%% ===================================================================
%%  P3-Electron v14.7  (August 5, 2026)  -- P7-Inflow residue.
%%  P7-Inflow is Appendix H of P2-N3.  Six prose sites re-pointed --
%%  the Q3 ladder's conditioning note, the D-P3-2 fence and its
%%  "what counts as a solution" clause, the O-P3-4 response, the
%%  symbol-glossary row for L-INT, and the Appendix Q3 leg-L2 status
%%  line.  This paper never cited P7 by key, only by name, which is
%%  why the merger's key-scoped ship 4 did not reach it.  The import
%%  remains exactly as conditional as it was and still says so.
%% ===================================================================
%% ===================================================================
%%  P3-Electron v14.3  (July 30, 2026)  -- P2-N3 v14.0 conformance.
%%  P3 imports Q3 (the family count) from P2 "with its complete
%%  conditioning, verbatim" -- so the conditioning language is conformed
%%  wholesale to the capacity architecture: Budget Conjecture -> capacity
%%  theorem T-N3-6 (conditional on the coupling clause + integrality
%%  lemma L-INT); H1 -> closed in the negative (rigidity); H2 -> L-INT.
%%  21 sites: the conditioning section, both notation-table rows, the
%%  status table, Appendix Q3 (budget block eq:appE-budget, leg-L2
%%  status, closure, register rows), D-P3-2 (problem + solution),
%%  O-P3-4 (voice + response), the fence inventory, both bibitem
%%  Relevance notes, the stale conj:budget label pointers (P2 v14.0
%%  carries no such label), the P2-verbatim quote (P2's own words
%%  changed; now quoted at its v14 wording, section pointer 9.5 -> 9.6),
%%  and the undecidability remark (the anticipated obstruction has
%%  been proved -- P2's rigidity lemma).  No P3 theorem, value, or
%%  falsifier changed.
%% ===================================================================
%% ===================================================================
%%  P3-Electron v14.2  (July 29, 2026)  -- P2-N3 retitle propagation.
%%  P2-N3 is retitled "Why Three Generations: A THREE-LEG Derivation of N = 3
%%  from BI-6, MSMF, and GDOS Morse Stability" (was "A Closed Derivation").
%%  Reason: P2-N3's own main theorem T-N3-5 is "Conditional derivation of
%%  N = 3 (three-leg pincer)", conditional on five structural hypotheses --
%%  including the BI-6 Budget Conjecture, which A2 states is not derived
%%  anywhere in the cohort -- plus two empirical inputs.  The cohort's prose
%%  already flagged that conditioning everywhere; only the title claimed
%%  "Closed", and titles propagate into every bibliography.
%%  T-N3-5 KEEPS its own name: the theorem is conditional and says so.
%%   * Two descriptions of P2-N3 conformed to its retitle: "the three legs of
%%     P2's closed result" -> "P2's result" (the sentence already says "three
%%     legs", so "three-leg result" would only repeat it), and "the closed
%%     count of P2, imported here with its conditioning" -> "the three-leg
%%     count of P2 ...".  The conditioning language is untouched.
%% ===================================================================
%% ===================================================================
%%  P3-Electron v14.1  (July 29, 2026)  -- internal-affairs sweep.
%%   * AN INTERNAL TOOLCHAIN FILE PATH was in print, set in \texttt{} so it
%%     rendered as a literal path:
%%       "(\texttt{[P3-Support]/P3-PHASE1-AUDIT-2026-06-11.md}), per the
%%        cohort's grep-before-citing protocol"
%%     Five leaks in one parenthetical -- support directory, internal audit
%%     filename, working date, internal review phase, internal protocol name.
%%     The reproducibility claim is KEPT: every ledger location was verified by
%%     direct search in the cited paper rather than from memory, and a reader
%%     can check each row the same way.
%%   * The Q6/positron opener no longer narrates this Part's own revision
%%     history ("long before this Part existed", "The earlier versions of this
%%     argument ... carried the positron as a fence", "What has changed is ...
%%     has since derived").  The intellectual dependency is kept in full:
%%     P5-CPT derives the origin of antiparticles at theorem grade below
%%     quantisation, which is what lets this Part answer Q6 rather than fence
%%     it.  Objection 8, D-P3-4 and the PET-scan argument all survive.
%%  No value, equation, grade or citation changed.
%% ===================================================================
%% ===================================================================
%% v14.0 (July 24, 2026): THE ORIGIN OF POSITRONS -- THE SIXTH QUESTION
%%  (author-commissioned; the campaign's design report is the internal
%%  record). NEW Part V between The Excited Copies and Pointlikeness:
%%  the origin of antiparticles imported at theorem grade from the CPT
%%  companion (the circle's i, the clock's i, the handshake that forces
%%  the twin in the real bulk before quantisation, the definitional
%%  charge flip for fermions), and the positron read as the conjugate
%%  readout of the electron's one basin -- so the sixth question
%%  collapses into the first. Subtitle and question apparatus updated
%%  from five to six throughout (cover, abstract, Executive Summary,
%%  status table, significance, falsification programme, ledger,
%%  conclusions); later Parts renumbered with the roadmap rebuilt; the
%%  positron objection converted from fence to pointer; the registered
%%  debt kept open and narrowed to the spinor-level corollary; four
%%  references added (the 1931 prediction and the three precision
%%  equality tests) and all first-citation links recomputed.
%% ===================================================================
%% ===================================================================
%% v13.3 (July 24, 2026): MENU-A SHAPE-UP (references + registries)
%%  (1) References reorganised in two sections per the cohort default:
%%      A = the fourteen cohort papers in canonical programme order,
%%      B = the external literature alphabetically; every entry now
%%      closes with the location of its first citation. All entries
%%      carried over verbatim.
%%  (2) The fifteen objections receive their cohort registry tags
%%      (the paper's debt registry has carried the D- prefix since
%%      the previous version).
%%  (3) The source-ledger table's dated source stamps removed (the
%%      cohort's pinless style); its one section-dependent row
%%      retargeted to the N=3 companion's current numbering; the
%%      universal-identity row updated to the QM companion's current
%%      apparatus (theorem T-A8.9, cohort ID T-QM-9, now proved
%%      there), with the row's grade raised accordingly.
%%  (4) The remaining reader-facing stamps of this paper's own
%%      revision history removed; the recorded withdrawal of the
%%      earlier tilted-landscape reading is kept as fact, without the
%%      version number.  No other change anywhere.
%% ===================================================================
%% ===================================================================
%% v13.2 (July 24, 2026): DEBT REGISTRY RENAMED (cohort convention)
%%  The seven-entry open-problem registry is renamed from the O- prefix
%%  to D- ("registered debt"), because the cohort-wide convention
%%  reserves O-Suffix-N for the Nth numbered objection. All in-text
%%  uses renamed; a one-sentence convention note added where the
%%  registry is introduced; the CPT companion's quoting sites are
%%  renamed in the same shipment. Additionally, nine section pinpoints
%%  into the N=3 companion, written against that paper's earlier
%%  numbering, are corrected to its current sectioning (each target
%%  verified by content in the deployed companion PDF). No other
%%  change anywhere.
%% ===================================================================
%% ===================================================================
%% v13.1 (July 24, 2026): MICRO-ERRATUM (cross-paper pinpoint + pins)
%%  (1) The citation of P2-N3's Morse-positivity fence corrected to
%%      that paper's current numbering (the strict-positivity
%%      postulate pair sits at 6.3/6.4; the companion appendix
%%      reference was already correct).
%%  (2) The twelve dated version parentheticals in the companion-paper
%%      bibliography entries removed, matching the cohort's pinless
%%      reference style. No other change anywhere.
%% ===================================================================
%% v13.0 (July 19, 2026): PROMOTION TO THE [GG-v13] SERIES (Wave 1 of
%%   the 19-paper campaign; edit script p3_wave1.py). Base: [GG-v11]
%%   Arisaka-GG-P3-Electron-v11.14; deployed to [GG-v13] as v13.0.
%%   Promotion recorded in these banner comments only; no reader-facing
%%   history. Mechanical/structural edits only:
%%   (1) STANDARDIZED PART-I CLOSE: new closing section "The cohort
%%   inheritance and the roadmap of the nine Parts"
%%   (sec:inheritance-and-roadmap) at the end of Part I. Its first
%%   subsection (sec:inheritance) opens with the nineteen-paper roster
%%   paragraph, carries the family-portrait walkthrough MIGRATED
%%   VERBATIM (three seam adaptations: "Two branches" -> "Two
%%   phenomenology branches"; "(bold border)" dropped -- the frozen map
%%   carries no self-reference marker; the closing hand-off now points
%%   to Part II) from the former head of sec:p2-import, adds a NEW
%%   Foundations-Branch paragraph in this paper's voice (P4-Real: the
%%   origin of the i the electron's quantum mechanics runs on; P5-CPT:
%%   the positron as the handshake's first receipt -- one sentence
%%   each, roster level, no new claims), and closes with the frozen
%%   v1.4 nineteen-paper cohort map (verbatim master copy from A2-GG6
%%   v13.3, internal node names MP4/MP5; ONLY the label changes, kept
%%   as fig:cohort-map so every existing reference resolves). The
%%   old seventeen-paper map tikz (Part II) is RETIRED. The second
%%   subsection (sec:roadmap) is a NEW four-paragraph walkthrough of
%%   the nine Parts + NEW roadmap figure (fig:parts-roadmap-p3), with
%%   Part III Ground-State-ness highlighted as the Part carrying the
%%   central claim (the ground-state uniqueness of sec:central-claim).
%%   sec:p2-import retitled "The sister paper N=3 and its fences"
%%   (label kept); the Part-II pointer sentence to the map updated.
%%   (2) COUNTS: cohort-sense seventeen -> nineteen (1 prose site);
%%   the two semantic "seventeen" sites protected (the seventeen-layer
%%   cascade caption; the rhetorical "three to seventeen").
%%   (3) MACROS: PaperPFour (GG-P4-Real) and PaperPFive (GG-P5-CPT)
%%   providecommands; ASix renewed to GG-A6-GRIP (the sty default
%%   still renders the retired Gi4 name; the bibitem label already
%%   read A6-GRIP). (4) BIB: ArisakaP4Real + ArisakaP5CPT bibitems
%%   (house style; roster-level timeless Relevance; cover titles read
%%   from the deployed [GG-v13] P4-Real/P5-CPT files), cited from
%%   sec:inheritance. (5) ONE-LINE ToC: GGPart renewed per the
%%   P4-Real v3.2 preamble pattern (Overview Part entries drop the
%%   " --- description" tail). (6) PaperVersion v13.0, PaperDate
%%   July 19, 2026. Physics, numbers, grades, the ground-state
%%   derivation, mass values, and the falsifier tables: unchanged
%%   (protect-asserted; Part III through the P2-N3 bibitem is
%%   byte-identical). Script: p3_wave1.py.
%% v11.14 (July 16, 2026): cohort table standard (author-approved, P4 v2.17 pattern): sub-small table fonts -> \small; p-column tables widened toward full text width; targeted corrections listed.
%% v11.13 (2026-07-14, Phase 3 landscape instance) -- presentation only.
%%   After the horizon-independence corollary (cor:horizon-independence), added
%%   the electron-scale form of the calibrated landscape contrast: unique
%%   vacuum returns one alpha everywhere + exposed to one measurement vs a
%%   10^500-vacua landscape that accommodates the same uniformity only by
%%   one-bubble descent in eternal inflation (measure-problem price) -- identity
%%   as necessity-exposed vs inheritance-immune. Points to A10 (O-Cosmos-90) for
%%   the full priced-not-refuted treatment. Reuses existing KKLT2003 cite; no
%%   new bibitem, no values changed. Honors no-string-theory-polemic directive.
%%   Script: p3_landscape.py.
%% v11.12 (2026-07-14, SHP) -- integrate the second horizon problem
%%   (A10-Cosmos v12.102 Sec 63) into Part III Ground-State-ness. Three
%%   presentation-only additions; the GGA physics is P3's own.
%%   (1) After the Theorem 8.1 "fences" paragraph (now THREE remarks): a
%%       new third remark on the non-spatial (scale+phase) landscape
%%       coordinates, then Corollary (cor:horizon-independence):
%%       electrons in causally disconnected regions read the same
%%       attractor because they bound the same bulk -- identity by
%%       geometry, not history. Followed by a paragraph naming this the
%%       particle-scale face of A10's second horizon problem (mold +
%%       ordering), with the shared quasar alpha / m_e/m_p exposure at
%%       1e-5..1e-6.
%%   (2) "Why this matters beyond physics": the temporal-universality
%%       sentence (water molecule 12 Gyr ago) gets its SPATIAL twin
%%       (same Balmer lines across the sky / causally disconnected
%%       regions), cross-ref to the corollary + A10 second horizon.
%%   (3) Wheeler one-electron-universe paragraph: the causal (worldline)
%%       vs acausal (attractor) contrast made explicit -- Wheeler's
%%       shared-trajectory identity cannot survive the second horizon
%%       problem; the GGA reading needs only "same bulk," so it answers
%%       across the horizon where Wheeler cannot. Forward-cite A10.
%%   No new bibitems (ArisakaA10Cosmos already present). No values,
%%   counts, statuses, or results changed. Script: p3_v1112_shp.py.
% v11.10 (July 2, 2026): cohort universal-indentation pass (author-
%   directed): indentfirst loaded (first paragraphs after headings
%   now indent). Per-paper stray-noindent review deferred to the
%   v2.0 pass. No content changed.
% v11.9 (July 2, 2026): cohort multi-Arisaka citation split pass
%   (charter natbib rule; author-directed 2026-07-02): 1
%   multi-key cites split into citealp/citet chains; fixes the
%   same-author-same-year comma-run rendering. No content changed.
% Bib cross-citation titles reconciled to canonical cover titles (cross-citation integrity), 2026-06-27.
% A10 bib-title reconciled to canonical cover title (cross-citation integrity), 2026-06-27.
% ===== P3-Electron v11.6 (2026-06-27): cohort de-contamination (protect-list aware). =====
% Shed GG's own self-description: dropped the self-applied scale-profile adjective from the
% 6D/six-dimensional bulk noun (KEEP '6D Bulk' cohort title); the OGGEP boundary-projection /
% boundary-readout family and the bulk-to-boundary dictionary reworded to bulk-to-boundary /
% bulk--boundary correspondence; the canonical-metric scale-profile and its scale-profile
% integral renamed from the self-applied geometric adjective; the BI6 six-dimensional descent
% de-self-described; Noether transport reworded to boundary-transported. KEPT all external
% AdS/CFT comparison, the Maldacena projection-from-bulk citation, the Randall--Sundrum
% throat lineage + RS glossary/bib cells, the explicit RG-running disclaimer language, the
% canonical cohort paper-title bib cross-citations, and all label/ref/eqref args + comments.
% Body only (after the document body marker). No physics / results / values changed. =====
% ===== P3 v11.5 (2026-06-25): cohort central-claim funnel (consequence variant). =====
% Added the shared open-system funnel (sec:central-claim/fig:central-claim) with this paper's own
% payload. Same funnel as A9/A10/A11. No new physics.
% ===== P3-Electron v11.4 (2026-06-24) =====
% Added subsec:muon-summary (12.7) 'Summary: what the muon's mass and lifetime, together,
%   tell us' -- broader-audience / life-science (A11-Origin) register on the significance
%   and uniqueness of deriving BOTH mass (basin floor) and lifetime (gate-crossing rate)
%   from one GDOS/GRIP object; valley/ridge metaphor; GRIPin/GRIPout/GA/GGA in plain terms;
%   honesty note carried from 12.6. Fills near-empty p31. New content only; nothing changed.
% ===== P3-Electron v11.3 (2026-06-24) =====
% Added Section sec:lifetime to Part IV (The Excited Copies): the muon lifetime as a
%   GRIPin descent rate of the non-ground muon GA across its GSSB gate (S=pi) toward the
%   electron GGA. Ties to A6 GRIP-ST7 (width ladder ~ e^-pi*k), the weak current as
%   implementer, GKLS single-jump form (electron GGA = zero-gate limit, tau=inf = Q2
%   stability), verified numbers (LO 2.187us; +f+QED 2.19699us = measured to ppm; GF from
%   geometric v). Honest triage: GF Derived(cond.), m_mu Asserted -> tau_mu derived modulo
%   the Asserted mu depth; the GRIP reading is unconditional. Proposition prop:muon-lifetime.
%   New content only; no prior physics/values changed. Condensed version to follow in A9-SM.
% =====================================================================
%  P3-Electron v11.2 (migrated onto ucla-arisaka-gg-11) -- 2026-06-22
%  gg-10->gg-11; centered headers + homogenized Acknowledgments via gg-11.  The \LaTeX shim is KEPT (paper uses \LaTeX in body).
%  No prose/figure/number content changed.
% =====================================================================
% =====================================================================
%  Arisaka-GG-P3-Electron-v11.0 (Stage 3A: naming-convention theorem-id rollout) -- 2026-06-20
%  Official cohort theorem ids assigned: T-Electron-1..4 (4).
%  Appended (T-Electron-N) to own theorem-env titles; recalled classical
%  theorems left untagged.  No physics changed.
% =====================================================================
% ===== v11.0 (2026-06-16): holographic-RG reframing, Phase R2c. =====
%  Terminology only; NO physics changed. A2 + A3 bibitems: dropped 'AdS' from cited
%  titles. P3 already frames the scale axis as 'a position in resolution, not in space'.
%  Added holographic-RG disclaimer footnote; v10.11 -> v11.0.
% =====================================================================
% --- v10.11 (2026-06-16): adopt cohort-default Part-aware running header (sty v10.6).
%     Curated short Part labels added; running header shows 'Part N. <short>'. ---
% ALWAYS-ON PROJECTION CLARIFICATION (June 14, 2026): aligned with GG-A5-GDOS Sec 23 ('Why the Projection Is Always On'). The 6D->4D OGGEP/GDOS projection is always on and observer-independent; 'measurement' is only its macroscopic record-keeping special case (decoherence the microscopic one). Removed framing that tied the projection to observation/measurement; added (A5 Sec 23) cross-refs.
% GU-5 RENAME (June 14, 2026): cohort harmonization with GG-A4-Euclid -- the five-constant inventory and its theorem are named Geometric Universal Five Constants / GU-5 (\GUfive, \T{-GU5}); the older 'Conversion-Factor Pentad'/'Conversion-Factor Triad' wording and the 'T-CFP' theorem tag are retired.
\pdfoutput=1
%% ===================================================================
%% Arisaka-GG-P3-Electron-v1.0.tex
%%
%% CHANGELOG
%% v10.10 (June 12, 2026): Cohort-map figure adopted (author request).
%%   Table 2 (tab:inheritance) REPLACED by the seventeen-paper cohort
%%   map (fig:cohort-map; this paper highlighted in the Predictions
%%   frame; P2->P3 N=3 import arrow); the grep-verified version
%%   ledger remains App. B and the lead-in sentence now says so.
%%   Section 6 retitled and opened with a figure walkthrough so a new
%%   reader can grasp the seventeen-paper flow (root -> GG6 Trio ->
%%   boundary law -> pillars -> readouts -> capstone -> two
%%   phenomenology branches).  Uses new sty macros PaperCTwo /
%%   PaperCThree (sty June 12).  arXiv tarball rebuilt.
%% v10.9 (June 12, 2026): Preprint-identity convention fix (author,
%%   June 12): running header and title-page corner unified to the
%%   cohort convention UCLA/Arisaka-GG-P3-Electron. PaperNumber
%%   changed from the legacy GG-2026-Electron to Arisaka-GG-P3-
%%   Electron; the local fancyhead override (legacy UCLA-Arisaka/
%%   GG-2026-Electron) removed so the sty-generated header stands,
%%   as in the A-papers. NO content changes. arXiv tarball rebuilt.
%% v10.8 (June 11, 2026): Phase 6 arXiv production pass.
%%   \pdfoutput=1 added (line 1, arXiv pdflatex detection); version
%%   stamp bumped. NO content changes. Clean-room tarball built and
%%   verified (tex + sty only; paper is fully self-contained: all
%%   figures TikZ, bibliography inline). Submission: hep-ph primary,
%%   hep-th cross; abstract 1235 chars (limit 1920).
%% v10.7 (June 11, 2026): R1 sync (author Go for R1, same day).
%%   A5-GDOS v10.8 derives the covariant non-Markovian kernel in
%%   closed form (spectral sum over the T9.1 lock tower; causal;
%%   passive => runaway/pre-acceleration-free, with the Q4
%%   mass-as-basin-level doctrine dissolving the classical
%%   negative-bare-mass obstruction; LL-exact to (hbar w/Mlock)^2),
%%   re-grading O7 Partially resolved -> RESOLVED.  P3's three O7
%%   mentions updated (sec:sensing passage, App-G pointer, App-B
%%   row); A5 stamps -> v10.8; A6 stamps v10.4 -> v10.6 (golden-case
%%   round; tab:inheritance, App-B, bibitem).  No other changes.
%% v10.6 (June 11, 2026): Conclusions expansion (author Go: 'devote
%%   your whole analysis to P3'). Two new Part-VIII sections between
%%   sec:why-century and the plain-English close, adapted from the
%%   June-11 author--assistant synthesis conversations: (1)
%%   sec:fourcells -- the 2x2 of force and radiation (four oldest
%%   dynamical facts as two master formulas on two curvature slices;
%%   tab:fourcells; work-criterion refinement; the two-dimensions-
%%   jointly sentence; Weyl-1918/1929 + KK historical diagnosis;
%%   geometrise-vs-quantise inversion cross-ref sec:susy-string;
%%   empirical inventory; status priced). (2) sec:century-openness
%%   -- openness as the missing half of Einstein's dream (Einstein/
%%   Bohr treaty; the 1963-1998 mathematics of openness; closed
%%   physics as the circulation sub-sector; 1926-2026 centenary with
%%   Born rule as A8 theorem; Kuhn discipline with pre-registered
%%   falsifiers; Einstein's three clauses, P3 as the matter clause;
%%   status priced INT).  New bibitems, all cited inline: Weyl1918,
%%   Schrodinger1926, Born1926, FeynmanVernon1963, JKO1998, Kuhn1962.
%% v10.5 (June 11, 2026): O7-closure sync (same-day author Go).
%%   A5-GDOS v10.7 derives the quantitative closure (drift =
%%   retarded flux; mobility closed-form; Larmor & Peters
%%   coefficients exact; C_q universal; Einstein pairing), re-grading
%%   O7 Genuinely open -> Partially resolved (residue R1 = covariant
%%   non-Markovian kernel).  P3's O7 mentions updated (sec:sensing
%%   passage, App-G pointer, App-B row, A5 bibitem Relevance); stamp
%%   refresh A5 v10.6->v10.7, A9 v10.7->v10.8, P2 v10.0->v10.1
%%   (tab:inheritance, App-B, bibitems). No other content changes.
%% v10.4 (June 11, 2026): Synchrotron round (author-approved June 11).
%%   (a) FIX of a v10.3-missed stale paragraph at the end of
%%   sec:sensing that still read 'acceleration in a field is GFF
%%   descent within a basin' -- the formulation withdrawn at v10.3.
%%   Replaced by the canonical worked example: the synchrotron
%%   (theta-sector bend = circulation, radiation damping = gradient
%%   sector, quantum excitation = diffusion) and its gravitational
%%   twin (binary inspiral), importing A5-GDOS v10.6's new
%%   radiative-completion section with its O7 fence travelling
%%   verbatim.  (b) App-G pointer to the A5 radiative completion.
%%   (c) App-B ledger row for the import.  (d) Stamp refresh:
%%   tab:inheritance A5 v10.4->v10.6, A9 v10.5->v10.7, P2
%%   v2.5->v10.0; App-B A5 v10.5->v10.6, P2 v2.7->v10.0; A5 bibitem
%%   stamp v10.5->v10.6.  (e) New bibitems, all cited inline:
%%   Larmor1897, HulseTaylor1975, Abbott2016.
%% v10.3 (June 11, 2026): Two-sector correction per the author's
%%   physics question of June 11 ("U(1) rotation along theta is not
%%   gradient descent"). The author is right: the earlier reading
%%   ("field tilts the GFF landscape; spatial drift = descent") was
%%   MIS-SECTORED -- the GFF basins live on the family stratum, not
%%   position space; an E-field curves the theta-connection. The two
%%   non-spatial dimensions partition Q5's dynamics: PHASE sector
%%   (6th) moves the electron -- conservative geodesic, no descent;
%%   SCALE sector (5th) hosts GRIP-In -- genuine GFF gradient descent,
%%   dissipative and LOCAL: transmutes (tau->mu->e) at a point,
%%   transports nothing. The tilted-landscape reading is WITHDRAWN
%%   (the INT tag exists so readings can be corrected without damage;
%%   nothing downstream depended on it -- verified). The legitimate
%%   dissipative channel of MOTION is radiation (Larmor; Dirac 1938
%%   reaction force), GDOS-read as the open channel (INT). Changes:
%%   Sec 20 retitled "What descends, and where" and rewritten;
%%   Reading rmk:sensing replaced (radiation arrow; corrected-at-
%%   v10.3 note); bead intuition replaced by the three-phenomena
%%   bubble-chamber reading (theta bends the track, dissipation
%%   shrinks it, 5th-dim descent ends it; the electron's track has no
%%   endpoint); Fig. 7 panels relabelled (left: geodesic motion,
%%   theta-sector, conservative; right: GRIP-In descent, scale
%%   sector, local) + caption rewritten; App G gloss subsection
%%   rewritten; status echoes synced (tab:status, tab:solutions,
%%   fence inventory, ES, Significance, ledger, Objection 6,
%%   plain-English conclusions). A9/P2 pointer texts still say
%%   "GFF-descent gloss" -- flagged for next cohort touch.
%% v10.2 (June 11, 2026): Part VI rewritten for the graduate reader
%%   per the author's direction of June 11. (1) Part retitled: "Why
%%   the Electron Moves -- The Phase Fiber, the Equivalence Principle
%%   for Charge, and Force as Geometry (Q5)" (old title used GFF,
%%   undefined at that point, and GFF is not the deepest origin).
%%   (2) NEW opening Sec "The sixth dimension is the electromagnetic
%%   fiber": self-contained, citation-light statement of the deep
%%   principle -- S^1_theta IS the U(1)_EM fiber bundle of the
%%   textbooks, made literal by AX-2/GGEP; A_mu = connection, F_munu
%%   = curvature; charge = winding (Klein); the equivalence principle
%%   extended from the metric to the gauge sector, so the electron
%%   follows phase curvature exactly as the apple follows metric
%%   curvature; clock-dial intuition with the stationary-phase
%%   (path-integral) grounding. (3) Sec "coupling" and Sec "force"
%%   leads rewritten to flow from the fiber picture, citations
%%   subordinated to prose (the citation-mosaic style the author
%%   flagged). No physics or claim statuses changed; the fiber
%%   section restates the derived Chain-B/AX-2 content (A5 Part VI)
%%   in pedagogical voice. Discussion renumbers to Secs 21-26
%%   (label-based refs unaffected).
%% v10.1 (June 11, 2026): Conceptual re-centering of Sec 16 per the
%%   author's scientific question of June 11 ("the form factor is the
%%   falsification instrument, not the answer to Q4"). The author is
%%   right, with one guarded step: "Fourier of a point is flat by
%%   definition" closes the OBJECT side only; the registration side is
%%   closed by Lemma RL (from AX-1) -- after which the author's
%%   statement holds in full. Changes: (1) Sec 16 retitled "The
%%   pointlikeness theorem and its observable shadow"; (2) the
%%   Pointlikeness Theorem RESTATED geometry-first (point support in
%%   the boundary spatial directions; no structural length in object
%%   or registration chain), with F == 1 now its displayed COROLLARY,
%%   introduced as "pure Fourier bookkeeping"; (3) NEW Remark "On the
%%   status of the form factor": F is not load-bearing -- it is the
%%   falsification interface retained because kill criterion F2 must
%%   name an observable and experiment speaks F; contrast with the
%%   old bounds-driven posture made explicit; (4) Sec 16.1 intro,
%%   Fig. 6 caption, Sec Significance Q4 paragraph, and App F intro
%%   re-framed accordingly. No physics changed; the constitutional
%%   answer (AX-1 + AX-2 + non-spatial structure + RL) was already
%%   primary in Secs 13-15 and is now primary in Sec 16's statement
%%   as well.
%% v10.0 (June 11, 2026): VERSION PROMOTION (author decision, June 11):
%%   v2.4 promoted to v10.0 for cohort version consistency, alongside
%%   P2-N3 v2.7 -> v10.0 and C2-Hubble v1.9 -> v10.0, completing the
%%   17-paper v10 cohort (11 A + 3 P + 3 C) consolidated in [GG-v10].
%%   Content identical to v2.4 except: this changelog entry, the
%%   \PaperVersion stamp, and the P2-N3 bibitem stamp v2.7 -> v10.0
%%   (promoted simultaneously). Master copies: [GG-v10]/.
%% v2.4 (June 11, 2026): Hostile review round 2 (drift audit after the
%%   v1.0->v2.3 revision arc; 0 FATAL / 3 MAJOR / 5 MINOR; see
%%   [P3-Support]/P3-HOSTILE-REVIEW-ROUND2-2026-06-11.md):
%%   M1 P3's own A9/P2 bibitem stamps refreshed v10.6->v10.7,
%%      v2.6->v2.7 (self-inflicted trail from the v2.2 title sweep).
%%   M2 App-B ledger Location strings updated in nine rows (A5 v10.5,
%%      A9 v10.7, P2 v2.7) to match the shipped cohort.
%%   M3 Part V Sec 13: spin-slot clarification at the "no fourth slot"
%%      claim (spin enters via the spinor's parallel transport along
%%      the same composite connection -- connection coupling, not a
%%      new term in the worldline Lagrangian).
%%   m1 ES item (iv): "(Appendix A)" -> "(Appendix B)" (v1.9
%%      re-lettering echo). m2 Part V Sec 14 opening rewritten as a
%%      hand-off from Sec 13 (the one flow stutter found). m3 Part I
%%      fence inventory: sensing line updated to gloss-on-derived-law
%%      framing. m4 Fig. 8 caption: "interpretive" -> "interpretive
%%      gloss on the derived geodesic law". m5 plain-English
%%      conclusions: one-law clause added to the sensing sentence.
%% v2.3 (June 11, 2026): Front-matter refinements (author request):
%%   (1) ES tightened by ~5 lines (gateway sentence compressed; ES Q4
%%   name-list dropped; "what is new" item (iv) compressed; keyword
%%   list trimmed by two entries) so Executive Summary + Keywords fit
%%   pages 2-3 exactly; (2) Overview of Contents and List of Figures
%%   combined onto page 4 (sty macros inlined into one page block,
%%   styles preserved; \GGOverviewOfContents/\GGListOfFigures calls
%%   replaced). Layout verified by pdftotext: p1 cover+abstract,
%%   pp2-3 ES+Keywords, p4 Overview+LoF, p5+ full TOC.
%% v2.2 (June 11, 2026): Title disambiguation (author decision, June
%%   11): subtitle "Five Century-Old Questions" -- garden-path
%%   ambiguous (parses as five-hundred-year-old; the author himself
%%   stumbled) -- replaced by "The Five Oldest Questions about the
%%   Electron" on the cover, in the pdf metadata, and at the two
%%   in-prose echoes (Part III close: "two of the century's
%%   questions"; Conclusions: "the five oldest questions").
%%   Objection 4's singular "a century-old question" kept (no
%%   counting-word collision). Cohort sweep in the same pass (June-10
%%   protocol): A9 v10.7 and P2 v2.7 bibitems updated -- new title,
%%   stamp v2.2, and framing refreshed from the v1.7-era "field
%%   response as GFF descent" to the v2.0 framing (composite geodesic
%%   motion from A5 Part VI + descent gloss), discharging the residual
%%   flagged at v2.0; cohort summary sheet title/version cells updated.
%% v2.1 (June 11, 2026): References expanded for student learning per
%%   the author's direction: 46 NEW historically significant originals
%%   (1687 Newton through 2012 Aoyama et al.), every one verified real
%%   (risky coordinates web-checked: Okun-Zeldovich PLB 78 597;
%%   Feinberg-Goldhaber PNAS 45 1301; Brodsky-Drell PRD 22 2236;
%%   Stoney Phil. Mag. S5 38 418), every one cited inline at least
%%   once at a substantive site (~28 citation-site edits across Parts
%%   I, III-VII and Appendices C-G), and every one carrying a solid
%%   one-paragraph student-oriented Relevance. Thin Relevance
%%   paragraphs upgraded (Thomson, Helgason). Bibliography: 41 -> 87
%%   items, alphabetical order preserved. L90 re-audited clean.
%% v2.0 (June 11, 2026): DRASTIC Q4/Q5 revision per the author's review
%%   ("read A5-GDOS Part VI -- Unification of GR and QED; the answers
%%   are rooted in AX-2 GGEP; current solutions superficial"). Main
%%   text: NEW Part V section "What AX-2 makes a particle: two charges
%%   on one composite connection" (minimal worldline coupling as THE
%%   complete matter interface; unified equation of motion reproduced
%%   from A5 Part VI; "a spatial profile is not a variable of the
%%   matter sector"; GR-style retirement of "what is the charged
%%   body?"); Part VI sec:force REPLACED by "The force law as
%%   composite geodesic motion" (parallel chains digest; Q5 answered
%%   as generalized free fall -- "not an influence the electron
%%   detects but the shape of the electron's world"; division of
%%   credit restated, R4 intact: classical Maxwell-Lorentz system
%%   incl. sign structure arrives derived in Chain B; quantum spin-1
%%   reading remains QED's); sec:sensing reframed as the open-system
%%   GLOSS on the geodesic answer (INT pricing kept); coupling section
%%   gains holonomy-momentum statement; pointlikeness proof gains
%%   constitutional Step 0 (AX-2 coupling completeness). Appendices:
%%   App F Step-0 pointer; App G REPLACED by the A5-Part-VI digest
%%   (Chain A with 2pi + warp integrals, M_Pl^2 = pi M_6^4(1-e^{-2K});
%%   Chain B phase->connection->Maxwell->Lorentz->Coulomb; unified
%%   equation; gravity-electricity dictionary table; three shared-
%%   origin ingredients; descent gloss demoted; exercises extended).
%%   Status synced at every layer (tab:status, tab:solutions, Sec 19,
%%   ES, ledger): Q5 force law now THM (A5 Part VI chains), descent
%%   reading explicitly gloss-INT. All reproductions cite A5 inline.
%% v1.9 (June 11, 2026): Appendices dramatically expanded per the
%%   author's plan of June 11, on the A2-GG6 appendix template:
%%   NEW App. A "Summary of Abbreviations" (A2 App.-A format,
%%   longtable, ~33 entries, pointer to A2 App. B for the full
%%   Dictionary); App. B = claim-status ledger (unchanged); NEW App. C
%%   "Derivations for Q1" (GGA/GFF-ST7 assembly; the full dyadic
%%   charged-lepton codebook reproduced from A9 with its code-by-code
%%   reasoning, first-order masses from v=246.331354 GeV, exact ratios
%%   84/5 and 625/3; the QD completion 637/640, 159/160, 641/640 and
%%   the QD masses; alpha at M_Z = 2^J with QD 127.9296875 vs PDG
%%   127.930(8), alpha(0) = 2^J+N^2 with QD completion as A9 reports;
%%   e from T-Euclid-4; the full Herm_2(H) construction of
%%   Spin(1,5)=SL(2,H) reproduced from A2); NEW App. D "Derivations
%%   for Q2" (CP^2 Morse skeleton indices 0/2/4, basins-vs-saddles
%%   spectroscopy argument, gate calculus Gamma ~ e^-S with the
%%   phase-space caveat, the four-step no-exit-gate assembly); NEW
%%   App. E "Derivations for Q3" (P2's Theorem L1 reproduced with full
%%   proof -- phase counting (N-1)(N-2)/2, Jarlskog, PDG value; the
%%   cascade-closure lemma with proof sketch (Witten/Helgason cited);
%%   the Budget Conjecture verbatim with its honesty note and H1-H2;
%%   leg L3 ratio formulas evaluated at N=2,3,4; closure); App. F =
%%   the Q4 form-factor argument (retitled for parallelism; content
%%   unchanged); NEW App. G "Derivations for Q5" (commutant
%%   masslessness -> 1/r, exchange-sign credit, GFF-ST6 monotonicity
%%   + tilt formalism + two-regime split, INT status restated; "what
%%   a student should now be able to do" close); App. H = anchors
%%   (unchanged). All copied derivations cite their parents inline
%%   (A9-SM, P2-N3, A2-GG6, A6-GRIP). Helgason 1979 added to the
%%   bibliography (verified real). Appendix part subtitle updated.
%% v1.8 (June 11, 2026): Part VII restructured into a full Discussion
%%   per the author's plan of June 11 (triumph-before-triage ordering,
%%   V9-4): Sec 19 Significance (NEW: five solutions one-by-one +
%%   tab:solutions + what-changes); Sec 20 Uniqueness (former
%%   comparison, doubled: Wheeler, compositeness + rishons/Harari +
%%   mass paradox, NEW Kerr-Newman/Carter g=2 lineage, QFT identity,
%%   NEW anthropic/landscape engagement, classical electron, division
%%   of labour); Sec 21 Sharp contrast with SUSY and string models
%%   (NEW, adapted from A2-GG6's comparison Parts: shared machinery /
%%   moduli-vs-integers and the anti-landscape / SUSY partner-vs-basin
%%   / discriminator table tab:contrast / honest credits); Sec 22
%%   Prediction for Falsification (former Secs 19+20 unified and
%%   doubled: P1-P5 each with anchor + experimental future + live
%%   falsifier in the V9-6 pattern; F1-F5 tags preserved for all
%%   cross-refs; NEW "what would NOT falsify" negative-space paragraph;
%%   P3 wording corrected QED -> Standard-Model dressing per Objection
%%   11); Sec 23 Open problems (extended to seven, O-P3-1..7, each
%%   with problem / why it matters / what counts as a solution); Sec
%%   24 Common Objections and Responses (NEW, 15 objections in the
%%   A2-GG6 closing-objections format with honest-acknowledgement
%%   language; includes the m_e-residual objection at full strength).
%%   Seven bibitems added, all verified real: Carter 1968 (Kerr-Newman
%%   g=2), Harari 1979 (rishons), Green-Schwarz 1984, GSW 1987,
%%   Candelas et al. 1985, Randall-Sundrum 1999, Susskind 2003.
%%   Labels preserved: part:VII, sec:prior, sec:predictions, sec:open;
%%   sec:kill retired (was unreferenced).
%% v1.7 (June 11, 2026): Phase 5 cohort sync (see [P3-Support]/
%%   P3-PHASE5-SYNC-REPORT-2026-06-11.md; cohort edit script
%%   cohort_p3_sync_fixes_2026-06-11.py). Cohort side: \PaperPThree +
%%   \PaperFullPThree added to ucla-arisaka-gg-10.sty; A9-SM v10.6
%%   pointer paragraph + ArisakaP3Electron bibitem (the A9 <-> P2
%%   pattern); P2-N3 v2.6 reciprocal pointer + bibitem; A5-GDOS v10.5
%%   stale "GG-P3-Thermo" slot corrected to tentative GG-P4-Thermo.
%%   All three recompiled clean. P3 side (this file): bibitem version
%%   stamps refreshed to the Phase-5 bumps (A5 v10.5, A9 v10.6, P2
%%   v2.6, all June 11, 2026); A11 stamp verified correct at v10.3 /
%%   June 10 (J4 closed); preamble note on the local \PaperPThree
%%   stand-in updated (sty now defines it; \providecommand yields).
%%   No content changes. Residuals flagged in the sync report: A9's
%%   internal depth-2 vs depth-4 enumeration (J5, author decision);
%%   \ASix renders "GG-A6-Gi4" cohort-wide (Surgery-2 rename pending);
%%   other papers' bibitem stamps for A5/A9 now trail by one notch
%%   (the same residual P2's Phase 5 recorded).
%% v1.6 (June 11, 2026): Phase 4 hostile-referee fixes (0 FATAL,
%%   2 MAJOR, 5 MINOR; see [P3-Support]/P3-HOSTILE-REFEREE-REPORT-
%%   2026-06-11.md):
%%   B1 (MAJOR) Lemma RL statement-vs-proof daylight closed: wavelength
%%      sub-clause derived in the channel-level proof (operational
%%      restatement of scale-freedom); App B branch (b) acquires the
%%      explicit elastic/zero-energy-transfer scoping sentence. O-P3-1
%%      unchanged.
%%   C1 (MAJOR) Sign-rule citation support: Schwinger1948/Feynman1966
%%      (neither contains the spin-1 exchange derivation) -> Weinberg
%%      1995, + clause crediting A9's own tree-level exchange-sign
%%      argument (verified, 3 sites in A9). Both displaced refs remain
%%      cited at their correct sites; no orphans. Hurwitz name-drop
%%      annotated "1898 theorem, cited in A2" (C2 hygiene).
%%   A1 "nineteen orders" -> "more than eighteen" (10^18.7); A2 "five
%%      orders below the proton's" -> "more than four" (10^4.6);
%%   B2 "twelve decimal places" (x2) -> "parts in 10^12"/"twelve
%%      digits"; B3 QD-alpha completion marked "as A9 reports".
%%   Arithmetic block: all printed numbers reproduce programmatically
%%   (m_e^QD to all printed digits; ladder, e^-35, E_GUT, M_lock,
%%   Fig-1 axis conversions, Table-3 PDG values).
%% v1.5 (June 11, 2026): Author readability review. (1) NEW one-page
%%   Preface ("To the reader who kept the questions") opens Part I:
%%   friendly, philosophically grounded, addressed to the first-year
%%   graduate reader; reading contract restated. (2) Part VIII expanded
%%   from single arc section into full Conclusions: NEW section "Why a
%%   century?" (five structural reasons the questions stayed open:
%%   disciplinary scattering; answered-by-grammar; the success trap;
%%   the inputs culture; the closed-system blind spot -- the last
%%   imported from P2's methodological reflection by citation), with
%%   the deferral credited as honest discipline, not blindness; NEW
%%   four-subsection plain-English close per style-guide V9-3 ("The
%%   wider view" / "in one sentence" / "beyond physics" / "what we hope
%%   a careful reader will take away") + warm wide-audience closing
%%   paragraphs; fifty-year arc kept VERBATIM as the final personal
%%   section (author-approved J3 text untouched). Part VIII retitled
%%   "Conclusions: The Century, the Closing, and the Fifty-Year Arc".
%%   Mermin 1989 ("shut up and calculate", Physics Today 42(4) 9,
%%   correctly attributed to Mermin) added to bibliography with
%%   Relevance line. Marker-density check: one new After-all in the
%%   close, one in the preface; arc's existing close untouched.
%%   Edit script: [P3-Support]/p3_v1.5_edits.py.
%% v1.4 (June 11, 2026): Author figure review. (1) A9-SM Figure 9 (the
%%   GRIP cascade on CP^2 at N=3, tau/mu/e Morse diagram) reproduced as
%%   fig:grip-cascade-cp2, placed beside the basin landscape in Part IV;
%%   caption adapted (A9 internal refs -> citations; Witten 1982 added
%%   to the bibliography, verified real: J. Diff. Geom. 17 (1982) 661).
%%   (2) fig:basin-landscape enlarged to full text width (yscale 1.40),
%%   x-axis title moved under the axis, shifted left (author request).
%%   (3) fig:formfactor enlarged to full text width (yscale 1.45),
%%   x-axis title likewise; experimental-reach label relocated into the
%%   plot area; reach band moved to background layer so labels stay
%%   legible. All three previewed page-by-page before integration
%%   (preview-first); generator preview-figs.tex updated in
%%   [P3-Support]. Edit script: [P3-Support]/p3_v1.4_edits.py.
%% v1.3 (June 11, 2026): Figures + comprehensive tables (author
%%   directive, June 11). Six figures, all previewed page-by-page per
%%   the preview-first rule (generator: [P3-Support]/preview-figs.tex):
%%   Fig. bulk-cross-section (adapted from A2's warped-bulk figure;
%%   caption rewritten for P3, internal A2 refs replaced by citations);
%%   Fig. grip-two-regimes (adapted from A6's two-regime pipeline);
%%   Fig. grip-cascade (adapted from A6, SPECIALISED to N=3: gate boxes
%%   relabelled S[4->2]=2pi, S[2->0]=pi to match P2/A9 index convention;
%%   PBI-4 compensator box dropped as out of P3 scope); Fig.
%%   basin-landscape (NEW: schematic 1D cut, three basins, two tolled
%%   gates, GGA, GRIP-In descent); Fig. formfactor (NEW: proton vs
%%   composite-at-Lambda vs F==1; schematic); Fig. sensing-regimes
%%   (NEW: drift-within-basin vs hop-through-gate panels). All cited
%%   in text via \figref (L74); captions [short]{long} (L75).
%%   \GGListOfFigures added to front matter. Tables: three NEW booktabs
%%   tables in the cohort format (caption above): tab:inheritance
%%   (Part II map), tab:cascade (lepton cascade assignment with PDG
%%   values), tab:predictions (P1-P5 with bold Class column per L58);
%%   the three v1.0 tables (status/ledger/anchors) restyled from ruled
%%   to booktabs, captions moved above, content unchanged. Local macros
%%   \CPN, \Stot added for the adapted A6 figure. Edit script:
%%   [P3-Support]/p3_v1.3_edits.py.
%% v1.2 (June 11, 2026): Phase 3 house-style completion (Style Guide 10)
%%   + author directive: in-situ physics intuition for grad students.
%%   (a) Seven "Physics intuition." paragraphs at point of use: GFF
%%   landscape as Landau functional / ground-state conformation (III);
%%   mass as level, hydrogen -13.6 eV analogy (III); spin double cover,
%%   belt trick (III); stability as absence of destinations, ground-
%%   state-atom analogy (III); gates as Gamow barriers, actions in
%%   exponents (IV); scale direction as Wilsonian RG zoom, KK-vs-depth
%%   contrast (V); form factor as wavelength ruler, proton 0.84 fm
%%   anchor (V); overdamped-bead reading with explicit disanalogy note
%%   (VI). One marker max per remark (density rule). (b) Part-end
%%   plain-English closes for Parts I-IV, VII (V and VI already closed;
%%   V's "agreed to die" kept as the titular close). (c) L71 sweep:
%%   banned-phrasing greps now return zero (KK contrast rephrased to
%%   "extra dimensions that are spatial"; "curled-up" removed; "compact
%%   phase direction" kept -- topological sense, grep-clean). (d) First-
%%   mention plain-English glosses for GDOS, GFF, GRIP-In/Out, OGGEP;
%%   Dictionary pointer to A2 App. B (Surgery 4 note). (e) Two-level
%%   front matter: \GGOverviewOfContents added before full TOC (charter
%%   Decision 4); abstract trimmed toward the 150-180 word target (L64/
%%   L69), cover-page fit verified by pdftotext (L68). (f) All three
%%   overfull boxes fixed (status-table colspec; canonical metric to
%%   display math; ledger row reworded). (g) Surgery-1 Prefix-Suffix-N
%%   IDs NOT adopted, matching P2-N3 v2.5 sister precedent -- flagged
%%   in the Phase-3 report for the author. Edit script:
%%   [P3-Support]/p3_v1.2_edits.py.
%% v1.1 (June 11, 2026): Author-review revisions (Phase-2 report J1-J6).
%%   (J1) Postulate RL PROMOTED to Lemma RL, derived from AX-1 (LC,
%%   Locality and Causality) of A1 v10.3: the constitutional statement
%%   quantifies over "every admissible boundary intervention protocol";
%%   clarification 2 extends LC to open evolution maps and measurement
%%   instruments; clarification 3 attaches observables to points
%%   (microcausality) and excludes fundamental extended objects. Label
%%   post:RL kept for cross-ref stability. Theorem "Pointlikeness" now
%%   holds within the declared axiom system (no paper-local fence);
%%   App B Step 2 rewritten as the two-branch derivation (spacelike
%%   support barred constitutionally; retarded memory generates no
%%   equal-time spacelike profile) + "what AX-1 does and does not
%%   contribute" remark (circularity pre-emption, R3) + universality
%%   remark. O-P3-1 narrowed to the static-limit formalization. F5
%%   reformulated (flaw-in-derivation). F2 extended (substructure now
%%   strikes AX-1 itself). ES / abstract / Part-I fence inventory /
%%   status table / App-A ledger / A1+A8 Relevance lines synchronized.
%%   (J3) Part VIII fifty-year arc: v1.0 voice author-approved; flag
%%   removed. (Author direction) Review-article framing: cover note,
%%   abstract sentence, ES paragraph, Part I "Who this paper is for" --
%%   written for 1st-year physics graduate students as refresher and
%%   gateway to the cohort. Edit script: [P3-Support]/p3_v1.1_edits.py.
%% v1.0 (June 11, 2026): Phase 2 complete draft (first complete draft per
%%   charter versioning). Drafting order per charter Sec. 6: Parts III,
%%   IV, VI (existing synthesis), then Part V (Q4 new core), then Parts
%%   I-II, VII-VIII + appendices. All upstream attributions cite the
%%   locations grep-verified in [P3-Support]/P3-PHASE1-AUDIT-2026-06-11.md
%%   (27-row sync map). New fenced items born in this version: Postulate
%%   RL (Readout Locality) + conditional Pointlikeness Theorem (Part V);
%%   interpretive Reading "sensing as GFF descent" (Part VI), owned as
%%   P3's reading, not attributed to A5. P2-N3 fences (Budget Conjecture,
%%   H1-H2, reachability-as-interpretation) imported verbatim in Part IV.
%%   m_e honesty discipline: QD value 0.511097845 MeV vs CODATA
%%   0.51099895069(16) MeV, residual 1.9e-4 declared at every occurrence
%%   incl. abstract level; alpha Rb/Cs >5sigma discrepancy noted. R6
%%   literature added, every reference web-verified real (Phase 1/2).
%%   Bibliography: C1 v10.4 house format; cohort stamps as of June 11,
%%   2026; A11-Origin added (T-GGA-as-Ground-State source, per A9
%%   sec:universal-identity attribution). Fifty-year arc drafted as
%%   AUTHOR-VOICE PLACEHOLDER flagged for the author's personal rewrite.
%% v0.1 (June 11, 2026): Phase 0 skeleton (8-Part architecture, v10
%%   toolchain, 3-pass clean). Archived in [P3-Archive].
%% ===================================================================

%% ---- vv15.8 (August 19, 2026) ----
%% The front-matter showcase pages given breathing room.
%% A showcase page's free height is now distributed by weighted stretch
%% glue -- a sixth at the top, a third above the plate, a third below it,
%% a sixth at the foot -- instead of pooling above the headline and below
%% the caption, which left a broad band of white at each end of the page
%% and crowded the three elements into the middle third.
%% Three source forms were found in the cohort and each is handled.  A
%% minipage frame becomes a minipage of EXPLICIT height with the [s]
%% inner alignment, because a minipage is a vbox of natural height and
%% glue inside one does not stretch; the height is \textheight minus
%% \topskip.  A \begingroup frame keeps its page-level glue and changes
%% only the weights.  An unframed page -- there were eight, five of them
%% showcase tables carrying a longtable, which cannot live inside a
%% minipage -- gains page-level glue for the first time, which is why it
%% had been printing hard against the top of the text block.
%% 1 showcase page in this paper.  Layout only: not one word,
%% number, figure or table row is changed by this ship.
\documentclass[11pt,letterpaper]{article}

\usepackage{ucla-arisaka-gg-11}
\usepackage{indentfirst}
\renewcommand{\LaTeX}{LaTeX} % avoid \@ clash from \LaTeX in \GGAcknowledgments (v8-v10 sty); cohort-standard shim

%% ---- Per-paper identity -------------------------------------------
\PaperSeries{GGP}
\PaperNumber{Arisaka-GG-P3-Electron}
%% ------------------------------------------------------------
%% v14.14 -> v15.0, August 15, 2026.  STAGE 1 of the v15
%% migration: MECHANICAL.  The fourth paper conversion.
%%   a4paper -> letterpaper.  \textwidth 452.9679 -> 469.75502pt,
%%   +3.7 %%.  Plates placed by the A4 constant now print 3.7 %%
%%   larger; Stage 3 measures them and frozen decision 3 leaves
%%   above-house alone.  A9, C1 and P1 each lost a page to the
%%   widening; this one is watched for the same thing.
%%   190 printed British spellings -> 0, and 1 more in the PDF
%%   METADATA (pdfsubject), which is not printed text but ships
%%   inside the file where a properties panel shows it.
%%   The two `Programme' sites in the bibliography are NOT
%%   protected titles.  P3 quotes A1's title as "...GG-Theory
%%   Programme" and A11's the same way.  A1's OWN title reads
%%   Program, and A5, A9, A10 and P1 all quote both as Program.
%%   P3 was the only paper still carrying the older form, so this
%%   is a coherence repair against the cohort's own text.
%%   `felled' is PROTECTED -- past tense of to fell, correct
%%   English, reached by the -elled branch.
%%   1 \hline removed: booktabs only.
%%   Edited BY OFFSET rather than by text anchor -- this paper
%%   hard-wraps its source and anchors copied from a flattened
%%   scan do not exist.
%%   NO PROSE WAS WRITTEN IN THIS STAGE.
%% ------------------------------------------------------------
%% ------------------------------------------------------------
%% Stage 2A, same day.  Front matter and nine thin captions.
%%   FRONT MATTER: Stage 0's census said "no LoF, no LoT, no
%%   Overview" and was half wrong -- P3 had an Overview and a
%%   List of Figures, HAND-INLINED from the style file under an
%%   author request to share one page.  The style now does that
%%   itself (\GGfrontmatteronepagetrue, as in C3-BH and P1-KK),
%%   so the request is met BY the standard rather than around it.
%%   The LIST OF TABLES was genuinely missing, against nine
%%   captioned tables.
%%   NINE THIN CAPTIONS extended to the section 8 minimum, every
%%   existing sentence kept VERBATIM.  Section 14.2 reserves
%%   rewriting a caption's claim; none is rewritten.  Each
%%   addition says what the columns are for.  NEW PROSE -- listed
%%   by table and page in the report for review or rewriting.
%% ------------------------------------------------------------
%% ------------------------------------------------------------
%% Stage 2B, same day.  Ten short caption forms.
%%   Rendering page 5 after Stage 2A showed the new List of
%%   Tables printing FULL captions -- Table 1 over five lines,
%%   Table 2 over six -- because ten of twenty-two captions had
%%   no short form and \listoftables falls back to the whole
%%   paragraph.  A caption written to section 8's 260-character
%%   minimum IS a paragraph, so the minimum and a bare \caption{}
%%   cannot both be satisfied: every long caption owes a short one.
%%   C2-Hubble's rules kept -- 95 characters, WRITTEN rather than
%%   truncated, and balanced by assertion.  On C2 a truncating
%%   sweep cut inside TeX quotes and ended two entries on function
%%   words; nothing here is cut.
%%   The twelve captions that already had a short form are
%%   untouched.  NEW PROSE, ten one-line titles.
%% ------------------------------------------------------------
%% ------------------------------------------------------------
%% Stage 2C, same day.  Eight Plain-English Part introductions.
%%   EIGHT, not ten.  Part X is the Appendices and back matter
%%   gets none.  Part IX ALREADY ENDS in a section the author
%%   wrote and titled "Conclusions, in plain English", so a
%%   "Part IX in plain English" beside it would print the same
%%   promise twice, four pages apart.  Checked before writing.
%%   ONE Contents entry each: \section[SHORT]{LONG}, never
%%   \section plus \addcontentsline -- the inherited template did
%%   both and put two Contents lines per introduction into A8,
%%   A9, A10, C1 and C2.  Asserted here: 8 sections, 0 of them.
%%   ALL EIGHT ARE NEW PROSE IN THE AUTHOR'S VOICE, listed by
%%   Part and page in GG-Report-364 for review or rewriting.
%%   Standard physics is credited at full strength in each
%%   before anything is added, and where a Part rests on a
%%   companion the introduction says so -- Part IV owns the
%%   terminus and NOT the family count.
%% ------------------------------------------------------------
%% ------------------------------------------------------------
%% Stage 4, same day.  Palette -- 12 violations in 5 pictures.
%%   3 bare `draw' (a 100%%-black border) -> hue borders; 8 box
%%   fills above !18 compressed into the section 8 band; keyword
%%   weights made explicit.  palette_audit 12 -> 0.
%%   AND THE WIDTH CLAMP WAS FIXED RATHER THAN REVERTED BY HAND.
%%   On its first run it clamped two PATH STROKES: the free-energy
%%   landscape curve at 1.3pt, and the 1.6pt line drawing this
%%   paper's own prediction F == 1, set heavier ON PURPOSE than the
%%   proton and composite-electron curves it is contrasted against.
%%   Clamping that one would have given the paper's claim the same
%%   weight as its foils.  That is the THIRTEENTH object this clamp
%%   has destroyed across six papers -- A10's detector spots and EPR
%%   source markers, A9's legend swatch and interval bars, C1's scan
%%   spans, C2's two bars carrying two meanings by two weights, C3's
%%   span bars and arrow head -- and every single one was an inline
%%   \draw on a path, never a node border.  Section 8's weight band
%%   governs BOX RULES.  The clamp now runs inside `/.style={...}'
%%   bodies only and PRINTS the path strokes it leaves alone.
%%   Six ships had each reverted this by hand; it is now fixed once.
%%   NO PROSE WAS WRITTEN IN THIS STAGE.
%% ------------------------------------------------------------
%% ------------------------------------------------------------
%% Stage 5, same day.  Integrity -- seven missing companions.
%%   A7-Qi4, C2-Hubble, C3-BH, P1-KK, P6-Proton, W1-Symmetry and
%%   W2-Holonomy had no bibitem.  P3 carries the twenty-two-paper
%%   cohort map, so it printed a map of twenty-two while its
%%   bibliography knew fifteen.
%%   THE THREE-COMPANION PATTERN IS FIVE FOR FIVE AND P3 IS THE
%%   WORST CASE: C1, C2, C3 and P1 were each missing exactly P6,
%%   W1 and W2, the three newest papers; P3 is missing those and
%%   four more, being older still.
%%   A6 IS NOT ADDED.  P3 already cites it as ArisakaA6Gi4; C3
%%   and P1 use ArisakaA6GRIP for the same paper.  Report 360
%%   recorded the split; resolving it is one decision and one
%%   cohort sweep, and patching it here would deepen it.
%%   EVERY RELEVANCE NOTE GRADES ITS COMPANION HONESTLY.  Three
%%   of the seven are roster level only and SAY SO -- C2 and C3
%%   carry no result this paper uses, and P1's collider verdict
%%   does not touch the electron.  P6 is the substantive one: two
%%   particles, two absolute-stability claims, one ledger, and
%%   two standing falsifiers that would be lost together.
%%   NEW PROSE: seven Relevance notes, listed in GG-Report-364.
%% ------------------------------------------------------------
%% ------------------------------------------------------------
%% Stage 5B, same day.  The prose that cites the seven.
%%   Stage 5 added seven bibitems and left seven ORPHANS.  A
%%   bibliography entry nothing points at is a roster padded to
%%   look complete, and section 11's Stage 5 says the companions
%%   must appear "each with the prose that cites it".
%%   P6-Proton gets a paragraph of its own at the stability
%%   section -- the substantive attachment, and the only one:
%%   two particles, two absolute-stability claims, one integer
%%   ledger, two falsifiers that would fall together.
%%   W2-Holonomy attaches at the winding-number sentence,
%%   because the mechanism argued there IS what W2 classifies.
%%   A7-Qi4 attaches at the GRIP two-regime definition, for the
%%   runtime vocabulary and nothing else.
%%   W1, C2, C3 and P1 attach in the cohort-map caption at
%%   ROSTER LEVEL, and the caption sentence SAYS roster level --
%%   three of them carry no result this paper uses, and writing
%%   four notes that all claimed substance would have been the
%%   easy version and the dishonest one.
%%   The three roster citations are separate \citealp calls:
%%   two Arisaka keys in one cite print as bare commas and drop
%%   references, which is the defect Report 361 shipped riders
%%   for on A10 and C2.
%% ------------------------------------------------------------
%% ------------------------------------------------------------
%% Stage 6, same day.  The one new sparse page, cleared.
%%   Sparse-page scan vs the A4 rebuild: the baseline's single
%%   sparse page (p69, a Part VIII paragraph tail) is GONE, and a
%%   new one appeared at p6 -- the eleventh List of Tables entry
%%   alone on a page, the front-matter overflow section 7 names.
%%   Section 7's remedy is \captionsetup{list=no} on a coherent
%%   CLASS of floats, which here would have hidden three appendix
%%   tables to save one line.  Two List of Figures entries were
%%   wrapping to two lines instead, so shortening those two short
%%   forms recovers TWO lines and hides nothing.  Measured after
%%   the attempt, per section 7, not reasoned about.
%% ------------------------------------------------------------
%% ------------------------------------------------------------
%% Stage 7, same day.  A defect in my own new prose.
%%   Stage 2C joined each introduction's lines with
%%     re.sub(r"\n(?!\n)", " ", body)
%%   which turns "A.\n\nB." into "A.\n B." -- a SINGLE newline,
%%   which LaTeX reads as ordinary space.  All eight introductions
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%%   of the three paragraphs each was written as.
%%   Caught by rendering p19 and reading it.  The .tex was valid
%%   TeX and every gate item was already zero, so nothing but the
%%   page could have caught it.  P1-KK inserted its closes without
%%   the collapse and is unaffected -- checked, not assumed.
%%   Part VII's introduction had since taken the W2-Holonomy
%%   citation from Stage 5B, so the repair carries that through
%%   rather than reverting it.
%% ------------------------------------------------------------
%% ------------------------------------------------------------
%% Stage 8, same day.  SHIP.  P3-Electron v14.14 -> v15.0.
%%   The fourth paper conversion.  A4 -> Letter, 190 printed
%%   British spellings + 1 in the PDF metadata, front matter to
%%   the standard with the List of Tables it never had, ten short
%%   caption forms, nine thin captions extended, EIGHT Plain-
%%   English Part introductions, 12 palette violations cleared,
%%   and seven missing companions with the prose that cites them.
%%   GATE: 125 pages (A4 baseline 113; Letter is the shorter page,
%%   so a conversion ADDS pages -- P1-KK went 200 -> 213 the same
%%   way).  errors 0 | undefined 0 | multiply 0 | overfull hbox 2,
%%   none above 20pt, against a baseline of 1 | overfull vbox 0.
%%   THE WIDENING FAILURE MODE DID NOT STRIKE.  A9, C1 and P1 each
%%   lost a showcase plate to the 3.7 %% widening and orphaned a
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%%   ten TikZ pictures, and no \clearpage/figure[p] pairing for the
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%%   introduction cleared a one-line orphan at p61.  Ownership
%%   asserted against v14.14 first -- the Part XII lesson from
%%   P1-KK, where I trimmed the author's paragraph believing it
%%   was my own.
%% ------------------------------------------------------------
\PaperVersion{v20.2}
\PaperDate{August 22, 2026}


%% ---- Paper-local macros -------------------------------------------
\newtheorem{conjecture}[theorem]{Conjecture}
\providecommand{\GRIPin}{\ifmmode\mathsf{GRIP\text{-}In}\else\textsf{GRIP-In}\fi}
\providecommand{\GRIPout}{\ifmmode\mathsf{GRIP\text{-}Out}\else\textsf{GRIP-Out}\fi}
\providecommand{\GGA}{\ifmmode\mathsf{GGA}\else\textsf{GGA}\fi}
%% \PaperPThree entered the sty June 11, 2026 (Phase 5); this local
%% \providecommand now yields to the sty definition and is kept only
%% for builds against pre-Phase-5 sty copies.
\providecommand{\PaperPThree}{\textsf{GG-P3-Electron}}
%% \AEleven is not yet in the v10 sty (which stops at \ATen); local
%% stand-in per the C1 precedent, \providecommand so a future sty wins.
\providecommand{\AEleven}{\textsf{GG-A11-Origin}}
\providecommand{\PaperPFour}{\textsf{GG-P4-Real}}%% v13.0: Foundations Branch member (canonical form, Cohort-Map-19 v1.4)
\providecommand{\PaperPFive}{\textsf{GG-P5-CPT}}%% v13.0: Foundations Branch member (canonical form, Cohort-Map-19 v1.4)
\renewcommand{\ASix}{\textsf{GG-A6-GRIP}}% A6 Gi4 -> GRIP (cohort, May 2026); sty default still renders the retired name
%% One-line Part entries in the Overview of Contents (cohort standard;
%% pattern from the P4-Real v3.2 preamble): drop the " --- description"
%% tail; the description remains on the Part title page.
\makeatletter
\renewcommand{\GGPart}[3][]{%
  \clearpage
  \refstepcounter{part}%
  \def\gg@parthdr{#1}\ifx\gg@parthdr\@empty\def\gg@parthdr{#2}\fi
  \addcontentsline{toc}{part}{\protect\textbf{Part \thepart}. #2}%
  \markboth{Part \thepart.\ \gg@parthdr}{Part \thepart.\ \gg@parthdr}% running pointer
  \thispagestyle{plain}%
  \begin{center}
    \vspace*{1.2em}
    {\Large\bfseries Part \thepart}\\[0.45em]
    {\huge\bfseries #2}\\[0.35em]
    {\large #3}
  \end{center}
  \vspace{0.5em}
  \GGThickLine
  \vspace{0.8em}
}
\makeatother
\providecommand{\Ir}{\ensuremath{I_r}}
\providecommand{\Stheta}{\ensuremath{S^1_\theta}}
\providecommand{\yE}{\ensuremath{y_e}}
\providecommand{\alphainv}{\ensuremath{\alpha^{-1}}}
\providecommand{\SLtwoH}{\ensuremath{\mathrm{SL}(2,\mathbb{H})}}
\providecommand{\CPN}{\ensuremath{\mathbb{C}P^{N-1}}}
\providecommand{\Stot}{\ensuremath{S_{\mathrm{tot}}}}
\providecommand{\FGFF}{\ensuremath{F_{\mathrm{GFF}}}}
\providecommand{\SmaxBI}{\ensuremath{S^{\mathrm{max}}_{\mathrm{BI6}}}}
\providecommand{\JCKM}{\ensuremath{J_{\mathrm{CKM}}}}
\providecommand{\VCKM}{\ensuremath{V_{\mathrm{CKM}}}}
\providecommand{\cM}{\ensuremath{\mathcal{M}}}

\hypersetup{
  pdftitle = {The Electron as the Ground State of Nature: The Six Oldest Questions about the Electron, Closed and Fenced within GG-Theory},
  pdfauthor = {Katsushi Arisaka},
  pdfsubject = {GG-Theory program -- the electron as the unique ground geometric attractor of its boundary stratum},
  pdfkeywords = {GG-Theory, electron, identity, stability, pointlikeness, generations, alpha, GGA, GDOS}
}

\begin{document}
% ---- v14.6 (August 2, 2026) ----
% Significance section gains the closing subsection 'The
% electron on the two fibres': the six solutions sorted by fibre
% --- identical-and-permanent as circle-side holonomy classes
% (Q1: classes do not age; sameness needs no enforcement),
% placed-and-priced as interval-side (mass as the terminus
% address, muon rate as a GRIP-In event, Q2 stability as no
% inverse transport); Q6 positron as the same class read in the
% mirror (address orientation-blind, labels not). 'An electron
% is a holonomy class wearing a mass.' Part of the P-series
% completion sweep.

% ---- v14.5 (August 1, 2026) ----
% Added full-page figure fig:lepton-descent in Part IV (The Excited
% Copies), sec:ladder: the three charged generations + neutrino
% seesaw floor + leptogenesis on the GRIP descent axis r=ln(EGUT/mu)
% (E_GUT=M_Pl/2, lock at r=K=35). External cropped asset
% p3_lepton_descent.pdf; figref hook in the figure-intro paragraph.


%% ===================================================================
%%  COVER PAGE
%% ===================================================================
\thispagestyle{empty}
\GGTitlePage%
  {The Electron as the Ground State of Nature}%
  {The Six Oldest Questions about the Electron, Closed and Fenced within \GGTheory{}}%
  {\parbox{0.92\textwidth}{\centering\small
   A companion preprint of the Predictions Branch, sister to \PaperPTwo{}
   ($N=3$), establishing that the electron's identity, absolute stability,
   excited copies, mirror twin, pointlikeness, and response to fields are
   six faces of one fact --- the electron is the unique ground geometric
   attractor (\GGA{}) of its boundary stratum --- with every remaining
   assumption named. Offered as a review-article gateway for the first-year
   graduate student who has carried these six questions past
   graduation.}}

%% ===================================================================
%%  ABSTRACT
%% ===================================================================
\begin{abstract}
\noindent
Every electron in the universe is exactly like every other: the same mass,
the same charge, the same spin. No electron has ever been seen to decay,
or to reveal an inner structure. Two heavier copies of it exist --- and
only two. Every
electron has a mirror twin --- the positron, of exactly equal mass and
exactly opposite charge. And every electron somehow senses an electric field and falls
toward the nearest proton. Since 1897, physics has treated these as six
separate mysteries, answering some in fragments and others not at all.

This paper assembles, within Grand Geometric Theory, a single answer: the
electron is the unique ground state of its sector of the boundary of a
six-dimensional geometry. Identity and its measured values,
absolute stability, the two excited copies that terminate at three, the
absence of substructure at any scale, the response to fields, and the
mirror twin are derived as six faces of that one fact --- with every step that remains
conjectural fenced by name, and the standard fragments credited where
they are real. It is written as a review, for the reader beginning
graduate study who noticed these questions and was told to move on.

After all, the most common particle of our existence deserves more than
six separate accidents; it deserves to be the theorem the other facts
were always pointing at.
\end{abstract}

%% ===================================================================
%%  EXECUTIVE SUMMARY
%% ===================================================================
\begin{ExecutiveSummary}
The question behind this paper is the oldest in particle physics, and the
most personal one a physicist can ask of the matter in his own hands: what
\emph{is} an electron, that it should be what it is? Six specific
questions have stood open since the electron's identification in 1897.
\textbf{Q1} (identity): why is every electron exactly identical --- and
why \emph{those} values of mass, charge, and spin? \textbf{Q2}
(stability): why is the electron absolutely stable? \textbf{Q3} (copies):
why do the muon and tau exist as heavier copies, and why are there
exactly two? \textbf{Q4} (pointlikeness): why does the electron show no
size and no substructure at any scale ever probed? \textbf{Q5} (sensing):
why does an electron respond to an electric field at all? \textbf{Q6}
(the twin): why does the electron have an antiparticle, and what is
the positron?

\paragraph{Who this paper is for.} This paper is written as a review
article, for the first-year physics graduate student --- the critical
thinker who finished a degree carrying exactly these six naive,
fundamental questions and was told, by silence or by syllabus, to move
on. It is offered as a refresher: the questions are taken seriously,
the standard answers priced exactly, and one geometric viewpoint
developed far enough to show the six as one. It is simultaneously a
gateway: every imported theorem is proved in the cohort papers it
cites. The status tags below are the reading contract: nothing is
asserted above its price.

\paragraph{The honest standard-physics ledger.} This paper front-loads
what standard physics genuinely answers, because its thesis survives only
alongside that credit. Q1 has a real partial answer: in quantum field
theory all electrons are excitations of one field, so exact likeness is
automatic --- but the field's mass, charge, and representation are free
inputs: the answer explains sameness but none of its content. Q2 has a correct bookkeeping argument --- lightest
charged particle plus charge conservation --- which presupposes exactly
the unexplained spectrum termination that is Q3. Q5's sign rule (opposites
attract) is a genuine theorem of QED, credited here without reservation.
Q3 and Q4 have, in standard physics, no explanation of any kind; Q6's
twin is explained only formally (QFT + the CPT theorem, credited) ---
what it \emph{is} goes unaddressed.

\paragraph{The one fact.} Within \GGTheory{} the six questions have one
answer: \emph{the electron is the unique Ground Geometric Attractor
(\GGA{}) --- the ground state --- of the charged-lepton stratum of the 4D
boundary of the 6D bulk.}\footnote{Throughout the cohort, the 6D bulk is read on the field-theory side of the bulk--boundary correspondence: the fifth (scale) dimension is the renormalization-group axis $r=\ln(E_{\mathrm{GUT}}/\mu)$, not a Randall--Sundrum spatial dimension, and the scale profile denotes RG running; the explicit renormalization-group construction is given in \citet{ArisakaA2GG6}.} Identity: every electron is the readout
of the same unique ground basin (theorem within \GDOS{}; \GFF{}-ST7), with
its values derived --- $y_e = N/(L^3 2^{J+L+1})$ and
$m_e^{\rm QD} = 0.511098$~MeV against the measured $0.510999$~MeV
(declared residual $1.9\times10^{-4}$);
$\alphainv = 2^J + N^2 = 137$ QD-completed to $137.036$; spin-$\tfrac12$
from the quaternionic structure $\mathrm{Spin}(1,5)=\SLtwoH$. Stability:
the ground basin has no exit gate --- there is nothing downhill, so the
electron cannot decay (theorem within \GDOS{}, importing \PaperPTwo{}'s
landscape). Copies: the muon and tau are the depth-1 and depth-0 basins
of the same landscape --- geometrically excited electrons --- and the
ladder ends at three; this is \PaperPTwo{}'s result, imported with its complete conditioning (two empirical inputs; the coupling clause with the integrality
theorem L-INT, residue R-INT), never re-derived and never overclaimed. The twin: the positron is the conjugate readout of the
same basin --- the origin of antiparticles imported at theorem grade
from \PaperPFive{}, the same-basin reading priced, its promotion
registered (D-P3-4). Sensing: the force itself is derived ---
Newton's and Coulomb's laws descend in parallel from one bulk onto
one equation of motion (AX-2): responding to a field is generalized
free fall; the coupling's existence, quantization, and strength
$\alpha$ are derived; the open-system arrows are priced as
interpretive glosses; the sign rule's quantum reading remains QED's
theorem, credited.

\paragraph{The new core: pointlikeness from non-spatial structure.} Q4 is
this paper's new derivational content. Under AX-2 a particle \emph{is} two charges
on one composite geometry--gauge connection --- mass on the metric
sector, quantized holonomy charge on the gauge sector --- with no slot
for a size; and the electron is not a small object
\emph{in} space: its entire structure --- dyadic depth, winding, cascade
level --- lies along the two non-spatial directions of the bulk, the
scale interval $\Ir$ and the phase circle $\Stheta$ (\ATwo{}'s theorems).
In space it therefore \emph{must} appear as a point: all of its extension
is orthogonal to space. The mass is a basin level, not field self-energy
--- the divergence crisis dissolved, not renormalized away; the spin
a double-cover label, not a rotation --- no superluminal surface
needed. The
operational claim, that the structural form factor is identically unity
at every scale, is proved via a lemma, Readout Locality (RL: the
bulk-to-boundary readout introduces no 4D length scale), \emph{derived} from the
constitutional axiom AX-1 (Locality and Causality) --- with one
technical step (the static-limit factorization) registered as open. The sharp edge is pre-registered: \emph{no substructure will ever be
found, at any scale} --- compositeness models predict a scale; this
framework forbids one forever.

\paragraph{Predictions and kill criteria.} The paper is killed by: (F1)
any observed electron decay ($\tau_e > 6.6\times10^{28}$~yr, Borexino); (F2) any confirmed substructure at any scale; (F3) a fourth
charged lepton (\PaperPTwo{}'s fences inherited); (F4) $m_e$
off the QD value beyond the declared $1.9\times10^{-4}$, or
$\alphainv$ off its QD completion, once the $>5\sigma$ Rb/Cs
discrepancy in $\alpha$ is resolved; (F5) a demonstrated flaw in the AX-1 derivation of Lemma RL, demoting
the pointlikeness theorem to conditional status; (F6) a confirmed
electron--positron asymmetry (mass, charge, or $g$), killing the Q6
answer before it killed CPT. The electron $g-2$ (0.13 parts per trillion) is engaged as the
empirical anchor of structurelessness, not claimed as a \GGTheory{}
computation.

\paragraph{What is new in this paper.} (i) The conjunction thesis stated
and defended: standard physics has fragments, each presupposing inputs
the geometry derives, none connected to the others; no framework has
previously explained all six as one theorem-complex about one ground
state. (ii) Part VI's derivation of pointlikeness --- the first cohort
statement converting non-spatial structure into a form-factor
prediction, its readout-locality lemma derived from AX-1. (iii) The two-regime unification of Q5
with Q3: field response is within-basin descent, decay through-gate
descent, one mechanism. (iv) The complete status ledger (Appendix~B):
every load-bearing step tagged with its upstream location. (v) The
sixth question housed: the positron as the conjugate readout of the
one basin (Part~V).

After all, a particle that has carried the same three numbers through
every experiment since 1897 deserves better than to have them carried as
inputs; it deserves a geometry in which there is exactly one basin at the
bottom of the world, and it is sitting in it.
\end{ExecutiveSummary}

\GGKeywords{%
electron; positron; identity; absolute stability; pointlikeness;
three generations; ground state; \GGA{}; \GDOS{}; \GFF{};
\GRIPin{}; spin-1/2; $\alphainv=137$; Yukawa codebook;
\GGTheory{}}


%% ---- v15.2: the showcase headline and its two plates ----------
%% \Large is the house default as of Report 391.
%% v11.5 (August 17, 2026): THE DEFINITION IS IN THE STYLE FILE NOW.
%% The comment above is the record of why it was here -- the style
%% file is shared, and changing it meant rebuilding every arXiv
%% package.  That was done, so what is left is what this paper sets.
%% THE BOXES HOLD THE UNSCALED tikzpicture; THE \resizebox STAYS AT
%% EACH USE SITE.  So the body copy is exactly the body copy it
%% always was, at 0.733 and 0.676 \textwidth, and the showcase copy
%% is the same drawing at 0.66 and 0.61 -- ninety per cent.  Scaling
%% DOWN is the safe direction: rendered rule weights shrink, so the
%% showcase copy cannot cross the house 0.956 pt ceiling.  A5's
%% failure mode runs the other way, from a copy made WIDER.
%% Filled at \setstretch{1}, which is what both figure sites run,
%% probed inside the environment (Report 392).  It matters more for
%% a tikzpicture than for a table: both plates carry multi-line
%% nodes and \baselinestretch sets their internal leading.
\newsavebox{\GGplateLandscape}
\sbox{\GGplateLandscape}{\setstretch{1}\begin{tikzpicture}[
 yscale=1.40,
 font=\small,
 arr/.style={->, line width=0.80pt, draw=black!70},
 floorline/.style={dashed, draw=black!45, line width=0.5pt},
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 desc/.style={-{Stealth[length=2.6mm]}, line width=1.1pt, draw=blue!60!black},
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%% axes
\draw[arr] (-0.3, -0.4) -- (-0.3, 6.0) node[anchor=south] {$\FGFF$};
\draw[arr] (-0.4, -0.3) -- (12.8, -0.3);
\node[font=\footnotesize\itshape, anchor=north east] at (12.6, -0.50)
 {configuration coordinate on the family stratum $\mathbb{C}P^{2}$ (schematic 1D cut)};
%% the landscape curve
\draw[line width=1.3pt, draw=black!80] plot[smooth, tension=0.75] coordinates {
 (0.0, 5.4) (1.0, 4.3) (2.3, 3.45) (3.0, 3.55) (3.9, 4.30)
 (4.9, 3.1) (5.9, 2.55) (6.7, 2.7) (7.5, 3.30)
 (8.6, 1.6) (10.0, 0.85) (11.2, 1.4) (12.2, 4.9) };
%% basin floors (dashed levels)
\draw[floorline] (2.3, 3.45) -- (13.0, 3.45) node[anchor=west, font=\footnotesize] {$m_\tau$};
\draw[floorline] (5.9, 2.55) -- (13.0, 2.55) node[anchor=west, font=\footnotesize] {$m_\mu$};
\draw[floorline] (10.0, 0.85) -- (13.0, 0.85) node[anchor=west, font=\footnotesize] {$m_e$};
\node[font=\scriptsize\itshape, anchor=west, text=black!60] at (11.55, 0.45) {(levels not to scale)};
%% particles in basins
\fill[black!75] (2.55, 3.46) circle (1.8pt) node[lab, below=2pt, xshift=-5mm] {$\tau$ --- depth 0\\ \GA{} (metastable)};
\fill[black!75] (6.2, 2.56) circle (1.8pt) node[lab, below=2pt, xshift=4mm] {$\mu$ --- depth 1\\ \GA{} (metastable)};
\fill[blue!60!black] (10.0, 0.86) circle (2.2pt) node[lab, below=3pt, text=blue!60!black]
 {$e$\\ depth 2\\ \textbf{\GGA{}: no exit gate}};
%% gates (saddles)
\draw[gatemark] (3.9, 4.42) -- (3.9, 4.18);
\node[lab, text=red!70!black, anchor=south] at (3.9, 4.50) {\GSSB{} gate\\ toll $S = 2\pi$};
\draw[gatemark] (7.5, 3.42) -- (7.5, 3.18);
\node[lab, text=red!70!black, anchor=south] at (7.5, 3.50) {\GSSB{} gate\\ toll $S = \pi$};
%% GRIP-In descent arrows along the curve
\draw[desc] (2.9, 3.75) to[bend left=28] (4.85, 3.45);
\draw[desc] (6.6, 3.0) to[bend left=28] (8.5, 2.0);
\node[lab, text=blue!60!black, anchor=west] at (0.0, 1.05)
 {\textbf{\GRIPin{} descent $\tau \to \mu \to e$}\\
 implemented by the weak interaction;\\
 each hop pays its gate toll $e^{-S}$};
%% no lower basin annotation
\node[lab, text=black!65, anchor=west] at (8.7, 4.9)
 {nothing below depth 2:\\ the landscape's global minimum\\ (\GFF{}-ST7 uniqueness)};
\draw[-{Stealth[length=2mm]}, draw=black!55] (9.5, 4.45) to[bend right=20] (9.85, 1.2);
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\end{tikzpicture}}

%% ---- v15.2 showcase page: THE LANDSCAPE AND THE CASCADE -----
%% v15.1 showcased Table 4, the six questions with their grades.
%% Honest, and dull: a reader arriving from the homepage met a grid
%% of status tags.  Figures 6 and 7 are the paper's own picture of
%% the same result, and the paper's prose already pairs them --
%% 'Figure 6 draws the whole story in one picture; Figure 7 states
%% the same chain as a Morse diagram.'  On the body pages they are
%% one page apart; here they are one above the other, which is what
%% a showcase page can do that a body page cannot.
%% Table 4 is back to being an ordinary body table, unchanged.
%% SIZES MEASURED: stacked at body width the plates alone are 491.4
%% pt against a 650.43 pt \textheight, which does not close; side by
%% side the widest legible pair is 0.52 and 0.44, which renders Fig
%% 6's \scriptsize annotations at 71 per cent of a size already
%% small on the body page.  0.66 and 0.61 stacked is 443.0 pt and
%% closes with about 35 pt to spare.
%% Unnumbered captions, so Figures 1-11 keep their numbers.
%% -----------------------------------------------------------
\clearpage
%% Self-filling showcase frame (Report 462): a minipage of EXPLICIT
%% height with the [s] inner alignment, so the interior glue stretches,
%% and 1 : 2 : 2 : 1 weights -- top, above the plate, below it, bottom.
%% The height is \textheight MINUS \topskip; see the report for why.
\noindent\begin{minipage}[t][\dimexpr\textheight-\topskip\relax][s]{\textwidth}
\vspace*{\stretch{1}}
\centering
\GGShowcaseHead{The Whole Electron Story in One Landscape,\\[3pt]
and the Same Chain as a Morse Diagram}
\par\vspace*{\stretch{2}}
{\setlength{\abovecaptionskip}{5pt}%
\small\captionof*{figure}{\textbf{Two drawings of one object.} Above: a one-dimensional cut through the \GFF{} Morse landscape on the family stratum. The three charged leptons are the three basins and their floors are the masses; the two \GSSB{} gates carry the tolls $S = 2\pi$ and $S = \pi$; the observed $\tau \to \mu \to e$ decay chain is one descent that pays both and halts in the deepest basin, which has no exit gate. Below: the same chain as its Morse skeleton, three critical points and two gates, accumulating to $S_{\mathrm{tot}} = 3\pi$ and exactly saturating the \BIsix{} budget. Four of this paper's six questions are visible in the drawing: identity is the one deepest basin, stability is its having no way out, the copies are the two way stations, and the decay hierarchy is the tolls in the exponents. Pointlikeness is the fifth, and it is the statement that the horizontal axis is not a direction of space. In full: Figures~\ref{fig:basin-landscape} and~\ref{fig:grip-cascade-cp2}, pp.~\pageref{fig:basin-landscape}--\pageref{fig:grip-cascade-cp2}.}}
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\par\vspace*{\stretch{1}}
\end{minipage}
\clearpage
%% ---- end showcase page -------------------------------------
%% Front matter, v15.0: the four standard macros.  This block used to be
%% twenty-four lines of etoc plumbing copied out of the style file, under
%% the comment "Overview of Contents + List of Figures combined on one
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%% TABLES, absent until now against nine captioned tables, arrives with it.
\clearpage
\GGfrontmatteronepagetrue
\GGOverviewOfContents
\GGListOfFigures
\GGListOfTables
\GGTableOfContents


%% ===================================================================
%%  PART I -- THE FIVE QUESTIONS AND THEIR CENTURY
%% ===================================================================
\GGPart[The six questions]{The Six Questions and Their Century}{What has, and has not, been explained since 1897}
\label{part:I}

\section{Preface: to the reader who kept the questions}
\label{sec:preface}

This paper is written for a particular reader, and it may as well say
so at once. You have finished a degree in physics. Somewhere in the
first weeks of quantum mechanics --- perhaps the day indistinguishable
particles were defined, perhaps the day the periodic table fell out of
the Pauli principle --- you noticed something the course did not pause
on: every electron in the universe is \emph{exactly} the same, and the
whole edifice silently depends on it. Later you noticed more. The
electron never decays, though nearly everything else does. It has two
heavier siblings, and only two, for no reason anyone offered. It is a
point --- not small, but sizeless --- and the one time you asked what
that does to the field energy, the answer involved a subtraction you
were asked not to look at too hard. And it responds to fields: you
computed the response a hundred times without once being told what,
underneath the vector calculus, \emph{responding} is.

If you asked about any of this, you were told --- kindly, and not
wrongly --- that these are deep waters, that the formalism handles it,
and that the problem set is due Friday. So you did what a good student
does: you kept the questions and deferred them. This paper is
addressed to the version of you that never quite threw them away.

Let us be precise about what kind of questions they are, because their
kind is the reason they survived a century untouched. They are not
puzzles \emph{within} physics, of the sort a cleverer calculation
settles; they are questions about why the inputs of physics are what
they are --- and a framework whose inputs are inputs cannot answer
them, any more than a dictionary can explain why its words mean what
they mean. To answer such questions one does not need more cleverness;
one needs a deeper layer, in which yesterday's inputs become today's
theorems. The claim of this paper --- made within one specific
framework, \GGTheory{}, and priced with a candor the reader is asked
to hold us to --- is that such a layer exists, and that on it the six
childhood questions collapse into a single fact: \emph{the electron is
the ground state of its corner of the world.} Identity, stability, the
two siblings, the mirror twin, the sizelessness, the sensing --- one
fact, six shadows.

A word on how to read what follows. This is a review and a gateway,
not a textbook and not a sermon. Every imported theorem is cited to
the companion paper that proves it; every step that is not a theorem
is named as what it is --- conjecture, hypothesis, empirical input, or
interpretation --- in the status table that anchors the paper and in
the ledger that closes it; and Part~\ref{part:VIII} lists, in advance,
the experimental results that would kill the whole construction. You
are not asked to believe; you are asked to audit. The questions were
yours before they were ours.

After all, the measure of a foundation is not whether it silences the
child's questions, but whether it can finally afford to take them
seriously.

\section{The six questions}
\label{sec:five-questions}

In 1897 J.~J.~Thomson measured the charge-to-mass ratio of cathode rays
and announced a body smaller than the atom \citep{Thomson1897} --- the
particle Stoney had already named from electrolysis \citep{Stoney1894}
and whose magnetic fingerprint Zeeman resolved the same year
\citep{Zeeman1897}. Within three decades it had revealed the
quantization of charge \citep{Millikan1913}, scattered X-rays like a
point \citep{Compton1923}, diffracted like a wave
\citep{deBroglie1925,DavissonGermer1927}, and forced both the
exclusion principle \citep{Pauli1925} and the relativistic wave
equation \citep{Dirac1928} into existence --- an equation that
promptly predicted, from consistency alone, the electron's own mirror
twin \citep{Dirac1931}, photographed within the year
\citep{Anderson1933}. The
particle he found has since become the most precisely characterized
object in science --- and the questions a child might ask about it remain,
in standard physics, substantially unanswered. We state them as they have
stood for a century:

\begin{description}[leftmargin=2.2em,itemsep=2pt]
\item[Q1 (Identity).] Why is every electron exactly identical to every
other --- and why does it carry precisely the mass
$m_e = 0.511$~MeV, the charge $-e$, and spin-$\tfrac12$, rather than any
other values?
\item[Q2 (Stability).] Why is the electron absolutely stable, to better
than $6.6\times10^{28}$ years?
\item[Q3 (Copies).] Why do the muon and the tau exist --- two heavier
particles identical to the electron in every quantum number except mass
--- and why exactly two, with the ladder terminating at three families?
\item[Q4 (Pointlikeness).] Why is the electron a point --- no measured
size, no substructure, at any scale ever probed --- and why does that not
cost it an infinite self-energy?
\item[Q5 (Sensing).] Why does an electron respond to an electric field at
all --- what is it about the electron such that it ``feels'' the field
and accelerates toward the nearest proton?
\item[Q6 (The twin).] Why does the electron have an antiparticle --- the
positron, a twin of exactly equal mass and exactly opposite charge,
predicted in 1931 and found in 1932 --- and what \emph{is} it, if the
electron is the unique ground state? (Q6 is numbered sixth because it
is the sixth question the century left open in this form; in the body
it is taken up in Part~\ref{part:positron}, between the copies and the
pointlikeness, where its answer naturally lives.)
\end{description}

The claim of this paper is not that standard physics has said nothing
about these questions --- Part~I's burden is precisely to credit what it
has said --- but that \emph{the conjunction has never been explained}.
Standard physics offers fragments: an ontological convention for
identity, a bookkeeping argument for stability, nothing for the
generations, an experimental upper bound for the size, a sign rule for
the force --- each presupposing unexplained inputs, none connected to the
others. Within \GGTheory{} the six questions have one answer, and the
fragments become consequences.

\paragraph{Who this paper is for.} This paper is written as a review
article, for the first-year graduate student in physics --- for the
critical thinker who finished a degree carrying exactly these six
naive, fundamental questions and was told, by silence or by syllabus,
to move on. Part~I requires undergraduate quantum mechanics; imported
machinery is introduced at the point of use, with its rigorous
development cited rather than reproduced. The intended outcome is a
cleared mind, not a converted one: the status table of
\S\ref{sec:status-table} prices every claim, the kill criteria of
Part~\ref{part:VIII} say where the framework can be shot, and the reader
who wants the full treatment will find, in the cohort papers of
Part~\ref{part:II}, the few years of serious work that these questions
have always deserved.

\section{The honest status table}
\label{sec:status-table}

The paper's method is a status discipline inherited from its sister paper
\PaperPTwo{} \citep{ArisakaP2N3}: every load-bearing step is tagged as
\textbf{THM} (theorem, with grep-verified upstream location),
\textbf{CONJ} (named conjecture), \textbf{POST} (named postulate or
hypothesis), \textbf{EMP} (empirical input), or \textbf{INT}
(interpretive reading), and the tag travels to every layer of the paper
including the abstract. Table~\ref{tab:status} is the paper in one page;
Appendix~\ref{app:ledger} is its machine-checkable expansion.

\begin{table}[ht]
\centering
\caption[The six questions: standard status, the answer here, and its grade.]{The six questions: honest standard status, \GGTheory{} answer,
and claim status. Tag vocabulary in \S\ref{sec:status-table}; full
per-step ledger with verified upstream locations in
Appendix~\ref{app:ledger}. Each row pairs what standard physics has established with what this paper claims on top of it, and the last column says at what grade the claim is held, so a reader can see at once which answers are proved here, which are inherited from a companion, and which are still owed.}
\label{tab:status}
\small
\renewcommand{\arraystretch}{1.25}
\begin{tabular}{@{}p{0.075\textwidth}p{0.265\textwidth}p{0.265\textwidth}p{0.265\textwidth}@{}}
\toprule
\textbf{Q} & \textbf{Standard physics (credited)} & \textbf{\GGTheory{} answer} & \textbf{Status} \\
\midrule
Q1 identity &
One-field ontology explains sameness; $m_e$, $e$, spin-$\tfrac12$ remain
free inputs &
Unique \GGA{} readout; $y_e$, $m_e$ from codebook; $e$ derived;
spin-$\tfrac12$ from $\mathrm{Spin}(1,5)=\SLtwoH$ &
THM (\GDOS{}-internal) + codebook; spin: THM; $m_e$ residual
$1.9\times10^{-4}$ declared \\
\addlinespace
Q2 stability &
Lightest charged + charge conservation (correct; presupposes Q3's
spectrum) &
Ground basin has no exit gate; \GRIPin{} halts &
THM given \GFF{}-ST7; Q3 conditioning inherited \\
\addlinespace
Q3 copies &
None. Three families an input since 1936 &
$\mu,\tau$ = depth-1, depth-0 basins of the electron's landscape;
$N=3$ forced &
Imported from \PaperPTwo{}: EMP + AX (coupling clause) + THM
(L-INT, residue R-INT); reachability INT \\
\addlinespace
Q4 point &
None. Pointlike by construction; renormalization sidesteps the
self-energy crisis; bounds only &
All structure along non-spatial $\Ir, \Stheta$; mass = basin level; spin
= double-cover label; $F(q^2)\equiv1$ &
THM via Lemma RL, derived from AX-1 (one formalization step open,
D-P3-1); ingredients THM (A2, A4, A9) + AX-2 coupling completeness (\AFive{}) \\
\addlinespace
Q5 sensing &
Sign rule derived (QED, credited); existence, quantization, strength of
coupling unexplained &
Force law derived as composite geodesic motion (Newton \& Coulomb in
parallel from one bulk; AX-2); $\mathrm{U}(1)$, quantization, $\alpha$
derived; arrows in their sectors (radiation: motion; \GRIPin{}: decay) &
THM (\AFive{} Part VI) + codebook; arrow readings INT; quantum sign
reading QED's, credited \\
\addlinespace
Q6 twin &
Necessity at the formalism level (QFT) + pairing constraints (CPT),
both credited; what the twin \emph{is} unaddressed &
Twin forced in the real bulk, pre-quantization (handshake, imported
\PaperPFive{}); positron = conjugate readout of the same basin &
THM (imported: T-P5-A/B/C, C2) + INT (same-basin reading, named);
promotion owed (D-P3-4) \\
\bottomrule
\end{tabular}

\end{table}

\section{The central claim: the electron as the ground state of nature as an open-system observable}
\label{sec:central-claim}

It is worth stating, in one place, the recognition this paper shares with the whole \GGTheory{} cohort. No physical system is closed --- so the four-dimensional world is a lawful projection (\OGGEP{}, \AX{3}) of the six-dimensional bulk, and that projection \emph{is} observation itself; its dynamics is the open-system law \GDOS{} (\AFive{}), forced by the geometric \GiFour{} (\ASix{}) and quantum-information \QiFour{} (\ASeven{}) pillars. It follows that the electron --- its mass, its identity, and its stability --- is a \emph{registered observable} of one projection: the ground state of nature, fixed by the geometry rather than chosen --- which is why this paper can derive it, and why a single clean measurement can refute it. The funnel below is shared, in structure, with the companion papers \ANine{}, \ATen{}, and \AEleven{}; only the payload differs.

\begin{figure}[hbt!]
\centering
\resizebox{0.627\textwidth}{!}{%
\begin{tikzpicture}[
 node distance=19mm,
 every node/.style={font=\sffamily\footnotesize, align=center},
 box/.style={draw=black!55, rounded corners, minimum width=115mm, minimum height=12mm},
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 elab/.style={font=\sffamily\scriptsize\itshape, fill=white, inner sep=1.5pt}
]
\node[box, fill=violet!10] (open) {\textbf{Every physical system is open}\\ a particle, the universe, a living cell --- none can be isolated from its environment};
\node[box, fill=blue!8, below of=open] (oggep) {\textbf{\OGGEP{}} (\AX{3}): the lawful projection \;6D bulk $\to$ 4D boundary\\ \textit{this projection is observation itself} \;\; {\scriptsize[\AOne{}, \AEight{}]}};
\node[box, fill=yellow!13, below of=oggep] (gdos) {\textbf{\GDOS{}}: the dynamics of the open-system projection\\ \textit{an observable is the value at a stationary seam} \;\; {\scriptsize[\AFive{}]}};
\node[box, fill=orange!14, line width=1pt, below of=gdos] (obs) {\textbf{The electron as the ground state of nature}\\ (its mass, its identity, its lifetime) --- \textit{a registered observable, not a free input}};
\node[box, fill=green!12, below of=obs] (pill) {\textbf{\GDOS{} is forced} by the \GiFour{} pillars {\scriptsize[\ASix{}]} and the \QiFour{} pillars {\scriptsize[\ASeven{}]}};
\node[box, fill=orange!16, line width=1pt, below of=pill] (concl) {$\Rightarrow$ \textbf{it is determined}\\ {\footnotesize read off one geometry --- why every electron is identical to every other}};
\draw[arrow] (open)  -- node[elab,right]{no closed 4D theory exists}            (oggep);
\draw[arrow] (oggep) -- node[elab,right]{the projection must be a definite law}  (gdos);
\draw[arrow] (gdos)  -- node[elab,right]{apply to this paper's sector}          (obs);
\draw[arrow] (obs)   -- node[elab,right]{and the law is not arbitrary}           (pill);
\draw[arrow] (pill)  -- node[elab,right]{projection forced $\Rightarrow$ observable forced} (concl);
\end{tikzpicture}}
\caption[The open-system funnel shared across the \GGTheory{} cohort.]{\textbf{The central claim, as one deductive funnel}, shared across the \GGTheory{} cohort. Because no physical system is closed, the four-dimensional world is a lawful projection (\OGGEP{}, \AX{3}) of the six-dimensional bulk, and that projection is observation itself; its dynamics is \GDOS{}, forced by the \GiFour{} and \QiFour{} pillars. The same funnel opens the companion papers \ANine{}, \ATen{}, and \AEleven{}; only the payload differs --- here, the electron as the ground state of nature.}
\label{fig:central-claim}
\end{figure}

\section{The claim of this paper, and its fences}
\label{sec:claim}

The defensible strong claim --- and the only claim this paper makes ---
is the conjunction:

\begin{quote}
\emph{The electron's identity (with its values), its absolute stability,
its excited copies (with their count), its exact pointlikeness, and its
response to fields --- with the positron as the same fact read in the
mirror --- are six faces of one fact: the electron is the unique
ground state --- the \GGA{} --- of the charged-lepton stratum of the
boundary. No prior framework has explained these five together, because
no prior framework had the one fact of which they are faces.}
\end{quote}

The fence inventory, complete, in one place: two empirical inputs
(observed CP violation; $N_\nu = 3$) and the coupling clause plus the integrality theorem L-INT with its
named topological residue (R-INT), all imported from \PaperPTwo{} with Q3; one lemma new to this paper (RL, Readout Locality), derived in
Part~\ref{part:VI} from the constitutional axiom AX-1, with its one
formalization step registered as open (D-P3-1); one interpretive layer
(the open-system arrows of Part~\ref{part:VII} --- radiative
dissipation for motion, scale-sector \GRIPin{} for decay --- glosses
on the derived geodesic law, not the law itself); the QD-layer
residual $1.9\times10^{-4}$ on $m_e$, declared wherever the mass is
mentioned; and the QED credit for the sign rule, stated wherever the
force is mentioned. Nothing else in the paper is conditional, and nothing
conditional is stated as unconditional. The paper's kill criteria are
pre-registered in Part~\ref{part:VIII}; the fifty-year question deserves a
paper that cannot be embarrassed, and the fences are how it earns that.

After all, a claim in physics is worth exactly what its declared
conditions make it worth --- and the discipline of declaring them is
not the tax this paper pays for its strong thesis; it is the reason the
thesis can be strong.

\section{The cohort inheritance and the roadmap of the ten Parts}
\label{sec:inheritance-and-roadmap}

\noindent
Before the inheritance is unpacked (Part~\ref{part:II}) and the six
questions are taken up one by one
(Parts~\ref{part:III}--\ref{part:VII}), it is useful to lay out two
reader-orientation maps on the same opening: a panorama of the
twenty-two-paper cohort in which this paper stands
(\S\ref{sec:inheritance}, Figure~\ref{fig:cohort-map}), and a
panorama of the ten Parts of the present paper
(\S\ref{sec:roadmap}, Figure~\ref{fig:parts-roadmap-p3}). A reader
of any later Part should be able to flip back to this Section and
orient themselves in both directions: which cohort companion carries
which imported result, and where the present argument stands in the
ten-Part arc.

\subsection{The cohort inheritance}
\label{sec:inheritance}

\GGTheory{} is a twenty-two-paper research program
\citep{ArisakaA1Constitution} --- eleven A-papers, six P-papers, three C-papers and two white papers --- whose structural claim is that the observed
laws are the boundary operational description of a real
six-dimensional bulk --- four macroscopic spacetime dimensions plus
one scale direction $\Ir$ and one compact phase circle $\Stheta$ ---
governed by four axioms and an integer ledger
$(M,N,L;J,K) = (1,3,5;7,35)$ \citep{ArisakaA3BI6}. Within that
program this paper is a member of the Predictions Branch --- the
electron paper: the deployment of the derived machinery on the
oldest particle in physics, under the thesis that the electron is
the unique ground state --- the \GGA{} --- of its boundary stratum.
Like every member paper of the cohort, it restates what it imports
and owns what it proves, so that a reader who never opens a
companion loses the provenance but not the argument.

Before the closest relative, the family portrait. The reader new to
the program should spend one minute with
Figure~\ref{fig:cohort-map}, because the whole architecture can be
read off it top to bottom, and every Part of this paper will draw on
some box of it. \emph{One root:} the constitution \AOne{} states
four axioms and seven postulates and proves nothing else --- all
force is downstream. \emph{One bulk:} AX-2 compiles the root into
the GG6 Trio --- \ATwo{} builds the six-dimensional geometry
whose two non-spatial directions carry everything this paper says
about the electron, \AThree{} proves the anomaly cancellation that
locks the sectors together, and \AFour{} tells the history.
\emph{One boundary law:} AX-3 forces \AFive{} --- the open-system
dynamics that Part~\ref{part:III} uses for stability and
Part~\ref{part:VII} for radiation --- organized by the two pillar
papers \ASix{} (the geometric pillars: \GFF{}, \GRIPin{}, the
\GGA{}) and \ASeven{} (their quantum-information twins).
\emph{Three readouts:} \AEight{} recovers textbook quantum
mechanics, \ANine{} derives the Standard Model's 28 parameters ---
the codebook from which this paper's $y_e$, $m_e$, and $\alpha$
come --- and \ATen{} derives the cosmological inventory; \AEleven{}
closes the series. \emph{Two phenomenology branches:} everything below the
capstone is phenomenology --- falsifiable deployments of derived
results, which is why their arrows are dashed. This paper sits in
the cyan Predictions frame, third in its row after the
collider falsifier \PaperPOne{} and the family-number derivation
\PaperPTwo{}; the teal frame carries the cosmology siblings
\PaperCOne{}, \PaperCTwo{}, and \PaperCThree{}. The reader who
keeps this map in mind will never be lost: when Part~\ref{part:III}
cites a theorem, it comes from the green or yellow boxes; when a
number appears, it comes from \ANine{}; when a fence is restated,
it usually traveled up the $N{=}3$ arrow from \PaperPTwo{} --- to
which the Inheritance Part (Part~\ref{part:II}) turns in detail.

\paragraph{The Foundations Branch.} On the map's left flank stands
its third frame --- the Foundations Branch, a single column beside
the spine, whose shared subject is the boundary's complex structure;
its two members are recorded here at roster level, one sentence
each. \PaperPFour{} \citep{ArisakaP4Real} derives the origin of the
$i$ that the electron's quantum mechanics runs on --- the gauge
phase from the circle's quarter-turn, the state-space $i$ from the
causal clock --- and the shared complex structure their forced
agreement places on the charged sectors is exactly what the
electron, as the lightest charged state, carries. \PaperPFive{}
\citep{ArisakaP5CPT} gives the electron its twin: the positron is
the first receipt of that circle--clock handshake, with C, P, and T
read as orientation reversals of the three real bulk factors. Both
members carry P-series designators; their place at the spine's
flank, not the phenomenology rows, marks their foundational role.

The twenty-two-paper map, identical in every paper of the cohort, is
Figure~\ref{fig:cohort-map}, which closes this subsection.

%% ===================================================================
%%  The nineteen-paper cohort map (frozen v1.4 geometry), on its own
%%  page at the close of the cohort-inheritance subsection.  Verbatim
%%  copy of the v1.4 master (A1-Constitution Figure 3): no
%%  self-reference markers anywhere, so the figure is identical and
%%  simple for replication in all nineteen papers.  Only the internal
%%  node names MP4/MP5 differ from the master (collision avoidance).
%% ===================================================================
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 {\textbf{\PaperPSix{}} \\[-1pt] \footnotesize The guarded proton};

%% --- Row 7: Cosmology & Astrophysics Branch (C-series) ---
\node[cosmo] (C1) at (-50mm, -160mm)
 {\textbf{\PaperCOne{}} \\[-1pt] \footnotesize Kaxion dark matter};
\node[cosmo] (C2) at (0, -160mm)
 {\textbf{\PaperCTwo{}} \\[-1pt] \footnotesize Two Hubble constants};
\node[cosmo] (C3) at (50mm, -160mm)
 {\textbf{\PaperCThree{}} \\[-1pt] \footnotesize BH entropy $A/4$};

%% --- Foundations Branch column (v1.3: MP5 raised so its centre
%%     height matches the A11 row). MP4 and MP5 form a single
%%     left-flank column at x = -96mm: MP4 at y = -64mm (unchanged),
%%     MP5 at y = -113mm, level with GG-A11-Origin, so the column
%%     brackets the A8 row with a compact gap.
\node[fnd] (MP4) at (-96mm, -64mm)
 {\textbf{\PaperPFour{}} \\[-1pt] \footnotesize The origin of $i$};
\node[fnd] (MP5) at (-96mm, -113mm)
 {\textbf{\PaperPFive{}} \\[-1pt] \footnotesize Mirrors \& matter (CPT)};

%% --- White-Paper Branch column (v22): the right flank, at the mirror
%%     positions of the Foundations column.  The left flank feeds the
%%     spine; this one reads it, so every edge into it is dashed.
\node[wht] (W1) at (96mm, -64mm)
 {\textbf{\PaperWOne{}} \\[-1pt] \footnotesize Conservation without symmetry};
\node[wht] (W2) at (96mm, -113mm)
 {\textbf{\PaperWTwo{}} \\[-1pt] \footnotesize Sixteen open problems};

%% --- Branch frames (background layer) ---
\begin{scope}[on background layer]
\node[branchframe, draw=cyan!60!black, fill=cyan!4,
 fit=(P1)(P2)(P3)(P6)] (PFRAME) {};
\node[branchframe, draw=teal!60!black, fill=teal!4,
 fit=(C1)(C2)(C3)] (CFRAME) {};
\end{scope}
\node[branchlabel, text=cyan!40!black, anchor=east]
 at ([xshift=-3mm]PFRAME.west) {Predictions\\Branch\\(P-series)};
\node[branchlabel, text=teal!40!black, anchor=east]
 at ([xshift=-3mm]PFRAME.west |- CFRAME) {Cosmology \&\\Astrophysics\\Branch\\(C-series)};
%% Foundations column label (v1.3): interior placement, in the gap
%% between MP4 and MP5, anchored east so it sits immediately LEFT of
%% the vertical MP4->MP5 edge; house style (small violet) kept. The
%% "shared i" edge label occupies the RIGHT side of the same edge.
\node[branchlabel, text=violet!40!black, anchor=east]
 at ($($(MP4.south)!0.5!(MP5.north)$)+(-1.5mm,0)$) {Foundations\\Branch};
%% v22: the mirror label, held to the RIGHT of the W1->W2 edge --
%% \ATen{}'s grown border reaches x = 78.7mm and an east-anchored
%% label would run into it.
\node[branchlabel, text=brown!45!black, anchor=west]
 at ($($(W1.south)!0.22!(W2.north)$)+(1.5mm,0)$) {White-Paper\\Branch\\(W-series)};

%% --- Edges: A1 -> GG6 Trio ---
\draw[arrowrt] (A1.south) -- node[edgelabel,pos=0.55] {\AX{2}} (A2.north);
\draw[arrowrt] (A1.south) -- node[edgelabel,pos=0.55] {\POS{3}} (A3.north);
\draw[arrowdash] (A1.south) -- (A4.north);

%% --- Edges: GG6 Trio -> A5 ---
\draw[arrow] (A2.south) -- (A5.north west);
\draw[arrow] (A3.south) -- node[edgelabel,pos=0.55] {\AX{3}} (A5.north);
\draw[arrow] (A4.south) -- (A5.north east);

%% --- Edges: A5 -> pillars ---
\draw[arrow] (A5.south) -- (A6.north);
\draw[arrow] (A5.south) -- (A7.north);

%% --- Edges: A5 + pillars -> 4D-Physics Trio ---
\draw[arrow] (A6.south) -- (A8.north);
\draw[arrow] (A5.south).. controls (0, -72mm) and (0, -80mm).. (A9.north);
\draw[arrow] (A7.south) -- (A10.north);

%% --- Edges: 4D-Physics Trio -> A11 ---
\draw[arrow] (A8.south) -- (A11.north west);
\draw[arrow] (A9.south) -- (A11.north);
\draw[arrow] (A10.south) -- (A11.north east);

%% --- Edges: parents -> branch frames ---
\draw[arrowdash] (A9.south west).. controls (-40mm, -105mm)
 and (-84mm, -122mm).. (PFRAME.north west);
\draw[arrowdash] (A9.south east).. controls (40mm, -105mm)
 and (84mm, -122mm).. (PFRAME.north east);
%% v22 RE-ROUTE.  The old line descended through what is now the
%% GG-W2-Holonomy node, and there is no corridor left inboard of it.
%% A polyline rather than a Bezier: a bounding box contains control
%% points, and at the clearance this edge needs those would have sat
%% 24mm beyond any ink, scaling the whole plate down for nothing.
\draw[arrowdash, rounded corners=7pt] (A10.east) -- (127mm,-91mm)
 -- (127mm,-160mm) -- (CFRAME.east);
%% sister import inside the Predictions frame
\draw[arrowdash, draw=cyan!50!black]
 (P2.east) -- node[edgelabel,pos=0.5] {$N{=}3$} (P3.west);
% v22: the second sister import.  \PaperPSix{} says it of
% \PaperPThree{} -- "the sister paper supplies the method this paper
% runs."  Three letters, because a white-filled label wide enough to
% say "method" masks the whole arrow it annotates.
\draw[arrowdash, draw=cyan!50!black]
 (P3.east) -- node[edgelabel,pos=0.5] {GGA} (P6.west);

%% --- Foundations Branch edges (rerouted v1.3 for the raised MP5) ---
%% A2 -> MP4 (solid; Thm 0 arena feed) -- unchanged from v1.0
\draw[arrow] (A2.west) .. controls (-88mm,-30mm) ..
 node[edgelabel,pos=0.55] {Thm~0} (MP4.north);
%% MP4 -> A8 (solid; the origin of i). Departs the east side (MP4.south
%% carries the column edge to MP5) and lands on A8's top border,
%% 6mm left of the A6->A8 arrowhead, staying left of A6 throughout.
\draw[arrow] ([yshift=-3mm]MP4.east) .. controls (-69mm,-74mm) ..
 node[edgelabel,pos=0.45] {origin of $i$} ([xshift=-6mm]A8.north);
%% MP4 -> A2 (dashed deployment: complex-structure machinery), nudged
%% 3mm up the east side so the two east-side departures stay distinct.
\draw[arrowdash] ([yshift=3mm]MP4.east) .. controls (-70mm,-52mm) .. (A2.south west);
%% MP4 -> MP5 (v1.3: SOLID, per the reading conventions -- forced
%% descent, labelled). A short straight vertical between the pair;
%% the "shared i" label sits on the right side of the edge, the
%% Foundations Branch label on the left.
\draw[arrow] (MP4.south) --
 node[edgelabel, pos=0.5, anchor=west, xshift=1mm] {shared $i$}
 (MP5.north);
%% A9 -> MP5 (solid; ledger phases). Leaves A9's west side, dips
%% through the corridor below the A8 row and enters MP5.east
%% horizontally at the A11 row height. Exactly one clean crossing
%% (the A8->A11 spine edge, near x = -40mm); stays above the dashed
%% A9->PFRAME.north-west edge throughout.
\draw[arrow] (A9.west) .. controls (-40mm,-97mm) and (-58mm,-113mm) ..
 node[edgelabel,pos=0.6] {$\delta,\ \alpha_{31}$} (MP5.east);
%% MP5 -> A10 (solid; eta_B). The one long edge: runs left-to-right
%% through the clear corridor BELOW the A11 node (above the
%% Predictions frame), then climbs into A10's bottom border right of
%% the A10->A11 arrowtail; it leaves MP5.south vertically. Controls
%% lifted 5mm with the raised MP5 so the dip still clears A11's
%% bottom border. One clean crossing with each of the two dashed
%% A9->Predictions-frame edges.
\draw[arrow] (MP5.south) .. controls (-96mm,-128mm) and (55mm,-130mm) ..
 node[edgelabel,pos=0.5] {$\eta_B$} ([xshift=8mm]A10.south);
%% MP5 -> A8 (dashed; Wick-quartet/statistics feed for T-A8.12): with
%% MP5 level with A11 this is now a short straight upward edge from
%% the column's top-right corner into A8's bottom border, 8mm left
%% of the A8->A11 arrowtail. No crossings.
\draw[arrowdash] (MP5.north east) -- ([xshift=-8mm]A8.south);
%% --- White-Paper Branch edges (v22) ---
%% A3 -> W1: \AThree{} is \PaperWOne{}'s heaviest spine source and its
%% thematic terminus -- the \BIsix{} anomaly proof is where its
%% Green--Schwarz / Hopkins--Singer ladder ends.
\draw[arrowdash] ([xshift=8mm]A3.south) .. controls (58mm,-43mm) ..
 node[edgelabel,pos=0.55] {\BIsix{}} (W1.west);
%% A10 -> W2: \ATen{} is \PaperWTwo{}'s heaviest source of any kind.
%% At +15%% those two boxes overlap in x (never in y), so this is drawn
%% off A10's south-east corner, clear of the W1->W2 arrowhead.
\draw[arrowdash] (A10.south east) .. controls (84mm,-101mm) ..
 ([xshift=-6mm]W2.north);
%% W1 -> W2, solid and labelled: the mirror of the shared-i edge on the
%% left flank.  \PaperWTwo{} states the dependency itself -- it takes
%% "the structure that the arc arrives at, protection by topology
%% rather than by symmetry".
\draw[arrow] (W1.south) --
 node[edgelabel, pos=0.80, anchor=west, xshift=1mm]
 {symmetry $\to$ topology} (W2.north);

%% Centring pad, retired (v22): it cancelled a Bezier phantom that the
%% polyline above no longer creates; the bbox is now the ink.
\end{tikzpicture}}
\caption[The twenty-two-paper cohort map.]{The
twenty-two-paper cohort map of \GGTheory{}. The constitutional root
\AOne{} (violet, top) supplies the four axioms and seven postulates
from which the rest of the cohort descends: the GG6 Trio (\ATwo{},
\AThree{}, \AFour{}, red) realizes the bulk geometry; \AFive{}
(yellow) the boundary law; the \GDOS{} Trio pillars (\ASix{},
\ASeven{}, green) the geometric and quantum-information runtime; the
4D-Physics Trio (\AEight{}, \ANine{}, \ATen{}, blue) the textbook
readouts; and the closing capstone \AEleven{} (gold) the
quarks-to-consciousness identity cascade. Two framed branches carry
the phenomenology --- the \textbf{Predictions Branch} (cyan), whose
four papers hand their results along the row by the internal arrows
(\PaperPTwo{}'s $N{=}3$ into \PaperPThree{}, and that paper's
ground-attractor method, \textsf{GGA}, on into \PaperPSix{}), and the
\textbf{Cosmology \& Astrophysics Branch} (teal). The spine is
flanked by two columns of two, which do opposite jobs. On the left the
\textbf{Foundations Branch} (violet) feeds it: \PaperPFour{}, fed by
\ATwo{}'s Theorem~0 arena, manufactures the $i$ that \AEight{}
consumes, and \PaperPFive{} is the \ANine{}--\ATen{} interface, fed by
the ledger phases and feeding the $\eta_B$ chain across the width of
the map, with the shared-$i$ edge descending solid between them. On
the right the \textbf{White-Paper Branch} (brown) reads it:
\PaperWOne{} \citep{ArisakaW1Symmetry} walks the century from Noether to Hopkins--Singer, and
\PaperWTwo{} dissects the structure that arc arrives at ---
protection by topology rather than by symmetry --- across sixteen open
problems. The white papers derive nothing new, carrying every result
at its parent's declared grade; the single dashed feed drawn into each
names its heaviest source, not its only one. \emph{Reading
conventions:} solid arrows mark axiom-forced descent and carry an edge
label naming the driving axiom or postulate where most illustrative;
dashed arrows mark the deployment of derived results, or historical
links inherited without being constitutionally forced.
The branches this paper does not draw on are on the map all
the same, and are cited here at roster level, which is all
they can honestly claim from it:
\citealp{ArisakaC2Hubble}; \citealp{ArisakaC3BH};
\citealp{ArisakaP1KK}.}
\label{fig:cohort-map}
\end{figure}
\clearpage

\subsection{Roadmap of the ten Parts}
\label{sec:roadmap}

The rest of the paper is organized into nine further Parts, and
the walk through them is plotted in
Figure~\ref{fig:parts-roadmap-p3}. The present Part --- the
entrance --- is nearly done: it has put the six questions and
their century on the table, graded what standard physics does and
does not explain in the honest status table, drawn the central
claim as one funnel, fenced it, and laid out the two orientation
maps of this closing section. Part~II gathers the inheritance: the
framework minimum --- the six-dimensional bulk with its two
non-spatial directions, the open-system boundary law, the pillar
structure, and the codebook --- and the sister paper's $N=3$ with
its fences, so that every later import has its provenance stated
once and its conditioning attached.

Part~III is the paper's center of gravity, and it is highlighted in
the roadmap because it establishes the one fact of which every
later answer is a face: the ground-state uniqueness. Identity and
absolute stability are proved there as one theorem --- every
electron is the same readout because each is the unique deepest
basin, the \GGA{}, of the charged-lepton stratum (Q1), and no exit
gate leads out of that basin, so the electron cannot decay (Q2).
The derived values --- the Yukawa, the mass, the charge --- and the
horizon-independence corollary live in the same Part, because they
are what identity \emph{means} once it is a theorem.

Four Parts then read the same fact from four more sides. Part~IV
turns to the excited copies: $\mu$ and $\tau$ as geometrically
excited electrons, the ladder that ends at three --- Q3, imported
from \PaperPTwo{} with its conditioning stated verbatim --- and the
muon lifetime as a \GRIPin{} observable, the rate at which a
non-ground copy descends to the terminus. Part~V is new at this
version and turns the mirror sideways: the origin of positrons ---
the sixth question, the one the century answered before asking ---
with the origin of antiparticles imported at theorem grade from the
CPT companion \PaperPFive{}, and the positron read as the conjugate
readout of the electron's one basin (Q6), so that the sixth
question collapses into the first. Part~VI is the paper's own
derivational core, on the question no framework had touched: why
the electron is a point in space and nowhere else ---
pointlikeness derived from non-spatial structure (Q4), with its
observable shadow pre-registered. Part~VII answers why the electron
moves: the sixth dimension as the electromagnetic fiber, the
equivalence principle for charge, and the force law as composite
geodesic motion (Q5), with the open-system layer stating what
descends, and where.

The last three Parts weigh, close, and document. Part~VIII is the
discussion: the significance of the six answers, uniqueness
against prior approaches, the sharp contrast with supersymmetry and
string models, the pre-registered falsification table, the open
problems, and the common objections with their responses.
Part~IX concludes: why the questions waited a century, the view
from the last page, the conclusions in plain English, and the
fifty-year arc. Part~X is the workshop --- the appendices: the
abbreviations, the claim-status ledger, the complete derivations
for Q1--Q5 (Q6's derivation is the CPT companion's, imported in
Part~\ref{part:positron}), and the empirical anchors. Read in
order, the ten Parts compose a single self-contained argument; read
by need, each Part names its imports and can stand a visit on its
own.

%% ===================================================================
%%  Roadmap of the ten Parts (house architecture: A2-GG6 v13.3 /
%%  A10-Cosmos v13.3 / P5-CPT v3.41 pattern -- vertical Part column,
%%  right phase sidebar, Part III highlighted as the Part carrying
%%  the central claim: the ground-state uniqueness of
%%  sec:central-claim), clearpage-isolated minipage + \captionof.
%% ===================================================================
\clearpage
\null\vfill
\noindent\begin{minipage}{\textwidth}
\centering
\resizebox{0.93\textwidth}{!}{%
\begin{tikzpicture}[
 font=\sffamily\footnotesize,
 every node/.style={align=center, rounded corners=2pt, inner sep=3pt},
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 align=left, inner sep=2pt},
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%% --- Part I: entrance ---
\node[found] (I) at (0, 0)
 {\textbf{Part~I}\quad\textbf{The Six Questions and Their Century} \\[-1pt]
 \footnotesize What has, and has not, been explained since 1897; the honest status table; the central claim, fenced};

%% --- Part II: the inheritance ---
\node[appar] (II) at (0, -16mm)
 {\textbf{Part~II}\quad\textbf{Inheritance} \\[-1pt]
 \footnotesize The cohort results this paper consumes, by citation: the framework minimum; the sister paper's $N=3$};

%% --- Part III: the one fact (highlighted) ---
\node[innov] (III) at (0, -34.5mm)
 {\textbf{Part~III}\quad\textbf{Ground-State-ness} \\[1pt]
 \footnotesize Identity and absolute stability as one theorem (Q1, Q2): every electron the same \\[-1pt]
 \footnotesize readout of the unique deepest basin --- the \GGA{} --- with its derived values};

%% --- Parts IV--VII: four more faces ---
\node[princ] (IV) at (0, -53mm)
 {\textbf{Part~IV}\quad\textbf{The Excited Copies} \\[-1pt]
 \footnotesize $\mu$ and $\tau$ as geometrically excited electrons; the ladder ends at three (Q3); the muon lifetime};
\node[princ] (V) at (0, -69mm)
 {\textbf{Part~V}\quad\textbf{The Origin of Positrons} \\[-1pt]
 \footnotesize The twin forced in the real bulk (imported from \PaperPFive{}); the positron as conjugate readout (Q6)};
\node[princ] (VI) at (0, -85mm)
 {\textbf{Part~VI}\quad\textbf{Pointlikeness from Non-Spatial Structure} \\[-1pt]
 \footnotesize Why the electron is a point in space and nowhere else (Q4 --- the paper's own derivational core)};
\node[princ] (VII) at (0, -101mm)
 {\textbf{Part~VII}\quad\textbf{Why the Electron Moves} \\[-1pt]
 \footnotesize The phase fiber, the equivalence principle for charge, and force as geometry (Q5)};

%% --- Parts VIII--IX: weighing and summit ---
\node[results] (VIII) at (0, -117mm)
 {\textbf{Part~VIII}\quad\textbf{Discussion} \\[-1pt]
 \footnotesize Significance \,\textbar\, uniqueness \,\textbar\, strings and supersymmetry \,\textbar\, falsification \,\textbar\, open problems \,\textbar\, objections};
\node[summit] (IX) at (0, -133mm)
 {\textbf{Part~IX}\quad\textbf{Conclusions} \\[-1pt]
 \footnotesize The century, the closing, and the fifty-year arc --- in plain English};

%% --- Part X: back matter ---
\node[back] (X) at (0, -149.5mm)
 {\textbf{Part~X}\quad\textbf{Appendices} \\[-1pt]
 \footnotesize Abbreviations, the claim-status ledger, the complete derivations for Q1--Q5, the empirical anchors};

%% --- Vertical flow arrows (the highlighted fact in innov-orange) ---
\draw[arrow] (I.south) -- (II.north);
\draw[arrowinnov] (II.south) -- (III.north);
\draw[arrowinnov] (III.south) -- (IV.north);
\draw[arrow] (IV.south) -- (V.north);
\draw[arrow] (V.south) -- (VI.north);
\draw[arrow] (VI.south) -- (VII.north);
\draw[arrow] (VII.south) -- (VIII.north);
\draw[arrow] (VIII.south) -- (IX.north);
\draw[arrow] (IX.south) -- (X.north);

%% --- Phase labels (right sidebar); standard boxes: half-width =
%% 60mm, label x = 67mm; the innov box is wider (half-width 70mm),
%% its label sits at x = 75mm.
\node[phaselabel] at (74mm, 0mm) {\emph{Entrance}};
\node[phaselabel] at (74mm, -16mm) {\emph{Inheritance}};
\node[phaselabel, text=orange!70!black] at (75mm, -34.5mm)
 {\emph{\textbf{The one fact:}} \\ \emph{\textbf{the ground state}}};
\node[phaselabel] at (74mm, -77mm) {\emph{Four more} \\ \emph{faces}};
\node[phaselabel] at (74mm, -125mm) {\emph{Weighing \&} \\ \emph{summit}};
\node[phaselabel] at (74mm, -149.5mm) {\emph{Back matter}};

\end{tikzpicture}%
}
\par\bigskip
\captionof{figure}[Roadmap of the ten Parts of GG-P3-Electron.]{Roadmap of the ten Parts of \textsf{GG-P3-Electron}. The argument develops in six phases. \emph{Entrance} (Part~I): the six questions and their century, the honest status table, and the central claim with its fences. \emph{Inheritance} (Part~II): the cohort results this paper consumes, by citation, and the sister paper's $N=3$ with its fences. \emph{The one fact} (Part~III, highlighted): ground-state-ness --- identity and absolute stability proved as one theorem (Q1, Q2), with the derived values and the horizon-independence corollary. \emph{Four more faces} (Parts~IV--VII): the excited copies and the terminus of the ladder (Q3), the origin of positrons --- the twin forced in the real bulk and read as the conjugate readout of the one basin (Q6) --- pointlikeness from non-spatial structure (Q4), and why the electron moves (Q5). \emph{Weighing and summit} (Parts~VIII--IX): the discussion --- significance, uniqueness, the contrast with strings and supersymmetry, falsification, open problems, objections --- and the conclusions, from the century to the fifty-year arc. \emph{Back matter} (Part~X): the appendices, from the claim-status ledger to the complete derivations for Q1--Q5. Part~III is highlighted because it carries the paper's central claim --- the ground-state uniqueness of \S\ref{sec:central-claim}: the electron as the unique deepest basin, the \GGA{}, of its stratum --- of which the answers of Parts~IV--VII are four further faces, and on which every later Part stands.}
\label{fig:parts-roadmap-p3}
\end{minipage}
\vfill
\clearpage

%% ===================================================================
%%  PART II -- INHERITANCE
%% ===================================================================

\section[Part~I in plain English]{Part~I in plain English: what was never explained, and what this paper is for}
Six facts about the electron are so familiar that a physics course states them without pausing. Every electron is exactly like every other. None has ever been seen to decay. There are two heavier copies and only two. It behaves as a point, with no measured size. It responds to fields by a law nobody derives. And its antiparticle exists because an equation demanded it.

None of the six is a mystery in the sense of being unmeasured. Each is measured to extraordinary precision. What none of them has is a reason. The Standard Model takes the mass, the charge and the family count as inputs --- numbers written in by hand and then used with great success --- and a theory that begins by writing a number down cannot afterwards explain it.

This Part answers nothing. It states the six questions in the form a working physicist would recognize, gives standard physics full credit for the part of each that it does explain, and marks in a table what is left over. That table is the honest scorecard, and the rest of the paper is an attempt to fill in its last column. Where an answer rests on a companion paper rather than on this one, the table says so.

\GGPart[Inheritance]{Inheritance}{The cohort results this paper consumes, by citation}
\label{part:II}

\section{Framework minimum}
\label{sec:framework}

This is a companion paper: it derives nothing upstream and re-derives
nothing imported. The reader needs the following minimum, stated with the
source of each element; every attribution below was verified against the cited paper at its stated location rather than from memory (the per-item registry is Appendix~\ref{app:ledger}).

\paragraph{The bulk and its two non-spatial directions.} The
constitutional axioms of \AOne{} (among them \MSMF{}, ``Maximum
Symmetry, Minimum Freedom'') \citep{ArisakaA1Constitution} force a
six-dimensional bulk (Theorem~1 of \ATwo{}),
$\cM_6 = \cM_4 \times \Ir \times \Stheta$, with the canonical,
parameter-free metric (its Theorem~2)
\begin{equation}
ds_6^2 \;=\; e^{-2r}\,\eta_{\mu\nu}\,dx^\mu dx^\nu \;+\; dr^2 \;+\;
d\theta^2
\label{eq:canonical-metric}
\end{equation}
\citep{ArisakaA2GG6}. The two extra directions are a geometrized
scale/RG direction $\Ir$ and a compact phase direction $\Stheta$ ---
\emph{not spatial}, the load-bearing fact of Part~\ref{part:VI}. The bulk
Lorentz group satisfies $\mathrm{Spin}(1,5)\cong\SLtwoH$ (quaternionic;
A2's magic-square proposition). The integer ledger
$(M,N,L;J,K)=(1,3,5;7,35)$ is Diophantine-unique (A2, Theorem~6), with
\BIsix{} anomaly closure proved in \AThree{} \citep{ArisakaA3BI6}.
\figref{fig:bulk-cross-section} draws the bulk in cross-section --- the
one picture to keep in mind through Part~\ref{part:VI}.

\begin{figure}[ht]
\centering
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 branelab/.style={font=\bfseries\footnotesize}
]
\draw[arr] (-0.5, 4.4) -- (12.5, 4.4);
\node[energylab] at (0, 4.5) {$\mu = E_{\mathrm{seam}} = M_{\mathrm{Pl}}/2$};
\node[energylab] at (4, 4.5) {$\mu \sim 10^{12}$ GeV};
\node[energylab] at (8, 4.5) {$\mu \sim 10^{8}$ GeV};
\node[energylab] at (12, 4.5) {$\mu \sim M_{\mathrm{lock}} \approx 3.85$ TeV};
\node[font=\scriptsize] at (6, 5.35) {energy scale $\mu = E_{\mathrm{seam}}\,e^{-r}$};
\node[slicelab] at (0, 2.9) {$\cM_4$ slice (shrinks with $e^{-r}$)};
\draw[slice] (-0.7, 0.6) rectangle (0.7, 2.6);
\draw[slice] (3.6, 1.3) rectangle (4.4, 2.3);
\draw[slice] (7.7, 1.6) rectangle (8.3, 2.0);
\draw[slice] (11.85, 1.78) rectangle (12.15, 1.92);
\draw[faintarr] (0.7, 1.6) -- (3.6, 1.8);
\draw[faintarr] (4.4, 1.8) -- (7.7, 1.8);
\draw[faintarr] (8.3, 1.8) -- (11.85, 1.85);
\draw[arr] (-0.5, 0) -- (12.5, 0);
\node[font=\normalsize, anchor=north] at (0, -0.05) {$r = 0$};
\node[font=\normalsize, anchor=north] at (4, -0.05) {$r \approx 10$};
\node[font=\normalsize, anchor=north] at (8, -0.05) {$r \approx 20$};
\node[font=\normalsize, anchor=north] at (12, -0.05) {$r = K = 35$};
\node[font=\normalsize\itshape, anchor=north] at (6, -0.75) {RG-scale coordinate $r = \ln(E_{\mathrm{seam}}/\mu)$};
\node[branelab, anchor=south east, fill=white, inner sep=2pt] at (-0.5, 3.6) {UV boundary};
\node[branelab, anchor=south west, fill=white, inner sep=2pt] at (12.55, 3.6) {IR boundary};
\node[star, star points=5, star point ratio=0.45, draw=red!70!black,
 fill=red!16, minimum size=0.55cm, line width=0.4pt]
 at (12, 1.85) {};
\node[font=\normalsize\bfseries, anchor=west, text=red!70!black] at (12.45, 1.85)
 {lock at $r = K$};
\node[draw=green!50!black, fill=green!12, circle, minimum size=0.95cm,
 line width=0.4pt] (Sth) at (2.2, -1.8) {};
\node[font=\normalsize] at (2.2, -1.8) {$S^1_\theta$};
\draw[faintarr] (Sth.north) -- (2.2, -0.3);
\node[font=\normalsize, anchor=west] at (2.75, -1.8) {topological fiber, $\theta \in [0, 2\pi)$};
\draw[volcano] plot[smooth, samples=60, domain=-0.4:12.4]
 (\x, {0.55 + 1.40*exp(-1.40*\x) + 0.16*tanh(0.65*(\x-9))});
\node[font=\normalsize\itshape, text=orange!70!black, anchor=south] at (6.4, 0.58)
 {volcano potential (gravity localized at the UV boundary)};
\node[font=\normalsize\itshape, anchor=south] at (6, 3.1) {scale profile $e^{-r}$ governs the 4D slice width};
\end{tikzpicture}%
}
\caption[6D bulk cross-section: $\cM_4$ slices, RG-scale direction $\Ir$, phase fiber $\Stheta$.]{The 6D bulk in cross-section, adapted from the bulk paper. The horizontal axis is the scale direction $\Ir$ in the coordinate $r = \ln(E_{\mathrm{seam}}/\mu)$ with $E_{\mathrm{seam}} = M_{\mathrm{Pl}}/2$ --- a position in \emph{resolution}, not in space --- from the UV boundary at $r=0$ to the IR lock at the integer scale depth $r = K = 35$ of the ledger. Four representative 4D slices shrink with the scale profile $e^{-r}$ of the canonical metric; the phase circle $\Stheta$ (green) is fibered over every $r$, with one representative copy drawn. The slices are sketched at a non-physical aspect ratio for clarity: the true shrinkage at $r = 35$ is $e^{-35} \approx 6.3\times10^{-16}$. Everything the electron \emph{is} --- its dyadic depth, its winding, its basin --- is structure along these two non-spatial directions.}
\label{fig:bulk-cross-section}
\end{figure}

\paragraph{Derived constants.} \AFour{} \citep{ArisakaA4Euclid} supplies
the \GUfive{} constant-absorption lineage $\{c, G_N, \hbar; k_B, Q_B\}$
and the theorem T-Euclid-4 that the elementary charge is derived, not
primitive.

\paragraph{The open-system runtime.} \AFive{} \citep{ArisakaA5GDOS}
establishes \GDOS{} (= Geometric Dynamics of Open Systems), the
boundary law of open-system dynamics; \ASix{} \citep{ArisakaA6Gi4}
codifies its four pillars, of which this paper consumes the \GFF{}
landscape (= the Geometric Free-energy Functional --- the master
landscape whose valleys are the stable objects of the boundary) with
its structure theorem \GFF{}-ST7 (unique deepest attractor per
stratum), the regime definitions def:GRIPin/def:GRIPout (\GRIPin{} =
relaxation on a fixed landscape \citep{ArisakaA7Qi4}; \GRIPout{} = the rarer events that
rebuild the landscape itself), and the definition def:GGA; the regime theorem
\textsf{T-GGA-as-Ground-State} is proved in the capstone \AEleven{}
\citep{ArisakaA11Origin}. We record, as \PaperPTwo{} did, that \AFive{}'s
open problem O3 lists strict \GFF{} Morse-positivity as unsettled.

\paragraph{The codebook.} \ANine{} \citep{ArisakaA9SM} derives the
Standard-Model parameter sheet from the ledger; this paper consumes its
charged-lepton codebook (\S\ref{ssec:value-mass}), its dyadic-closure
$\alpha$ theorem (\S\ref{ssec:value-charge}), its identity section, its
forces section, and its weak-as-\GRIPin{} doctrine. \ATen{}
\citep{ArisakaA10Cosmos} closes the cosmological boundary and is
cited for cohort context; \PaperCOne{}
\citep{ArisakaC1Kaxion} deploys the \GGA{} vocabulary on the dark-matter
stratum and is the bibliographic precedent for its cohort use. A reader
meeting the program's acronyms will find the
canonical Dictionary of Program-Defined Acronyms --- each entry with a
plain-English physics intuition --- in \ATwo{}, Appendix~B. Figure~\ref{fig:cohort-map} --- the closing map
of Part~\ref{part:I} --- is the whole program in one view; the
version-by-version inheritance ledger, grep-verified entry by entry,
remains Appendix~\ref{app:ledger}'s.

\section{The sister paper \texorpdfstring{$N=3$}{N=3} and its fences}
\label{sec:p2-import}

\PaperPTwo{} \citep{ArisakaP2N3} is this paper's immediate predecessor
and closest relative: it proves --- under declared conditioning --- that
the family number is $N=3$, by three legs (CP-violation lower bound;
\GDOS{} Morse/budget upper bound; codebook cross-check). Everything this
paper needs from it is imported in Part~\ref{part:IV} \emph{with its
conditioning stated verbatim}; the division of labor is that
\PaperPTwo{} owns ``why three'' and this paper owns ``why the terminus is
what it is.'' The two papers share their ontology --- basins as
generations, gates as decays, the \GGA{} as the electron --- and their
honesty discipline; neither re-proves the other's theorems, and each
cites the other's fences.

This is all the apparatus the paper needs. What follows is the six
questions themselves --- and the reader who keeps one image, the
landscape whose deepest valley is the electron, will find every later
Part examining it from another side.
%% ===================================================================
%%  PART III -- GROUND-STATE-NESS: IDENTITY AND STABILITY (Q1 + Q2)
%% ===================================================================

\section[Part~II in plain English]{Part~II in plain English: what this paper borrows, and exactly where from}
This Part contains no new physics, and that is the point of it. The argument that follows needs a six-dimensional stage, two directions that are not space, a rule for how a large system looks to a small observer inside it, and a set of integers. All four are established elsewhere in the cohort, and reproving them here would make the paper longer and the audit harder.

So the Part is a list of imports. Each entry names what is taken, the paper that establishes it, and the exact place in that paper where it is established --- a theorem number, not a general citation, because a general citation is what lets a borrowed result quietly change strength on the way in.

A reader in a hurry can skip it and return when something downstream turns out to depend on an imported fact. A reader checking the work should not skip it. This is where the paper's dependencies are exposed, and any circularity --- a result borrowed from a companion that had itself borrowed it from here --- would have to appear in this list before it could hide anywhere else.

\GGPart[Ground-state-ness]{Ground-State-ness}{Identity and absolute stability as one theorem (Q1, Q2)}
\label{part:III}

\section{Identity: every electron is the same readout}
\label{sec:identity}

\subsection{The standard answer, credited in full}
\label{ssec:qft-identity}
We begin where an honest treatment must: quantum field theory has a real
partial answer to Q1, and it deserves to be stated at its full strength
before anything is added to it. In QFT all electrons are excitations of one
underlying field. Two electrons cannot differ in mass or charge for the same
reason that two ripples on one pond cannot disagree about what water is.
Exact likeness is automatic, and the formalism enforces it to all
orders, with the spin-statistics theorem \citep{Pauli1940} fixing how
the identical copies must be counted.
Any reader who has heard this answer and found it sufficient is in good
company; it is correct as far as it goes.

What the field answer does not do is explain the \emph{content} of the
likeness. It relocates Q1 into three questions it cannot address: why is
there exactly this field; why does it carry the mass $m_e$ and the charge
$-e$ rather than any other values; and why does it transform in the
spin-$\tfrac12$ representation rather than any other entry of Wigner's
classification of admissible representations \citep{Wigner1939}? In the
Standard Model all three are free inputs. The field ontology explains
\emph{sameness}; it explains none of the sameness's content. The remainder
of this Part supplies the content.

\subsection{The \texorpdfstring{\GGA{}}{GGA} statement}
\label{ssec:gga-statement}
The \GGTheory{} answer rests on the ground-state refinement of the cohort's
attractor vocabulary. \GFF{}-ST7 of \citet{ArisakaA6Gi4} guarantees every
boundary stratum a unique deepest attractor; Definition~def:GGA of
\citet{ArisakaA6Gi4} names it the Ground Geometric Attractor,
\begin{equation}
\GGA(\Sigma) \;:=\; \operatorname*{arg\,min}_{x\in\Sigma}\,\FGFF(x),
\label{eq:gga-def}
\end{equation}
the unique global minimum of the geometric free-energy functional on the
stratum $\Sigma$; and the capstone \citet{ArisakaA11Origin} proves the
regime theorem (\textsf{T-GGA-as-Ground-State}) that the cascade output at
each layer is not \emph{a} stable basin but \emph{the} ground state.
\ANine{} deploys exactly this refinement for the electron
(\citealp{ArisakaA9SM}, the section ``The geometric origin of identity'').

\begin{theorem}[Identity as unique-readout; status: theorem within \GDOS{} (T-Electron-1)]
\label{thm:identity}
On the charged-lepton boundary stratum $\Sigma_{\ell}$, the \GFF{} Morse
landscape admits exactly one \GGA{}. Every electron, anywhere on the 4D
boundary, is the readout of that single attractor: its mass is the \GFF{}
level at the minimum, its charge is the integer-normalized
$\mathrm{U}(1)_{\rm EM}$ eigenvalue on the unique stable cascade leg, and
its spin label is fixed by the boundary action of the bulk spinor group.
Consequently no two electrons can differ in any intrinsic property.
\end{theorem}

\begin{proof}[Proof, by assembly of cited results]
Uniqueness of the ground attractor is \GFF{}-ST7 \citep{ArisakaA6Gi4};
the identification of the electron with the depth-2 \GGA{} of the
$\mathbb{C}P^2$ family stratum is the generation-to-cascade assignment of
\ANine{} (its labeled lepton cascade-depth section, imported here as
Part~\ref{part:IV} below); the readout reading of boundary
particles is the universal-identity statement of \AEight{}
\citep{ArisakaA8QM}, recognized there as theorem T-A8.9 (cohort ID T-QM-9). The conjunction is the claim.
\end{proof}

The chemistry analogy of \ANine{} is exact and worth repeating, because it
is the right intuition for everything that follows: a molecule has many
stationary electronic configurations, but every water molecule in the
universe is identical --- and indefinitely stable --- because its electrons
occupy not merely \emph{a} stable configuration but \emph{the} lowest one.
The \GGA{} is ``ground state'' promoted to a constitutional principle.

\paragraph{Physics intuition.} The reader has met this structure twice
in graduate training, under other names. In condensed-matter language,
$\FGFF$ is an effective free energy on an order-parameter space, and
Eq.~\eqref{eq:gga-def} selects its global minimum --- the electron is to
its stratum what the true vacuum is to a Landau functional, with the
muon and tau as its metastable phases. In chemistry language, the
stratum is a configuration space and the \GGA{} its ground-state
conformation. The one unfamiliar move is that the landscape's
coordinates are not positions in space but structural directions of the
bulk --- scale and phase --- so the valleys are not \emph{places}; they
are \emph{kinds}. A particle species is a valley; its mass is how deep
the valley floor sits; and ``every electron is identical'' is the
statement that one valley has one floor.
\figref{fig:grip-two-regimes} draws the complete runtime this paper
consumes --- the descent, the two regimes, and the halt at the \GGA{}.

\begin{figure}[p]
\centering
\resizebox{0.88\textwidth}{!}{%
\begin{tikzpicture}[
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\node[dgibox] (DGI) at (0, 0) {\textbf{\DGI{}}\\[-1pt]
 {\scriptsize Dynamical Gauge Invariance --- the symmetric top: every gauge equivalence intact, nothing committed}};
\node[gffbox] (GFF) at (0, -22mm) {\textbf{$(\cF_{\GFF})$ \quad Geometric Free-Energy Functional}\\[-1pt]
 {\scriptsize the fixed landscape; descent with $d\cF_{\GFF}/dt \leq 0$ (GFF-ST6)}};
\node[gssbbox] (GSSB) at (0, -44mm) {\textbf{\GSSB{} \quad Geometric Spontaneous Symmetry Breaking}\\[-1pt]
 {\scriptsize branch selection at the saddles; Bogomolnyi tolls $S = \pi k$ (GRIP-ST3)}};
\node[gabox] (GA) at (0, -66mm) {\textbf{\GA{} \quad Geometric Attractor(s)}\\[-1pt]
 {\scriptsize stable basins en route --- possibly way stations ($\mu$, $\tau$, an excited atom); \GRIPin{} continues through their exit channels}};
\node[ggabox] (GGA) at (0, -88mm) {\textbf{\GGA{} \quad Ground Geometric Attractor}\\[-1pt]
 {\scriptsize the unique deepest basin (GFF-ST7) --- \emph{where \GRIPin{} halts}: the exit-channel set is empty}};
\draw[bigarrow] (DGI.south) -- (GFF.north);
\draw[bigarrow] (GFF.south) -- (GSSB.north);
\draw[bigarrow] (GSSB.south) -- (GA.north);
\draw[bigarrow] (GA.south) -- node[arrowtext, right=2pt]{exit channels: the descent continues} (GGA.north);
\node[inbox] (GIN) at (-58mm, -112mm) {\textbf{\GRIPin{}}\\[-1pt]
 {\scriptsize fixed-landscape regime (def:GRIPin)}\\
 {\scriptsize relaxation \emph{on} the landscape}};
\node[outbox] (GOUT) at (58mm, -112mm) {\textbf{\GRIPout{}}\\[-1pt]
 {\scriptsize landscape-rebuilding regime (def:GRIPout)}\\
 {\scriptsize transient, out of equilibrium}};
\draw[ribarrow] (GA.west) to[bend right=25]
 node[arrowtext, pos=0.55, below, sloped]{$\cF_{\GFF}$ landscape unchanged}
 (GIN.north);
\draw[outarrow] (GGA.south) to[bend left=18]
 node[arrowtext, pos=0.55, below, sloped]{$\cF_{\GFF}$ landscape reorganized}
 (GOUT.north);
\draw[ribarrow, dashed] (GIN.north) to[out=90, in=180]
 node[arrowtext, pos=0.35, left=2pt, text=cyan!55!black, font=\footnotesize\itshape]
 {within-stratum\\closed loop}
 (DGI.west);
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 {\textbf{\DGI{} \quad (next stratum)}\\[-1pt]
 {\scriptsize a new descent begins on the reorganized landscape}};
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 node[arrowtext, pos=0.5, right=3pt, text=orange!70!black, font=\footnotesize\itshape]
 {supplies the next\\initial datum $c_{\rm top}$};
\end{tikzpicture}}
\caption[The \GRIP{} cascade and its two regimes, in one picture (adapted from \ASix{}).]{\textbf{The \GRIP{} cascade and its two regimes, in one picture} (adapted from \ASix{} \citep{ArisakaA6Gi4}; the eighteen-layer deployment is \AEleven{} \citep{ArisakaA11Origin}). The central column is the runtime this paper consumes: from the fully symmetric top (\DGI{}), the system descends the fixed landscape $\cF_{\GFF}$, selects branches at the \GSSB{} saddles, and is captured into stable basins (\GA{}). From a \emph{non-ground} \GA{} --- a muon, an excited atom --- the descent continues through the basin's exit channels (\GRIPin{}, the weak interaction being Nature's implementer on the matter strata); at the \GGA{}, the unique deepest basin of \GFF{}-ST7, the exit-channel set is empty and \GRIPin{} halts. Only \GRIPout{} can act thereafter, reorganizing the landscape itself and starting the next stratum's descent. In one sentence: \GRIPout{} opens the landscape; \GRIPin{} finishes the journey; the \GGA{} --- the electron, on its stratum --- is where the journey ends.}
\label{fig:grip-two-regimes}
\end{figure}

Three remarks fence the claim honestly. First, Theorem~\ref{thm:identity} is
a theorem \emph{within} \GDOS{}: it consumes the open-system framework of
\AFive{} \citep{ArisakaA5GDOS} and the pillar structure of \ASix{}, with
their own declared axiomatic bases. It is not, and is not offered as, a
derivation acceptable to a reader who rejects the framework; it is the
statement that \emph{inside} the framework, identity stops being an input.
Second, the uniqueness statement \GFF{}-ST7 is a structure theorem of
\ASix{}; its Morse-positivity underpinnings connect to the open problem O3
of \AFive{}, which records the strict \GFF{} Morse-positivity question as
unsettled --- the same honesty note that \PaperPTwo{} carries
(\citealp{ArisakaP2N3}, its Postulate 6.3 and Appendix E). The fence
travels with the import. \emph{Third}, a remark that will look like a
liability and is in fact the theorem's sharpest feature: the attractor is
a property of the boundary \emph{landscape}, whose coordinates are the
non-spatial directions of the bulk --- scale and phase --- and not
positions in space at all. Nothing in Theorem~\ref{thm:identity} refers to
where an electron sits, or to whether two electrons have ever shared a
causal past. That is exactly what is needed, because the sameness of the
electron is not only a laboratory fact; it is a fact across the whole sky,
including regions that were never in causal contact --- and no account
built on shared history could reach them. The following corollary states
the point, and connects it to the companion cosmology.

\begin{corollary}[Horizon-independence; the second horizon problem, status: within \GDOS{}]
\label{cor:horizon-independence}
Because the charged-lepton \GGA{} is the unique deepest basin of a
landscape indexed by scale and phase --- not by spatial location ---
Theorem~\ref{thm:identity} holds pointwise on the entire boundary,
independently of causal structure. Two electrons in regions that never
exchanged a signal, even regions permanently beyond each other's horizon,
read out the \emph{same} attractor, because they are boundaries of the
\emph{same} six-dimensional bulk. The identity is guaranteed by the
geometry, not negotiated by any history.
\end{corollary}

This is the particle-scale face of what the companion \ATen{}
\citep{ArisakaA10Cosmos} names the \emph{second horizon problem}: the
observation that the sky is everywhere made of the same things --- every
electron of one mass and charge, every atom radiating the same lines ---
across regions the temperature horizon problem shows were never in contact.
There the puzzle is closed in two moves: this \emph{mold} (one
specification per object, from one bulk) and an \emph{ordering} argument
(the derived grand-unification-scale launch means the inflationary stretch
acted before any matter existed, so the agreements were inherited, not
negotiated). Theorem~\ref{thm:identity} supplies the first move at the
level of the single electron; \ATen{}'s Section on the second horizon
problem carries the cosmological half. The empirical exposure is shared and
already stringent: quasar-absorption spectroscopy bounds any spatial
variation of the dimensionless combinations that carry the electron's
identity --- the fine-structure constant \(\alpha\) and the
electron-to-proton mass ratio --- across the observable universe at the
\(10^{-5}\)--\(10^{-6}\) level, so a single confirmed variation would
refute the mold here exactly as it would there.

That exposure is also the cleanest way to see what separates this reading from the string landscape. A framework with a single vacuum must return one value of \(\alpha\) everywhere, and is exposed to a single discordant measurement; a framework with of order \(10^{500}\) vacua and no dynamical selection principle \citep{KachruKalloshLindeTrivedi2003} accommodates the same uniformity only by having our whole observable patch descend from one nucleation event in an eternally inflating background --- internally consistent, but at the price of the measure problem, which defers prediction of any further constant. The identity we measure is thus, in the one reading, a necessity exposed to falsification and, in the other, an inheritance immune to it. The companion \ATen{} \citep{ArisakaA10Cosmos} develops the contrast in full, in the closure-mode form that prices the landscape rather than refuting it.

\section{The content of identity: the derived values}
\label{sec:values}

Identity-as-uniqueness would be consistent with \emph{any} values of
$(m_e, e, \tfrac12)$. The framework's stronger claim is that the values
themselves are readouts. This section assembles the three value statements
with their individual statuses; none of them is new to this paper, and
each is grep-verified at its upstream location (Appendix~\ref{app:ledger}).

\subsection{The mass}
\label{ssec:value-mass}
\ANine{}'s minimal first-order codebook gives the electron Yukawa
\begin{equation}
y_e^{(1)} \;=\; \frac{N}{L^{3}\,2^{\,J+L+1}}
\;=\; \frac{3}{5^{3}\cdot 2^{13}}
\;=\; \frac{3}{1\,024\,000},
\label{eq:ye}
\end{equation}
built entirely from the \OGNfive{} integer ledger
$(M,N,L;J,K)=(1,3,5;7,35)$, whose Diophantine uniqueness is Theorem~6 of
\ATwo{} \citep{ArisakaA2GG6}. The QD (Quantum Descent) completion layer of
\ANine{} multiplies this by the structurally constrained rational
$\mathcal R_e = 1 + \tfrac{M}{2^{J}L} = \tfrac{641}{640}$, yielding
\begin{equation}
m_e^{\mathrm{QD}} \;=\; 0.511097845~\mathrm{MeV}.
\label{eq:meQD}
\end{equation}
The CODATA 2022 value is $m_e c^2 = 0.51099895069(16)$~MeV
\citep{CODATA2022}; the codebook value agrees at the
$1.9\times10^{-4}$ relative level --- four significant figures, with the
residual in the fourth figure declared, not hidden. We state plainly: the
mass derivation is \emph{codebook-level} --- derived modulo the named
A9-local lemmas of the QD layer --- and the $1.9\times10^{-4}$ residual is
the current precision of that layer. Nothing in this paper sharpens it;
Part~\ref{part:VIII} registers it as a kill criterion at exactly this
declared precision.

What matters for Q1 is not the last digit but the ontology: $m_e$ is the
\GFF{} level of the unique ground basin --- a property of the landscape,
not a dial of a Lagrangian. The same codebook, run at depths 0 and 1,
produces $m_\tau$ and $m_\mu$ (Part~\ref{part:IV}); the electron mass is
the bottom rung of a derived ladder, not an isolated constant.

\paragraph{Physics intuition.} The mass-as-level reading is closer to
familiar physics than it first appears. Nobody asks what the hydrogen
atom's $-13.6$~eV is ``made of'': it is the level at which the ground
configuration sits, fixed by the structure of the Hamiltonian, and
every hydrogen atom carries it exactly because every hydrogen atom
occupies the same level. Eq.~\eqref{eq:meQD} asks $m_e$ to be read the
same way --- not stuff accumulated around a point, but the level of the
unique lowest configuration, fixed by the integers of the geometry. The
codebook then plays the role spectroscopy plays for atoms: read the
levels, and check them against the structure that claims to fix them.

\subsection{The charge}
\label{ssec:value-charge}
The elementary charge is not primitive in \GGTheory{}: T-Euclid-4 of
\AFour{} \citep{ArisakaA4Euclid} derives $e$ within the \GUfive{}
constant-absorption lineage, and the fine-structure value is the dyadic
attractor coordinate of \ANine{},
\begin{equation}
\alphainv(M_Z) \;=\; 2^{J} \;=\; 128,
\qquad
\alphainv(0) \;=\; 2^{J} + N^{2} \;=\; 137.0,
\label{eq:alpha}
\end{equation}
with the QD completion bringing the zero-momentum value, as \ANine{}
reports, to the CODATA $137.036$ (\citealp{ArisakaA9SM}; the comparison value is CODATA 2022
$\alphainv = 137.035999177(21)$ \citep{CODATA2022}). Charge quantization
--- why every electron carries exactly $-e$ and not $-1.07\,e$ --- is the
topological-integer signature of the cascade: the charge is the eigenvalue
of a fixed integer-normalized generator on the unique stable cascade leg.
Status: codebook-level for the value; theorem-level (T-Euclid-4) for the
non-primitivity of $e$. Part~\ref{part:VII} returns to $\alpha$ as the
strength of the sensed force.

\subsection{The spin}
\label{ssec:value-spin}
Spin-$\tfrac12$ --- measured as a two-valuedness before it was named
\citep{SternGerlach1922}, carried relativistically by construction
since \citealp{Dirac1928} --- is the one value the Standard Model
cannot even parameterize --- it is a representation choice, made by hand from Wigner's
list \citep{Wigner1939}. In \GGTheory{} the choice is forced by the bulk:
the six-dimensional Lorentz group satisfies the accidental isomorphism
\begin{equation}
\mathrm{Spin}(1,5) \;\cong\; \SLtwoH,
\label{eq:spin15}
\end{equation}
the quaternionic entry of the magic $2\times2$ sequence over the division
algebras (\citealp{ArisakaA2GG6}, its Proposition on the magic square and
the explicit $\mathrm{Herm}_2(\mathbb{H})$ construction; the
classification underneath is Hurwitz's 1898 theorem, cited there). Weyl spinors of the 6D bulk are
two-component \emph{quaternionic} vectors; their boundary projection
carries an irreducible doublet structure, and the half-integer label of
the 4D electron is the shadow of the quaternionic double cover --- not a
choice among representations but the unique boundary readout of the bulk
spinor geometry. Status: structural theorem of A2's group theory.

\paragraph{Physics intuition.} The ``$\tfrac12$'' of spin-$\tfrac12$
never measured a rotation rate; it counts sheets. $\mathrm{SU}(2)$
wraps $\mathrm{SO}(3)$ twice --- a $2\pi$ turn lands a spinor on the
second sheet ($\psi \to -\psi$), and only $4\pi$ brings it home, the
fact made tactile by the belt trick. Wigner's classification says a
relativistic world is \emph{allowed} such double-sheeted
representations; it never says which one nature must use. Equation
\eqref{eq:spin15} answers with arithmetic: in dimension six the bulk
Lorentz group happens to \emph{be} a $2\times2$ quaternionic group,
whose minimal spinor is the doublet --- and the half-integer label we
measure in 4D is that double cover, seen from inside the boundary. The
dynamical reading --- spin \emph{without spinning} --- belongs to Q4 and
is developed in Part~\ref{part:VI}; the conjugate orientation of the
same double cover is the positron's half of the story, the sixth
question of Part~\ref{part:positron}.

\section{Stability: no exit gate from the ground basin}
\label{sec:stability-cite-p6}%
\noindent\emph{A companion at the other end of the same ledger.} \PaperPSix{} \citep{ArisakaP6Proton} argues that the proton never decays because its baryon number is a \emph{winding} of the compact geometry --- an integer, protected not by a symmetry that could be broken but by the impossibility of continuous motion through the whole numbers; the two mixed anomalies that survive are absorbed by the \BIsix{} Green--Schwarz inflow, leaving a single $\Delta B \in 3\mathbb{Z}$ door that no proton decay can pass. This Part argues that the electron never decays because there is no gate out of the deepest basin. The two arguments are independent and they are of different kinds --- that companion states the pair in one line, \emph{the electron is immortal because its basin has no exit gate; the proton because its winding has no unwinding operator} --- so the cohort carries two standing falsifiers rather than one claim made twice, and either could fail without touching the other. That is worth stating plainly, because a framework that has staked two independent absolute-stability claims has staked more than a framework with one.

\label{sec:stability}

\subsection{The standard answer, credited in full}
\label{ssec:standard-stability}
The textbook explanation of electron stability is two lines long and
correct: decay must conserve charge; the electron is the lightest charged
particle; therefore there is nothing for it to decay into. Anyone offering
a new account of electron stability must first acknowledge that this
argument exists, works, and has never failed.

It is nevertheless conditional bookkeeping, in precisely the sense Q1's
field answer was: it presupposes the spectrum. ``Lightest charged
particle'' is an empirical fact about the mass ladder, not an explanation
of it --- why is nothing charged lighter? why does the ladder terminate
where it does? --- and these questions are exactly Q3, unanswered in the
Standard Model for ninety years. Within the SM, absolute stability is an
accident of the input spectrum. The empirical anchor meanwhile is
spectacular: the Borexino bound on charge-violating decay --- the modern end of
the symmetry-test program founded by \citet{FeinbergGoldhaber1959},
probing the channel whose theoretical paradoxes
\citet{OkunZeldovich1978} mapped --- places
$\tau_e > 6.6\times10^{28}$~yr at 90\% C.L. \citep{Borexino2015},
more than eighteen orders of magnitude beyond the age of the
universe.

\subsection{Stability as ground-state-ness}
\label{ssec:gg-stability}
In \GDOS{} the electron's stability is not an accident; it is the second
face of Theorem~\ref{thm:identity}.

\begin{theorem}[No-exit-gate; status: theorem within \GDOS{} given
\GFF{}-ST7, with Q3's imported conditioning (T-Electron-2)]
\label{thm:stability}
The electron basin is the unique global minimum of the charged-lepton
stratum (the \GGA{}). Unlike the depth-0 and depth-1 basins, it possesses
no exit gate: there exists no admissible \GSSB{} gate, of any index and
any finite Bogomolnyi toll, leading out of it. \GRIPin{} halts there.
Consequently the electron cannot decay --- not because every channel is
blocked by a conservation law applied to an unexplained spectrum, but
because the landscape contains no downhill direction and no gate.
\end{theorem}

The statement and its proof environment live in \PaperPTwo{}
(\citealp{ArisakaP2N3}, its \S9.3: the depth-2 critical point is the
\GGA{}, ``No exit gate exists; this is why the electron has never been
observed to decay''), deployed on the \ANine{} cascade assignment
(Part~\ref{part:IV}). What this paper adds is the conjunction reading:
identity and stability arrive \emph{together}, as the two faces of
ground-state-ness --- all copies are identical because there is only one
deepest basin, and the copy persists because there is no deeper basin to
decay to. In the SM these are two unrelated facts (a field convention and
a spectrum accident); here they are one theorem about one minimum.

\paragraph{Physics intuition.} Why does a hydrogen atom in its ground
state not radiate? Not because a selection rule forbids it, but because
there is no lower level to radiate \emph{to}: stability is an absence
of destinations. Theorem~\ref{thm:stability} is that statement applied
to the electron itself. An excited atom and a muon are, in this
reading, the same kind of object --- occupants of a level with
somewhere lower to go --- and the electron, like the ground-state atom,
simply has nowhere. The added clause that distinguishes the theorem
from the textbook argument is the gate: in \GDOS{} a decay needs not
only a destination but an admissible exit, and the ground basin has
neither.

Three fences. \emph{(i)} The theorem is \GDOS{}-internal: it presupposes
\GFF{}-ST7 and the cascade machinery, and is not claimed to be derivable
in SM language. \emph{(ii)} Charge conservation itself is not assumed on
top: the boundary $\mathrm{U}(1)_{\rm EM}$ descends from the derived bulk
gauge factor (\ATwo{} Theorem~3; \AFour{} T-Euclid-4), so the standard
two-line argument survives \emph{inside} the framework as a consistency
check rather than as the explanation. \emph{(iii)} The claim that the
ladder above the electron terminates --- that there is no lighter charged
basin below and exactly two above --- is Q3, and it enters with every one
of \PaperPTwo{}'s declared conditions. Part~\ref{part:IV} states them.

\subsection{What would count as a refutation}
\label{ssec:stability-refutation}
The ground-state account is sharper than the bookkeeping account in one
observable respect: it forbids electron decay \emph{absolutely}, including
through any hypothetical charge-violating channel that bookkeeping cannot
address (a charge-violating decay would falsify the SM argument's premise
but not its logic; it would falsify Theorem~\ref{thm:stability} outright).
Every improvement of the Borexino bound is therefore a direct test, and
any observed decay, in any channel, kills this paper
(Part~\ref{part:VIII}, F1).

Two of the six questions are now one statement about one minimum.
After all, ``nothing can be lower'' is simultaneously the reason every
copy is alike and the reason every copy endures --- the first time in
this paper, but not the last, that two of the century's questions
collapse
into a single sentence.

%% ===================================================================
%%  PART IV -- THE EXCITED COPIES (Q3, IMPORTED)
%% ===================================================================

\section[Part~III in plain English]{Part~III in plain English: why every electron is identical, and why none has ever decayed}
Two of the six questions turn out to be one question, and this Part is where they meet.

Quantum field theory already explains why electrons are alike: they are excitations of a single field, and ripples on one pond cannot disagree about what water is. That answer is correct, and the Part states it at full strength before adding anything to it. What it does not explain is the \emph{content} of the likeness --- why this field, carrying this mass and this charge rather than any other. Nor does it explain stability: nothing in the field picture forbids the electron from decaying, it simply has nowhere to decay to given the particles that happen to exist.

The claim here is that both gaps close together if the electron is the deepest basin of a landscape the geometry fixes. Identity follows because there is one basin and one way to read it. Absolute stability follows because there is no gate out of the bottom. The two are not separate results that happen to agree; they are one statement about one object, and the derivations are written out in the appendix so that a reader can check they are not the same assumption counted twice.

\GGPart[The excited copies]{The Excited Copies}{$\mu$ and $\tau$ as geometrically excited electrons; the ladder ends at three (Q3)}
\label{part:IV}

\section{The ladder and its terminus}
\label{sec:ladder}

Q3 is the cleanest of the six questions historically: since the muon
appeared unbidden in cosmic rays \citep{NeddermeyerAnderson1937}
--- and since the tau completed the pattern at SPEAR \citep{Perl1975}
--- the copies have had no explanation of any kind in
standard physics. ``Who ordered that?'' has stood for ninety years. In QFT
the three charged leptons are three independent fields; nothing makes the
heavier two ``excited states'' of anything, and nothing prefers three to
seventeen. This paper neither derives the answer nor restates its proof:
the dedicated derivation is the sister paper \PaperPTwo{}
\citep{ArisakaP2N3}, and the division of labor is deliberate ---
\PaperPTwo{} owns \emph{why three}; the present paper owns \emph{why the
terminus is what it is}. This Part imports the result with its complete
conditioning, because Q2 and Q3 are logically entangled: the stability of
the electron is the statement that the ladder \emph{ends}, and the count
of the ladder is the statement of \emph{where}.

The imported picture, in five sentences. The three generations are the
three critical points of one \GFF{} Morse landscape on the family-projector
stratum $\mathbb{C}P^{2}$, organized as a \GRIPin{} cascade chain
\begin{equation}
\underbrace{[\,\mathrm{ind}=4\,]}_{\tau;\ \text{depth }0}
\;\xrightarrow{\;S=2\pi\;}\;
\underbrace{[\,\mathrm{ind}=2\,]}_{\mu;\ \text{depth }1}
\;\xrightarrow{\;S=\pi\;}\;
\underbrace{[\,\mathrm{ind}=0\,]}_{e;\ \text{depth }2\ (\GGA{})}
\label{eq:lepton-chain}
\end{equation}
(\citealp{ArisakaA9SM}, its labeled section
\texttt{sec:lepton-cascade-depth}; \citealp{ArisakaP2N3}, \S9). All three
are genuine Geometric Attractors --- index-0 minima of their depth-$n$
effective landscapes, which is why $m_\tau$ and $m_\mu$ are sharply
measurable --- but only the electron's basin is the ground state. The
masses are basin levels, produced by the same codebook as
Eq.~\eqref{eq:ye} at depths 0 and 1; the lifetimes are ordered by basin
depth, with each non-ground generation exiting through its \GSSB{} gate at
Bogomolnyi toll $2\pi$ (then $\pi$); and the entire observed
$\tau\to\mu\to e$ chain is a single \GRIPin{} descent, implemented
physically by the weak interaction first written down by Fermi
\citep{Fermi1934} --- the unique flavor-connecting
channel of the boundary gauge group (\citealp{ArisakaA9SM}, the
weak-as-\GRIPin{} doctrine). ``Geometrically excited states of the
electron'' is thus not a metaphor: $\mu$ and $\tau$ occupy higher basins
of the \emph{same} landscape whose ground state is the electron, exactly
as an excited atom occupies a higher level of the same Hamiltonian.

\paragraph{Physics intuition.} The gate-and-toll picture is Gamow's
alpha-decay mechanism lifted from a potential in space to a landscape
of structure. In alpha decay the rate carries $e^{-2\int |p|\,dr/\hbar}$
--- an action in an exponent; here each \GSSB{} gate carries a
Bogomolnyi action toll ($2\pi$, then $\pi$), and the cascade rates
carry the corresponding $e^{-S}$ suppressions, combined with
phase-space factors exactly as nuclear lifetime systematics combine
barrier penetrability with phase space (the quantitative accounting,
including why phase space dominates the $\tau$--$\mu$ lifetime ratio,
is \PaperPTwo{}'s \S9.4). The familiar tunneling grammar --- actions
in exponents, tolls at passes, lifetimes ordered by what stands between
a state and its destination --- transfers whole.

\figref{fig:basin-landscape} draws the whole story in one picture;
\figref{fig:grip-cascade-cp2}, reproduced from \ANine{}, states the
same chain as a Morse diagram --- the figure that first drew, in the
cohort, why exactly $(e, \mu, \tau)$; and Table~\ref{tab:cascade}
records the assignment quantitatively. The reader who keeps these two
figures has Parts~\ref{part:III} and~\ref{part:IV} of this paper. Figure~\ref{fig:lepton-descent} then places the same three generations on the cosmic descent --- the energy-and-time axis running from the seam through TeV-scale leptogenesis to the electron, with the neutrino seesaw floor below.

\begin{figure}[ht]
\centering
\resizebox{0.733\textwidth}{!}{%
\usebox{\GGplateLandscape}%
}
\caption[The three-basin \GFF{} landscape: $\tau$, $\mu$ way stations; $e$ the \GGA{}; gates with tolls $2\pi$, $\pi$.]{The charged-lepton landscape in one picture: a schematic one-dimensional cut through the \GFF{} Morse landscape on the family stratum $\mathbb{C}P^2$. The three generations are the three basins; their floors are the masses (levels schematic, not to scale); the two \GSSB{} gates carry the Bogomolnyi tolls $S = 2\pi$ and $S = \pi$; and the observed $\tau \to \mu \to e$ weak-decay chain is a single \GRIPin{} descent that pays both tolls and halts in the unique deepest basin --- the \GGA{}, which has no exit gate. Identity (one deepest basin), stability (no gate out of it), the excited copies (the two way stations), and the decay hierarchy (tolls in exponents) are all visible in this one drawing; pointlikeness is the statement that the horizontal axis is not a direction of space.}
\label{fig:basin-landscape}
\end{figure}

\begin{figure}[ht]
\centering
\resizebox{0.676\textwidth}{!}{%
\usebox{\GGplateCascade}%
}
\caption[The \GRIP{} cascade on $\mathbb{C}P^2$ at $N=3$: why exactly $(e,\mu,\tau)$ (reproduced from \ANine{}).]{The \GRIP{} cascade on the family-projector moduli $\Sigma_{\rm fam} = \mathbb{C}P^{N-1} = \mathbb{C}P^2$ at $N=3$, reproduced from \ANine{} \citep{ArisakaA9SM} in the ground-state (\GGA{}) reading. The Morse skeleton of the \GFF{} height function keeps its three critical points (indices 4, 2, 0) and Bogomolnyi actions $S_{[2k]\to[2(k-1)]} = \pi k$ \citep{Witten1982}, accumulating to $S_{\rm tot}(3) = 3\pi$ and exactly saturating the \BIsix{} budget --- the three-leg count of \PaperPTwo{}, imported here with its conditioning (\S\ref{sec:conditioning}). What the figure states precisely is the particle identification: all three generations are genuine Geometric Attractors --- index-$0$ basins of their depth-$n$ effective landscapes, which is why $m_\tau$ and $m_\mu$ are sharply measurable --- but only the depth-2 basin is the \emph{Ground} Geometric Attractor. The non-ground \GA{}'s relax toward it ($\tau\to\mu\to e$); the \GGA{} never decays. The index-4 and index-2 critical points are the \GSSB{} gates the descent crosses, not the particles; the two arrows are steps of a single \GRIPin{} descent on a fixed landscape, and the \GGA{} is where \GRIPin{} halts.}
\label{fig:grip-cascade-cp2}
\end{figure}

\begin{table}[ht]
\centering
\caption[The lepton cascade assignment, with empirical values.]{The lepton cascade assignment with empirical values (PDG 2024
\citealp{PDG2024}; lifetime bound \citealp{Borexino2015}). Depths,
indices, and tolls from the imported \PaperPTwo{}/\ANine{} chain
(Eq.~\ref{eq:lepton-chain}); the toll column is the exit gate
\emph{out of} the basin. Masses and lifetimes are measured; the
mapping of basins to particles is the imported theorem; the toll
values inherit the Part~\ref{part:IV} conditioning.}
\label{tab:cascade}
\small
\begin{tabular}{@{}llllll@{}}
\toprule
\textbf{Particle} & \textbf{Depth} & \textbf{Morse index} & \textbf{Exit toll} & \textbf{Mass [MeV]} & \textbf{Lifetime} \\
\midrule
$\tau$ & 0 & 4 & $S = 2\pi$ & $1776.93(9)$ & $2.903(5)\times10^{-13}$ s \\
$\mu$ & 1 & 2 & $S = \pi$ & $105.6583755(23)$ & $2.1969811(22)\times10^{-6}$ s \\
$e$ & 2 & 0 (\GGA{}) & \textbf{none} (no gate) & $0.51099895069(16)$ & stable; $\tau_e > 6.6\times10^{28}$ yr \\
\bottomrule
\end{tabular}
\end{table}

\begin{figure}[p]
\centering
\includegraphics[width=\textwidth,height=0.86\textheight,keepaspectratio]{p3_lepton_descent}
\caption[The lepton descent on the cosmic energy-and-time axis.]{The three
charged generations and the neutrino sector placed on the \GRIPin{}
descent axis $r = \ln(E_{\mathrm{seam}}/\mu)$ ($E_{\mathrm{seam}} =
M_{\mathrm{Pl}}/2$, the lock at $r = K = 35$), read down four quantities:
the cosmic scale factor $a$, the depth $r$, the energy $\mu$, and the
time $t$. From the seam --- where the neutrino Weinberg operator is
anchored --- the descent passes the lock, the heavy Majorana triplet and
TeV-scale resonant leptogenesis where the matter asymmetry
$\eta_B \simeq 6\times10^{-10}$ is born (\ATen{}, \AEleven{}), and then the
electroweak scale, where the charged-lepton Yukawas are read off
$v = 246$~GeV. The three generations land as basin levels of the one
$\mathbb{C}P^2$ cascade: $\tau$ (depth 0), $\mu$ (depth 1), and the
electron (depth 2, the \GGA{}) --- absolutely stable, the ground state of
the ladder and the terminus of this paper. The integer-ledger ratios
$m_\tau/m_\mu = 84/5$ and $m_\mu/m_e = 625/3$ are the derived content
(\ANine{}); the absolute masses are the codebook readout at their stated
grade. Below the electron lies the seesaw floor, $m_\nu = \pi v^2 /
E_{\mathrm{GUT}}$ suppressed from the seam, giving
$(m_1, m_2, m_3) \simeq (0.065,\, 8.6,\, 50.5)$~meV in normal ordering
with $\delta_{\mathrm{PMNS}} \simeq 196^\circ$. Drawn to scale within each
zone; the two axis breaks compress the quiet descent and the gap to the
seesaw floor.}
\label{fig:lepton-descent}
\end{figure}

\section{The conditioning, verbatim}
\label{sec:conditioning}

The charter of this paper requires \PaperPTwo{}'s fences to travel with
every import, at every level including the abstract. They are restated
here without dilution.

\begin{enumerate}[leftmargin=2.2em]
\item \textbf{Lower bound (L1) --- conditional on an empirical input.}
$N \ge 3$ follows from the observed non-vanishing of CP violation
(the Jarlskog invariant \citep{Jarlskog1985} $\JCKM \ne 0$, CP violation having been observed since \citealp{CCFT1964}): with fewer than three families a
unitary mixing matrix has no physical CP phase. Status: theorem given the
empirical input.
\item \textbf{Upper bound (L2) --- conditional on the coupling clause and
the integrality theorem L-INT (residue R-INT).} The bound $N \le 3$ consumes the capacity theorem T-N3-6 of \citet{ArisakaP2N3} ($\mathrm{Cap}(N) = \pi N$, saturating at $3\pi$; its Appendix~C records the two viable formulations), which is derived there from the family stratum's quantum geometry --- Berry transport and the Fubini--Study package, forced at the Born theorem's own grade by its adiabatic theorems T-AD-1--T-AD-3 --- conditional on the coupling clause (its Axiom AX-B) and the
integrality theorem L-INT, whose single topological residue R-INT
``is topological bookkeeping on a specific manifold, of the same kind
as checking orientability, not a conceptual gap'' ---
\PaperPTwo{}'s own words, adopted verbatim; its Appendix~H
discharges that residue on the benchmark
background. The two would-be hypotheses of the natural axiomatization are dissolved there: $H_1$ is closed in the negative (the rigidity lemma: every functorial descent of the bulk data vanishes), and $H_2$'s salvageable content is L-INT, now the derived theorem with
residue R-INT. The same
budget value is consumed, not derived, by \ASix{}'s cascade-closure
theorem T4.1, whose open problem M10 records the missing derivation.
\item \textbf{Reachability reading --- interpretation, not proof.} The
dynamical reading of $N<4$ --- a fourth family's relaxation road would
cost $\pi N(N-1)/2 > \pi N$, leaving its ground state dynamically
unreachable --- ``inherits the conjectural status of the budget and adds
none of its own rigor'' (\citealp{ArisakaP2N3}, \S9.5, verbatim). We use
it in this paper exactly as \PaperPTwo{} licenses: as the physical
interpretation that converts ``why this budget?'' into ``why must every
family be reachable?'', to which \GFF{}-ST7 is the cohort's declared
answer.
\item \textbf{Empirical anchors.} The lepton-counting input $N_\nu = 3$
from the $Z$ resonance \citep{ALEPH2006}, and the codebook's
four-significant-figure agreement on the mass ratios
($m_\tau/m_\mu = 16.817$, $m_\mu/m_e = 206.768$), are empirical
validations, not premises of the geometry.
\end{enumerate}

\figref{fig:grip-cascade} draws the budget accounting these fences
guard, specialized to the lepton stratum.

\begin{figure}[ht]
\centering
\resizebox{0.746\textwidth}{!}{%
\begin{tikzpicture}[
 font=\sffamily,
 stage/.style={draw=green!55!black, rounded corners=4pt, line width=0.80pt, minimum width=3.6cm, minimum height=2.2cm, align=center, fill=green!10},
 arrow/.style={->, line width=1.10pt, >=Stealth},
 budgetbox/.style={draw=olive!55!black, rounded corners=3pt, fill=yellow!15, align=center, font=\sffamily\footnotesize, minimum width=4.6cm},
 edgelabel/.style={font=\sffamily\footnotesize, fill=white, inner sep=1pt},
]
\node[stage] (DGI) at (0, 0) {\textbf{\DGI{}}\\ \footnotesize Dynamical\\ Gauge\\ Invariance};
\node[stage] (GSSB) at (5, 0) {\textbf{\GSSB{}}\\ \footnotesize Geometric\\ Spontaneous\\ SB};
\node[stage] (GA) at (10, 0) {\textbf{\GA{} / \GGA{}}\\ \footnotesize Geometric\\ Attractors\\ ($e$ = ground)};
\draw[arrow] (DGI) -- (GSSB) node[edgelabel, midway] {Wilson--Hosotani};
\draw[arrow] (GSSB) -- (GA) node[edgelabel, midway] {gradient flow};
\node[budgetbox] (S1) at (2.5, -2.7) {$S_{[4]\to[2]} = 2\pi$ \quad ($\tau \to \mu$ gate)};
\node[budgetbox] (S2) at (7.5, -2.7) {$S_{[2]\to[0]} = \pi$ \quad ($\mu \to e$ gate)};
\draw[arrow, gray!70] (DGI.south) to[bend right=10] (S1.north);
\draw[arrow, gray!70] (GSSB.south) to[bend right=10] (S2.north);
\node[draw=red!55!black, rounded corners=3pt, fill=red!12, align=center, font=\sffamily, line width=0.80pt, minimum width=10cm] (TOT) at (5, -4.6)
 {\textbf{Total cascade action on $\mathbb{C}P^{2}$ ($N=3$):}\\
 $\Stot = \sum_{k=1}^{N-1}\pi k = \pi N(N-1)/2 = 3\pi \;\le\; \SmaxBI = 3\pi$ \quad (\BIsix{} budget)\\
 \footnotesize exact saturation at $N = 3$; a fourth family's road could not be paid for};
\draw[arrow, dashed] (S1) -- (TOT);
\draw[arrow, dashed] (S2) -- (TOT);
\end{tikzpicture}%
}
\caption[The \GRIP{} cascade with the \BIsix{} budget, specialized to the lepton stratum at $N=3$.]{The cascade-with-budget accounting, adapted from \ASix{} \citep{ArisakaA6Gi4} and specialized to the charged-lepton stratum at $N = 3$. Each \GSSB{} gate costs its Bogomolnyi toll ($2\pi$ for $\tau\to\mu$, $\pi$ for $\mu\to e$); the chain sum $\Stot = \pi N(N-1)/2$ exactly saturates the \BIsix{} budget $\SmaxBI = 3\pi$ at $N = 3$. The budget value is the capacity theorem T-N3-6 of \PaperPTwo{} \citep{ArisakaP2N3} --- derived there from the stratum's quantum geometry, conditional on the coupling clause and the integrality theorem L-INT (residue R-INT),
and meeting the $N$-independence demand recorded as \ASix{}'s open problem M10 --- and every use of this figure inherits that conditioning verbatim (\S\ref{sec:conditioning}).}
\label{fig:grip-cascade}
\end{figure}

For the present paper the load-bearing consequence is modest and worth
stating exactly: \emph{Q2's ``no exit gate'' (Theorem~\ref{thm:stability})
does not depend on the upper bound $N \le 3$.} Even if a fourth family
were discovered --- killing \PaperPTwo{} and falsifier F3 below --- the
electron would remain the \GGA{} of its stratum unless the new state were
charged and \emph{lighter}. What the budget machinery adds is the
conjunction: the same finite resource that stops the ladder at three
guarantees that the terminus is reachable and final --- the universe not
only has a ground floor, it can always get there. That sentence is the
new content of this Part, and it carries the conjectural status of
ingredient 2 above.

After all, the muon was never an intruder. It is the electron, one
basin up --- and the ninety-year-old question ``who ordered that?''
dissolves into the older and better question of why a landscape should
have exactly three floors, which is the sister paper's to answer.

\section{The descent rate: the muon lifetime as a \GRIPin{} observable}
\label{sec:lifetime}

Part~IV has so far read the charged-lepton stratum \emph{statically}: the three
generations are the basins of the \GFF{} Morse landscape, their floors are the
masses, and the two \GSSB{} gates between them carry the Bogomolnyi tolls
$S_{[4]\to[2]}=2\pi$ and $S_{[2]\to[0]}=\pi$ (\figref{fig:grip-cascade}). But a
basin has a second, dynamical readout. A non-ground attractor does not merely
sit at its floor; it \emph{falls}, across its gate, toward the \GGA{}. The rate
of that fall is an observable, and for the muon it is the lifetime,
$\tau_\mu\approx 2.2~\mu$s. This section shows that the lifetime is as much a
\GRIP{} output as the mass: the mass is the floor of the basin, and the lifetime
is the rate at which the basin is vacated across its \GSSB{} gate.

\subsection{Two readings of one basin: the floor and the gate}
\label{subsec:floor-and-gate}

The runtime layer of \GRIP{} already carries this dynamical readout. The
seventh structure theorem of the pipeline (\ASix{} \citep{ArisakaA6Gi4},
\textbf{GRIP-ST7}) states that the generation decay-width ladder of unstable
boundary states is the direct projection of the cumulative cascade action: a
state that must cross a gate of toll $S=\pi k$ to leave its basin acquires a
width whose leading behavior tracks $e^{-\pi k}$. Mass and width are thus the
two faces of the same critical point --- the depth of the floor and the toll of
the gate.

The terminus makes the duality sharp. The electron is the \GGA{}: the unique
deepest basin, the one critical point with \emph{no} exit gate
(\S\ref{sec:ladder}, Theorem~\ref{thm:stability}). With no gate to cross there is
no descent, no width, and no decay: $\Gamma_e=0$, $\tau_e=\infty$. Absolute
electron stability, derived in Q2 as a statement about the \emph{form} of the
landscape, is therefore identically a statement about the \emph{rate} on that
landscape --- the gate-crossing rate evaluated at zero gates. The muon, one
basin up, has exactly one gate ($S_{[2]\to[0]}=\pi$); it falls, and the
finiteness of its lifetime is precisely the dynamical signature of being a
non-ground \GA{}.

\subsection{The weak interaction as the implementer of the descent}
\label{subsec:weak-implementer}

\GRIPin{} fixes \emph{that} the muon descends and \emph{across which} gate; the
weak interaction is what physically \emph{carries out} the crossing --- Nature's
implementer on the matter strata (\figref{fig:grip-cascade-cp2}). The gate
transition $\mu^-\to e^-\bar\nu_e\nu_\mu$ is the charged-current weak vertex
evaluated on the symmetry-broken ($v\neq0$) branch selected at the \GSSB{} stage.
Its strength is not a fitted constant but the geometric weak scale: the Fermi
coupling is
\begin{equation}
\frac{G_F}{\sqrt2}=\frac{1}{2v^2},
\qquad\text{i.e.}\qquad
G_F=\frac{1}{\sqrt2\,v^2},
\label{eq:GF-from-v}
\end{equation}
where $v$ is the boundary vacuum amplitude fixed by \ANine{}'s
Wilson--Hosotani theorem \citep{ArisakaA9SM} --- itself the readout of the one
electroweak \GRIPout{} event that built this landscape in the first place. The
coupling that sets the descent rate is therefore inherited from the same
geometry that dug the basins.

\subsection{The descent rate in closed form}
\label{subsec:rate-closed-form}

Treating the gate-crossing as a single inclusive jump into the
electron--neutrino continuum and evaluating the golden-rule rate with the
charged-current vertex gives the textbook leading-order width, now read as a
\GRIP{} quantity,
\begin{equation}
\Gamma_\mu^{(0)}=\frac{G_F^2\,m_\mu^5}{192\pi^3}
=\frac{m_\mu^5}{384\pi^3\,v^4}.
\label{eq:muon-rate}
\end{equation}
Each factor has a cascade meaning: $G_F^2$ is the squared geometric coupling of
the gate; $m_\mu^5$ is the phase-space measure of the descent --- the
basin-floor gap raised to the fifth power by the three-body leptonic final
state; and $192\pi^3$ is the dimensionless normalization of that final state.
The lifetime is $\tau_\mu=\Gamma_\mu^{-1}$.

The number is verified. With the empirical inputs the leading-order form
\eqref{eq:muon-rate} gives $\tau_\mu^{(0)}=2.187~\mu$s; restoring the exact
phase-space factor $f(m_e^2/m_\mu^2)=0.99981$ and the leading QED radiative
correction $1+\tfrac{\alpha}{2\pi}\!\left(\tfrac{25}{4}-\pi^2\right)
=1-4.2\times10^{-3}$ yields $\tau_\mu=2.19699~\mu$s, against the measured
$2.1969811(22)~\mu$s \citep{PDG2024} --- agreement at the part-per-million
level. Inserting the geometric scale $v=246.22$~GeV in \eqref{eq:GF-from-v}
reproduces $G_F$, and hence $\tau_\mu$, identically: the lifetime is anchored by
a geometric weak scale, not by a fitted weak constant.

\subsection{The descent as a CPTP semigroup}
\label{subsec:gkls-descent}

Rigorously, the descent is an open-system process: the boundary observer holds
the one-muon sector and traces over the electron and neutrinos. Under the
constitutional open-system rule (\GDOS{} \POS{4}; \ASix{}) the reduced
evolution is a CPTP semigroup, and for a single dominant gate it is generated by
one Lindblad jump operator
\begin{equation}
\mathcal L_\mu(\rho)=-i[H_{\rm eff},\rho]
+L_\mu\rho L_\mu^\dagger-\tfrac12\{L_\mu^\dagger L_\mu,\rho\},
\qquad
L_\mu=\sqrt{\Gamma_\mu}\,\lvert e\!\downarrow\rangle\langle\mu\rvert,
\label{eq:gkls-muon}
\end{equation}
so that the surviving-muon population obeys
$\rho_{\mu\mu}(t)=\rho_{\mu\mu}(0)\,e^{-\Gamma_\mu t}$. The exponential law is
the runtime \emph{form} of a non-ground \GA{} relaxing across its gate. The
contrast with the \GGA{} is exact and instructive: the electron sector carries
\emph{no} jump operator, because it has no gate; its reduced generator is purely
unitary, $\Gamma_e=0$, $\tau_e=\infty$. The single generator
\eqref{eq:gkls-muon}, evaluated at one gate versus zero gates, contains both the
muon's lifetime and the electron's absolute stability. Decay and permanence are
not two phenomena here but one \GRIP{} statement read at two depths of the same
cascade.

\subsection{\texorpdfstring{$\DGI\to\GSSB\to\GA$}{DGI->GSSB->GA} staging, and a
correction of one tempting misreading}
\label{subsec:lifetime-staging}

The lifetime sits in the runtime grammar exactly as the mass does.
\emph{\DGI{}}: the reduced generator \eqref{eq:gkls-muon} inherits the gauge
covariance of the parent charged current, so $\Gamma_\mu$ is a gauge-covariant
scalar --- no legal change of electroweak basis can alter it.
\emph{\GSSB{}}: the gate is the Bogomolnyi toll $S_{[2]\to[0]}=\pi$, realized
physically by the weak vertex on the broken branch. \emph{\GA{}/\GGA{}}: the
descent runs from the muon \GA{} to the electron \GGA{}, the exponential law is
its signature, and the \GGA{} is its terminus.

One misreading is worth closing off, because it is natural and wrong. It is
tempting to call the muon ``a \GA{} whose attractor is its own decay law.'' In
the \GRIP{} vocabulary the attractors are the \emph{basins}, not the laws, and
the muon is a \emph{non-ground} one: its lifetime is not the muon attracting
anything but the rate at which it is drawn toward the true attractor of the
stratum, the electron \GGA{}. The decay law is the shadow of the descent, not an
attractor in its own right.

\subsection{Status: a derived reading on a conditioned number}
\label{subsec:lifetime-status}

Honesty requires separating the reading from the number. The closed form
\eqref{eq:muon-rate} rests on two inputs of different provenance in the
\ANine{} codebook \citep{ArisakaA9SM}: the weak scale $v$ (equivalently $G_F$)
is \textbf{Derived (conditional)}, while the muon mass $m_\mu$ is
\textbf{Asserted} --- its cascade depth is the open lemma. Since
$\tau_\mu\propto 1/(G_F^2 m_\mu^5)$, the \emph{numerical} lifetime inherits the
Asserted status of the muon-mass depth: it is a structurally expressed
\GRIPin{} descent rate, derived \emph{modulo} that one Asserted depth, and is
not advanced as a parameter-free postdiction of $2.2~\mu$s. What is new and
\emph{unconditional} is the reading: the lifetime is the gate-crossing rate of
the cascade, the dynamical dual of the mass. The local perturbative rate and its
radiative corrections are the ordinary ones; \GRIP{} changes their origin (the
coupling is geometric) and their meaning (a runtime descent rate), not the
calculation.

\begin{proposition}[Muon lifetime as a \GRIPin{} descent rate]
\label{prop:muon-lifetime}
On the charged-lepton stratum $\Sigma_{\rm fam}=\mathbb{C}P^2$ the non-ground
geometric attractor $\mu$ relaxes to the ground attractor $e$ by a single
\GRIPin{} descent across the \GSSB{} gate $S_{[2]\to[0]}=\pi$, implemented by the
weak charged current with geometric coupling $G_F=1/(\sqrt2\,v^2)$. The reduced
one-muon sector is a CPTP semigroup with jump operator
$L_\mu=\sqrt{\Gamma_\mu}\,\lvert e\!\downarrow\rangle\langle\mu\rvert$ and
survival $\rho_{\mu\mu}(t)=e^{-\Gamma_\mu t}$, where
\[
\Gamma_\mu=\frac{G_F^2 m_\mu^5}{192\pi^3}=\frac{m_\mu^5}{384\pi^3 v^4},
\qquad
\tau_\mu=\Gamma_\mu^{-1}=2.197~\mu\text{s}
\]
(leading order $2.187~\mu$s; the exact phase space and leading radiative
correction give $2.19699~\mu$s, the measured value to the part-per-million).
The ground attractor $e$ has no exit gate, so $\Gamma_e=0$ and
$\tau_e=\infty$: absolute electron stability (Theorem~\ref{thm:stability}) is
the same statement evaluated at zero gates. Conditioning: $v$ (hence $G_F$) is
Derived (conditional) and $m_\mu$ is Asserted in \ANine{}, so the numerical
lifetime is derived modulo the Asserted $\mu$ depth, while the reading of
$\tau_\mu$ as the cascade's gate-crossing rate is unconditional.
\end{proposition}

The ladder of Part~IV is therefore two ladders at once. Read by floors it is the
mass ladder $m_\tau>m_\mu>m_e$; read by gates it is the lifetime ladder, the
$\tau$ falling fastest, the $\mu$ more slowly, and the electron not at all. The
same three basins, the same two tolls, the same single \GRIPin{} descent ---
seen once as where the generations sit, and once as how quickly they give way to
the one that stays. A static observable and a dynamical observable, drawn from
one cascade: the universality of \GRIP{} is that the mass and the lifetime are
not two inputs but two readings of the same geometry.

\subsection{Summary: what the muon's mass and lifetime, together, tell us}
\label{subsec:muon-summary}

It is worth stepping back from the equations and saying, in plain terms, what has
been done here --- because the lesson matters well beyond particle physics, and a
reader arriving at this program from biology or the study of the mind
(\AEleven{} \citep{ArisakaA11Origin}) will recognize the grammar.

Two facts about the muon are usually written into the rulebook of physics by
hand: how heavy it is, and how long it lives (about two-millionths of a second).
The picture in this paper is that they are not two facts but one. Imagine a
landscape of hills and valleys. Every kind of particle is a valley --- a place
the geometry permits a stable pattern to sit. The electron is the \emph{deepest}
valley on its sheet: there is nowhere lower to roll, so it never decays, and it
is exactly this that we proved as its eternal stability. The muon is a
\emph{higher} valley on the same sheet. It cannot stay; it rolls down, across the
ridge between the valleys, and ends as the electron.

In that picture the muon's \textbf{mass} is simply how deep its valley lies, and
its \textbf{lifetime} is how quickly it rolls across the ridge and out. Depth and
crossing-rate --- two readings of one and the same valley. The mass formula and
the lifetime formula (the $2.197$-microsecond number, reproduced to a part in a
million) are not independent assumptions bolted together; they are the static and
the dynamic face of a single geometric object. Obtaining \emph{both} from one
structure, rather than measuring two unrelated constants, is the economy that
distinguishes the \GDOS{}/\GRIP{} reading from the textbook one --- which it
otherwise leaves entirely intact.

This collapses two questions long treated as separate. \emph{What is a particle?}
(its identity, its mass) and \emph{how long does it last?} (its stability, its
lifetime) become the same question asked twice: once about where a valley sits,
and once about whether it has a way out. The electron's permanence and the muon's
mortality are then literally the same statement, evaluated with \emph{no} exit
gate versus \emph{one}. No competing framework reads a particle's existence and
its lifespan off a single geometry; that is the uniqueness of the construction.

For the life scientist the point is not the muon but the \emph{grammar}, which is
the one \AEleven{} carries all the way up. Valleys are attractors --- the stable
forms the world settles into (\GA{}), with one deepest, the ground form
(\GGA{}). Ridges are gates --- the thresholds a state must cross to change. Rolling
downhill is \GRIPin{}, relaxation toward a stable form on a fixed landscape. And
the rare events that re-carve the landscape itself, opening valleys that did not
exist before, are \GRIPout{} --- the electroweak vacuum here; the origin of life,
of the cell, of the conscious episode there. The muon is the cleanest specimen of
this grammar there is: a single elementary particle whose very existence and whose
lifespan are both nothing but geometry. If the bookkeeping is this exact for the
simplest case, the claim of \AEleven{} is that the same bookkeeping --- attractors,
gates, descents, and landscape-remaking events --- runs through atoms and molecules
to cells and minds, each a higher and richer attractor with its own gates and its
own characteristic times. The muon is the Rosetta stone: small enough to solve
exactly, and written in the same language as everything above it.

One honesty note carries over from \S\ref{subsec:lifetime-status}. How deep the
muon's valley lies --- its mass --- is, in the present codebook, still an assumed
input awaiting its closing lemma, so the precise lifetime number inherits that one
assumption. What is already secure, and what this Part adds, is the reading
itself: that a particle's mass and its lifetime are one geometric object seen
twice. That reading does not wait on the open lemma.


%% ===================================================================
%%  PART V -- POINTLIKENESS FROM NON-SPATIAL STRUCTURE (Q4: NEW CORE)
%% ===================================================================
%% ===================================================================
%%  PART V -- THE ORIGIN OF POSITRONS (new at v14.0; Internal
%%  Report 31, author-approved).  The sixth question: the origin of
%%  the antiparticle imported at theorem grade from P5-CPT, and the
%%  positron as the conjugate readout of the electron's one basin.
%%  ASCII only.  Inserted between The Excited Copies and
%%  Pointlikeness.
%% ===================================================================

\section[Part~IV in plain English]{Part~IV in plain English: the muon, the tau, and what this paper does and does not claim}
``Who ordered that?'' has stood since 1937. Standard physics treats the three charged leptons as three independent fields: nothing makes the heavier two excited versions of anything, and nothing prefers three to seventeen.

This Part is careful about ownership, and the care is not decorative. The derivation that there are exactly three lives in the sister paper, not here, and it is imported with its conditioning stated in full rather than quoted as a bare result. What this paper owns is the other half --- why the ladder ends where it does, and why the bottom rung is the particle we are made of.

The two halves are entangled, which is why the import has to be exact. Absolute stability is a statement about there being nothing below the electron, and that is only meaningful if the ladder is finite and its structure is known. A reader who wants the family count proved should read the sister paper. A reader who wants to know what the count costs, and what would falsify it, will find that here --- including the muon lifetime, computed rather than fitted, carrying the conditioning that computation inherits.

\GGPart[The origin of positrons]{The Origin of Positrons}{The sixth question: Dirac's reluctant twin and Anderson's photograph; the origin of antiparticles imported at theorem grade from the CPT companion; and the positron as the conjugate readout of the electron's one basin --- one object, two orientations of reading it}
\label{part:positron}

\section{The sixth question, and why it waited differently}
\label{sec:q6-history}

Five of this paper's questions share a biography: asked early, filed
away, unanswered for a century. The sixth has the opposite biography,
and the difference is instructive: it was \emph{answered} before
anyone had properly asked it --- and the answer was so spectacular
that physics mistook it for an explanation for ninety years.

The story is the most famous consistency crisis in the subject. In
1928 Dirac wrote down the relativistic wave equation the electron had
forced into existence \citep{Dirac1928}, and the equation immediately
returned more than it was asked for: alongside the positive-energy
electron states came a mirror family of negative-energy states that
could be neither discarded (the equation's completeness forbids it)
nor tolerated (an electron with states of arbitrarily negative energy
below it would radiate its way down forever --- no atom would be
stable). Dirac's first instinct was to hide the shadow in a filled
sea and identify its holes with the proton, the only positive
particle then known; the mass refused to cooperate. In 1931 he
conceded what the equation had been saying all along: the holes are a
\emph{new} particle, ``a new kind of particle, unknown to
experimental physics, having the same mass and opposite charge to an
electron'' \citep{Dirac1931}. The following year Carl Anderson,
photographing cosmic-ray tracks in a magnetized cloud chamber and
initially unaware of Dirac's prediction, recorded a particle bending
the wrong way with the electron's mass \citep{Anderson1933}. Theory
had predicted a twin from consistency alone; nature produced it
within the year.

Here is the mis-filing. What the episode established is that the
\emph{formalism} demands the twin: relativistic quantum theory cannot
be written without antiparticles, and quantum field theory
subsequently made the demand systematic --- every charged field
creates its particle and annihilates its antiparticle, one operator,
both signs. That is a genuine and permanent achievement, credited
here without reservation. But ``the equation predicts it'' names a
mystery rather than dissolving it. \emph{Why} does consistency want a
twin? What, in the furniture of the world rather than in the algebra
of a formalism, \emph{is} the positron? And for this paper the
question has a sharper, internal form, stated as Objection~8:
Part~\ref{part:III} proved the electron is the \emph{unique} ground
state of its stratum --- one basin, no second place to stand. A unique
ground state that did not accommodate the antiparticle would be
refuted by every PET scan performed today. Answering that in full
needs the origin of antiparticles at theorem grade, below
quantization, and the cohort's CPT companion \PaperPFive{}
\citep{ArisakaP5CPT} supplies exactly that, in the real geometry of
the bulk; the debt is registered by name as D-P3-4. On that import the
question can be met with a chapter rather than a fence. That is this
Part: the sixth question, asked
at last in the form the century skipped, and answered with the
imports priced.

\emph{The question, precisely.} \textbf{Q6 (The twin):} why does the
electron have an antiparticle --- a twin of exactly equal mass and
exactly opposite charge --- and what is the positron, if the electron
is the unique ground state of its stratum?

\section{The standard answer, and its edge}
\label{sec:q6-standard}

As with Q1, Q2, and Q5, standard physics has real content here, and
the thesis of this paper survives only alongside the credit.

\paragraph{What is genuinely explained.} Two things. First,
\emph{necessity at the level of the formalism}: one cannot write a
relativistic, causal, positive-energy quantum theory of a charged
field without antiparticle solutions; the Feynman--St\"uckelberg
identification organizes them, and quantum field theory builds them
into the operator content from the start \citep{Weinberg1995}.
Second, \emph{the pairing constraints}: the CPT theorem --- provable
from Lorentz invariance, locality, and hermiticity --- forces
particle and antiparticle to share mass, total width, and magnitude
of charge and magnetic moment. These are the two load-bearing walls
of the standard account, and both stand.

\paragraph{Where the edge is.} Ask three childishly direct questions
and the account goes quiet, in a specific and diagnosable way ---
\PaperPFive{} sharpens the diagnosis as ``three questions wearing one
coat.'' \emph{(i) Why does consistency want a twin at all?} The
theorems say that relativistic quantum theory without antiparticles
is inconsistent; they do not say what feature of the world the
inconsistency is protecting. \emph{(ii) Where does the twin first
exist?} In the standard account the antiparticle is born in the
quantization procedure --- it appears when operators are assigned to
Fourier components --- which leaves the question ``did the twin exist
before we quantized?'' sounding meaningless rather than answered.
\emph{(iii) What is the relation between the twin and the original?}
The CPT theorem \emph{constrains the pair} --- it is Depth-2
knowledge, in the grading \PaperPFive{} uses: given two objects, their
properties must match. It cannot say whether there are really two
objects at all. The equality of the electron and positron masses is,
in the standard account, an exact relation between two distinct
fields, enforced by a symmetry --- a fact that should strike the
reader as one coincidence deeper than it needs to be, exactly as two
identical electrons once did (Q1).

The sixth question therefore has the same shape as the other five:
a formalism that handles the fact perfectly while declining to say
what the fact is. And as with the other five, the missing layer turns
out to be geometric.

\section{The \texorpdfstring{\GGTheory{}}{GG-Theory} answer, imported at theorem grade}
\label{sec:q6-imported}

The derivation belongs to \PaperPFive{}, where it occupies a full
Part --- ``The Origin of Antiparticles'' --- and it is the sibling of
the origin-of-$i$ treatment in \citet{ArisakaP4Real}; this section
imports its three theorems in digest, at the level this paper's
argument needs, with the full proofs cited rather than reproduced
(the division of labor this cohort uses throughout; the reader who
wants the monograph treatment should read the companion's Part
directly). The derivation lives at a level most treatments never
visit: \emph{below quantization}, in the real geometry of the bulk's
solution spaces --- which is precisely why it can answer question
(ii) above, where the twin first exists.

\paragraph{The two real structures.} Recall the two non-spatial
directions of the bulk (Part~\ref{part:II}): the compact phase circle
$\Stheta$ and, on the 4D boundary, causal time. Each, independently,
equips the \emph{real} solution space of a charged bulk field with a
complex structure --- a real operator squaring to $-\mathbf{1}$:

\begin{description}[leftmargin=2.2em,itemsep=2pt]
\item[The circle (T-P5-A).] On each charge-$n$ sector, the
charge-normalized circle generator is a complex structure: rotating
the compact phase by a quarter turn \emph{is} multiplication by $i$,
and complex conjugation is orientation reversal of the circle,
$\theta \mapsto -\theta$. It is the unique such structure commuting
with the circle action --- up to sign. On neutral (weight-zero)
sectors it acts as zero: \emph{the circle can only complexify what it
moves}.
\item[The clock (T-P5-B).] On the same real solution space, the polar
phase of the time-translation generator is a complex structure ---
the positive-frequency splitting of the field, selected uniquely by
the positivity clause of the cohort's axioms. This is the $i$ of the
state space: the one quantization needs.
\end{description}

\paragraph{The handshake (T-P5-C).} Two independently forced
structures on one space must either agree or clash. The computation
that decides it is two lines, and worth performing once. An on-shell
mode of charge $n$ and energy $E>0$ is the real oscillation with
total dial angle $n\theta - Et$, i.e.\ $u_{+} = \cos(n\theta - Et)$.
The circle turns the fiber: $\cos \mapsto -\sin$. The clock advances
the phase a quarter period: $\cos \mapsto -\sin$. \emph{They agree}
--- but only on the pairing that puts charge $+n$ \emph{and} charge
$-n$ both at positive frequency; on the opposite pairing they
anti-agree. The Feynman--St\"uckelberg pairing is therefore not a
convention of quantization but the unique orientation under which two
independently forced real structures act as one complex structure on
shell. In the companion's summary: \emph{the existence of
antiparticles is the consistency condition between the sixth
dimension and causal time.} That answers (i). And because the whole
argument runs on real solution spaces, before any operator is
introduced, it answers (ii): the twins exist in the bulk, as real
geometric content, prior to quantization --- the descent to the
boundary only relabels them. For fermions, the further factorization
theorem (T-P5-C2) makes the charge flip \emph{definitional}: the
conjugate readout is the reversed winding, not a second postulate.

\paragraph{Physics intuition.} A charged mode is a single real wave
carrying one dial angle, $n\theta - Et$: so much circle, so much
clock. There are exactly two ways to read a dial --- clockwise and
counterclockwise --- and a reader who reverses \emph{both} the circle
and the clock sees the same wave with the labels flipped: opposite
winding, same energy. The twin is not a second wave; it is the second
way of reading the first one. Nature did not manufacture antimatter
to balance the books --- the books were written in real ink, and every
real oscillation admits two orientations of the same rotation. That
is why the twin was \emph{unavoidable} for Dirac: his equation was
the first place the circle and the clock were forced to agree in
public.

\section{The positron: the same electron, read in the mirror}
\label{sec:q6-readout}

Now return the imported theorems to this paper's landscape, where the
sixth question meets the first.

Part~\ref{part:III} established one basin: the electron is the unique
\GGA{} of the charged-lepton stratum --- one deepest valley, one set
of derived values, no second place for charged matter to rest. The
handshake supplies the missing half of the picture: every reading of
that basin comes in two orientations. The positron is \emph{the
conjugate readout of the same basin} --- the same level of the same
valley (hence exactly the electron's mass), read with the winding
reversed (hence exactly the opposite charge, by T-P5-C2's
factorization), with the spinor half of the statement carried by the
quaternionic structure of Eq.~\eqref{eq:spin15} applied to the
conjugate orientation (the remark of \S\ref{ssec:value-spin}, now
given its proper home). What the framework forbids --- what
Part~\ref{part:III}'s uniqueness theorem actually says --- is a second
\emph{basin}, not a second \emph{orientation}. One object; two ways
of reading it.

Three consequences repay attention; the first is the deepest.

\paragraph{Mass equality is trivial, not enforced.} In the standard
account, $m_{e^+} = m_{e^-}$ is an exact relation between two objects,
policed by the CPT theorem: Depth-2 knowledge, a constraint on a
pair. In the readout picture there is no pair to constrain --- where
there are not two things, nothing can differ. The most precisely
verified equality in particle physics is exposed as the least
surprising: it has the same status as the statement that a valley is
as deep read clockwise as counterclockwise. The economy is identical
to Q1's: identity was dissolved by counting objects correctly (one
attractor, many readouts), and the twin dissolves the same way (one
attractor, two orientations). \emph{The sixth question collapses into
the first.} Every electron is the same electron; the positron is the
same electron, read in the mirror.

\paragraph{The charge flip is definitional.} The positron does not
\emph{happen} to carry $+e$; the conjugate readout \emph{means} the
reversed winding, and charge is winding (Part~\ref{part:III}). Asking
why the positron's charge is exactly opposite is asking why the
reverse of a left turn is a right turn.

\paragraph{The daily-life anchor.} Positron-emission tomography is
conjugate-readout physics practiced in hospitals: a proton-rich
nucleus converts, the emitted positron thermalizes within millimeters
and meets an electron, and the pair annihilates into two back-to-back
511~keV photons --- the basin level of Part~\ref{part:III}, read out
twice with opposite orientations and returned to the field as pure
energy. Every PET image is, in this paper's terms, a tomogram drawn
in annihilation events of the one basin's two readings; the machine
works \emph{because} the twin is exact. (Wheeler's famous one-electron
fancy --- every electron and positron as one world-line zig-zagging
through time --- was, on this reading, a true instinct expressed one
level too literally; the companion paper records the contact.)

\paragraph{Why, then, a matter world?} If the twin is exact, why is
the universe made of electrons rather than an even mix? That is the
third of the three questions in the one coat, and it leaves the
electron's scope: the cosmic preference for one orientation is the
baryogenesis-and-leptogenesis chain, treated in the companion papers
(\citealp{ArisakaP5CPT}; \citealp{ArisakaA10Cosmos}). This paper
imports only the local statement: nothing about the boundary readout
of the electron's basin prefers one orientation --- the preference is
cosmological history, not lepton structure.

\section{Closed and fenced: the Q6 status}
\label{sec:q6-status}

Per the discipline of \S\ref{sec:status-table}, the sixth question's
answer is priced line by line.

\begin{table}[ht]
\centering
\caption[Q6: what is imported, what is interpretive, and what is owed.]{The Q6 status table: what is imported at theorem grade, what
is interpretive, and what remains owed. Tag vocabulary as in
\S\ref{sec:status-table}; the per-step registry rows are in
Appendix~\ref{app:ledger}. The three columns separate what is carried in at theorem grade from what is a reading of it and what remains owed --- Q6 being the question where those three are easiest to confuse with one another.}
\label{tab:q6-status}
\small
\renewcommand{\arraystretch}{1.25}
\begin{tabular}{@{}p{0.42\textwidth}p{0.13\textwidth}p{0.33\textwidth}@{}}
\toprule
\textbf{Statement} & \textbf{Status} & \textbf{Source} \\
\midrule
For every charged field, a twin of equal mass and opposite charge ---
forced, not chosen & THM (imported) & \PaperPFive{} T-P5-A, T-P5-B,
T-P5-C \\
\addlinespace
The twin exists in the real bulk, before quantization; the descent
only relabels it & THM (imported) & \PaperPFive{}, same chain \\
\addlinespace
For fermions the charge flip is definitional: conjugate readout $=$
reversed winding & THM (imported) & \PaperPFive{} T-P5-C2 \\
\addlinespace
The positron is the conjugate readout of the \emph{same} electron
basin (no second basin) & INT (named) & this Part,
\S\ref{sec:q6-readout}; \PaperPFive{}'s reading, adopted \\
\addlinespace
Promotion of that reading to a proved corollary of the bulk spinor
structure & OWED & D-P3-4 (\S\ref{sec:open}), unchanged \\
\bottomrule
\end{tabular}
\end{table}

\emph{What the fence does and does not cover.} The \emph{origin} of
the twin is no longer owed: existence, bulk-level residence, mass
equality, and the definitional charge flip are imported theorems. The
open residue is exactly one step --- proving, from the quaternionic
spinor structure of Eq.~\eqref{eq:spin15} applied to the conjugate
orientation, that every statement of Part~\ref{part:III} carries over
verbatim to the reversed reading: same basin level, same absence of
exit gates, spinor content conjugated and nothing else. That is
D-P3-4, registered before this Part existed and deliberately left
open by it: an honest chapter does not close its own fence by
enthusiasm.

\emph{The falsifier face.} The reading is exposed wherever the twins
could differ. The current precision record: the electron--positron
mass difference is bounded at $|m_{e^+}-m_{e^-}|/m < 8\times10^{-9}$
(90\% C.L., from positronium spectroscopy \citealp{Fee1993}); the
charge sum at $|q_{e^+}+q_{e^-}|/e < 4\times10^{-8}$
\citep{Hughes1992}; and the $g$-factors agree at
$(g_{e^+}-g_{e^-})/g = (-0.5\pm2.1)\times10^{-12}$, from the Penning
trap \citep{VanDyck1987} --- among the sharpest null tests in physics.
For the standard account these are tests of the CPT theorem; for this
Part they are sharper than that: a \emph{confirmed} asymmetry in any
of them would falsify not merely a symmetry of the pair but the claim
that there is no pair --- the conjugate-readout reading dies first,
before CPT does. The exposure is permanent, two-sided, and running in
laboratories now: the sixth question's answer, like the other five,
can be shot every day it stands.

After all, the century did not fail to answer the sixth question; it
answered it so well, so fast, that no one noticed the answer was a
description. The equation predicted the twin. It took the geometry to
say what the twin is: the same electron, read the other way around.


\section[Part~V in plain English]{Part~V in plain English: the one question that was answered before it was asked}
Five of these questions were asked early and then filed away. The sixth has the opposite history: it was answered in 1928, before anyone had properly asked it, and the answer was so spectacular that physics mistook it for an explanation for ninety years.

Dirac's equation returned more than it was asked for --- a mirror family of states that could be neither discarded nor tolerated --- and the resolution, that the mirror states are antiparticles, was confirmed by a photograph four years later. It is one of the great predictions in the subject and nothing here diminishes it.

But ``the equation requires it'' is a consistency argument, not a derivation. It establishes that the twin must exist; it does not say why the mathematics had a twin in it to begin with. This Part offers the missing half: the positron as the conjugate readout of the same basin, forced by the same geometry that fixes the electron. The status table at the end of the Part is unusually explicit about which parts of that are theorem-grade, which are readings of a theorem, and which are still owed --- because Q6 is the question where those three are easiest to confuse.

\GGPart[Pointlikeness]{Pointlikeness from Non-Spatial Structure}{Why the electron is a point in space and nowhere else (Q4 --- the new derivational core)}
\label{part:VI}

\section{The century of the point: from crisis to construction}
\label{sec:point-history}

Q4 is the only one of the six questions that was historically a
\emph{crisis} rather than a gap. The classical electromagnetic self-energy
of a point charge diverges linearly with the cutoff radius; at the
classical electron radius $r_e = e^2/(4\pi\epsilon_0 m_e c^2) \approx
2.8\times10^{-15}$~m the field energy alone exhausts the mass. Abraham
\citep{Abraham1903} and Lorentz \citep{Lorentz1909} built extended-electron
models and met the stability problem: a ball of charge explodes. Poincar\'e
\citep{Poincare1906} introduced the non-electromagnetic stresses that bear
his name to hold it together, at the price of an unexplained new force.
Dirac's 1938 classical theory \citep{Dirac1938} sharpened the point-charge
dynamics into the Lorentz--Dirac equation with its runaway solutions and
pre-acceleration --- pathologies that remain textbook material today. The
discovery of spin made the crisis worse: a classically spinning sphere of
any radius compatible with scattering data needs superluminal surface
speeds to carry $\hbar/2$ (the observation is as old as the proposal of
spin itself; \citealp{UhlenbeckGoudsmit1925}).

Quantum field theory did not resolve this crisis; it \emph{sidestepped} it.
Renormalization \citep{Tomonaga1946,Feynman1949,Dyson1949} keeps the
bare-point ontology and absorbs the infinity into a redefinition of
parameters, the program detonated by the 1947--48 measurements of
the Lamb shift and the moment anomaly
\citep{LambRetherford1947,KuschFoley1948}. The procedure is consistent and
spectacularly predictive, but as an answer to ``why is the electron
pointlike, and why does that not cost infinite energy?'' it answers ``by
construction, and because we subtract it.'' Meanwhile experiment has made
the point sharper than any theory required: no substructure has appeared
in $e^+e^-$ contact-interaction searches, with compositeness scales
excluded into the multi-TeV range \citep{EichtenLanePeskin1983,
ALEPH2006}, corresponding to structural radii below
$\sim10^{-19}$--$10^{-20}$~m (the precise figure is model-dependent, and
we deliberately do not quote a sharper one); and the electron magnetic
moment agrees with the QED prediction for a structureless point at the
$10^{-13}$ level \citep{Fan2023}, the argument by which Dehmelt assigned
the electron an ``intrinsic radius'' bound orders of magnitude below the
scattering bounds \citep{Dehmelt1988}, via the substructure analysis
of \citet{BrodskyDrell1980} --- itself model-dependent, as
Dehmelt knew and said. The Standard Model's verdict stands: the electron
is pointlike by construction, to the best precision ever attained, for no
stated reason.

\section{What AX-2 makes a particle: two charges on one composite connection}
\label{sec:ggep-particle}

Before the non-spatial-structure argument, we state the constitutional
foundation that this Part --- and, it will turn out, Part~\ref{part:VII}
--- stands on, because the pointlikeness answer is not an observation
about the electron; it is a consequence of what, under AX-2, a particle
\emph{is}.

AX-2 (\GGEP{}, the Geometry--Gauge Equivalence Principle) declares that
the primitive field of physics is a \emph{single composite
geometry-plus-gauge connection} on the bulk
\citep{ArisakaA1Constitution}: quantum and gauge structure are
geometrized, not appended, and the composite object
$\cA_{\rm tot} = \omega \oplus A$ --- the spin connection of the metric
together with the gauge connection --- is the whole of the world's
structural content (\ASix{}'s TGG pillar; the full deployment is
\AFive{}'s Part~VI, which this section and
Appendix~\ref{app:Q5} reproduce in digest \citep{ArisakaA5GDOS}). The
consequence for matter is exact and exhausting: a matter excitation
couples to the world through the minimal worldline Lagrangian
\begin{equation}
\mathcal L \;=\; \tfrac12\,m\,g_{\mu\nu}\,\dot x^\mu \dot x^\nu
\;+\; q\,A_\mu\,\dot x^\mu ,
\label{eq:ggep-worldline}
\end{equation}
and through nothing else --- one coupling to the metric sector,
weighted by the mass-energy $m$, and one to the gauge sector, weighted
by the holonomy charge $q$. Varying Eq.~\eqref{eq:ggep-worldline}
yields the single unified equation of motion of \AFive{}'s Part~VI,
\begin{equation}
\boxed{\;
m\Bigl(\ddot x^\mu + \Gamma^\mu_{\nu\lambda}\,\dot x^\nu\dot
x^\lambda\Bigr) \;=\; q\,F^\mu{}_{\nu}\,\dot x^\nu ,
\;}
\label{eq:unified-eom}
\end{equation}
in which the left side is the curvature of the metric (gravity, carried
by the scale dimension) and the right side is the curvature of the
gauge connection (electromagnetism, carried by the phase dimension):
one trajectory, two curvatures, no force ever postulated.

Three consequences carry this Part. \emph{First}, the electron's entire
4D interface with the world is exhausted by the data that contract with
the two curvatures: the mass $m$, the charge $q$, and the spin label
that fixes how its spinor rides the connection --- the spin entering
not as a third term in Eq.~\eqref{eq:ggep-worldline} but through the
spinor's parallel transport along the same composite connection:
connection coupling again, not a new slot. There is no fourth slot. \emph{Second}, each of those data is \emph{connection data}, not
matter distribution: $q$ is the integer-quantized holonomy momentum on
$\Stheta$ (charge quantization is the compactness of the phase circle);
$m$ is the \GFF{} level set by the dyadic depth along $\Ir$
(Appendix~\ref{app:Q1}); the spin label is the double-cover tag of the
bulk spinor group (Eq.~\ref{eq:spin15}). \emph{Third} --- and this is
the reorientation that dissolves Q4 --- a ``spatial charge
distribution'' is not a suppressed feature of such a particle; it is
\emph{not a variable of the theory's matter sector at all}.
Equation~\eqref{eq:ggep-worldline} has no slot in which a profile
$\rho(\vec x)$ could be written. The century asked ``why is the
electron's size zero?''; under AX-2 the prior question is ``what made
us expect a size?'' --- and the answer is that pre-\GGEP{} physics
mistook the two connection charges for properties of a material body,
and then went looking for the body. Status: the worldline coupling
\eqref{eq:ggep-worldline} and the unified equation
\eqref{eq:unified-eom} are reproduced from \AFive{}'s Part~VI, where
both chains are derived in full from the 6D bulk; AX-2 itself is a
constitutional axiom, and we say so.

\paragraph{Physics intuition.} Think of how general relativity retired
the question ``what pulls the apple?'' --- nothing pulls it; the apple
follows the geometry, and ``gravitational force'' is bookkeeping for
that. AX-2 performs the same retirement for ``what is the charged
body?'': there is no body to which charge is attached; there is a
worldline whose two couplings to the one composite geometry are what
we had been calling mass and charge. The electron is not a small
charged sphere that mysteriously lost its radius. It is a pure
position in spacetime dressed with two integers' worth of connection
data --- and a position has no size to lose.

\section{Structure along \texorpdfstring{$\Ir$}{I\_r} and \texorpdfstring{$\Stheta$}{S1\_theta}}
\label{sec:nonspatial}

\S\ref{sec:ggep-particle} said why no size is \emph{written into} the
electron: the worldline couples through two charges, and a spatial
profile is not a variable of the matter sector. This section says
where the electron's structure actually \emph{lives} --- because the
electron is not structureless; it is rich with structure, every bit of
it along directions that are not space. In the six-dimensional
bulk of \ATwo{}, the two non-boundary directions are not
spatial: Theorem~1 of \ATwo{} forces the bulk $\cM_6 = \cM_4 \times \Ir
\times \Stheta$ where $\Ir$ is the geometrized scale (RG-flow) direction
and $\Stheta$ the compact phase direction \citep{ArisakaA2GG6}. Neither
$\Ir$ nor $\Stheta$ is a small spatial circle in the Kaluza--Klein sense
the words might suggest; they are directions of \emph{scale} and of
\emph{phase} --- not space, but geometry --- orthogonal to space not in
the way a fourth spatial axis would be but categorically.

The electron's structure --- everything about it that is rich, organized,
and worthy of the word --- lives entirely along those two directions. Its
dyadic seam depth $2^{J} = 128$, the integer that sets
$\alphainv(M_Z)$ and the denominator $2^{J+L+1}$ of its Yukawa
(Eq.~\ref{eq:ye}), is a coordinate along $\Ir$; its $\mathrm{U}(1)$
winding, the integer that quantizes its charge, is a coordinate along
$\Stheta$; its cascade depth (the basin label of
Eq.~\ref{eq:lepton-chain}) indexes its position in the \GFF{} landscape
hung over those directions. The constant-absorption lineage of \AFour{}
\citep{ArisakaA4Euclid} tells the same story from the side of the
constants: what look like dimensionful mysteries in 4D are bookkeeping
along the scale direction.

\paragraph{Physics intuition.} What is it like for a direction to be
``scale''? Every graduate student has already moved along $\Ir$:
Wilsonian renormalization --- block-spin, coarse-grain, zoom --- is
motion along a scale axis, and the scale profile $e^{-2r}$ of the
canonical metric is that zoom written as geometry. The electron's
dyadic depth $2^{J}$ is a position along this axis in the same sense
that ``the physics at 1~GeV'' is a position on an RG trajectory --- a
location in \emph{resolution}, not in any room. The contrast with
Kaluza--Klein is then sharp: a KK theory asks how far around a small
circle in space a mode wraps, and gets a tower of spatial echoes; the
\GG{} question asks how deep in resolution a configuration sits, and a
depth leaves no echo in space. Only the first question leaves
footprints in a form factor.

We register the structural statement as a proposition with proof by
citation, because every ingredient is an established cohort theorem ---
and we name what it does \emph{not} yet say.

\begin{proposition}[Non-spatial support; status: assembly of A2/A4/A9
theorems (T-Electron-3)]
\label{prop:nonspatial}
Every structural attribute of the electron --- its mass (a \GFF{} basin
level over the scale direction), its charge (a winding integer on
$\Stheta$), its spin label (a quaternionic double-cover label of the bulk
spinor group, Eq.~\ref{eq:spin15}), and its dyadic depth $2^{J+L+1}$ ---
is a coordinate along the non-spatial directions $\Ir$, $\Stheta$ or a
label of the bulk group action. No structural attribute of the electron
is a function on 4D space.
\end{proposition}

If the electron's structure has no spatial component, then space, looking
at the electron, finds nothing to resolve. That is the intuition. But an
intuition is not a form factor, and the distance between them is the
honest work of this Part. The gap is real: \ATwo{} contains no theorem
that converts Proposition~\ref{prop:nonspatial} into a statement about
scattering experiments. We construct that statement now; the one locality
property it requires turns out to be supplied by the constitution
itself.

\section{Mass without self-energy; spin without spinning}
\label{sec:mass-spin}

Before the form factor, the two dissolutions that
Proposition~\ref{prop:nonspatial} already licenses.

\paragraph{Mass without self-energy.}
The classical crisis of \S\ref{sec:point-history} assumed that the
electron's mass is energy stored in the 4D field surrounding a point ---
an integral $\int \tfrac{\epsilon_0}{2}|E|^2\,d^3x$ that diverges as the
support shrinks. In \GGTheory{} that integral never appears: $m_e$ is the
\GFF{} level of the ground basin (\S\ref{ssec:value-mass}), a property of
the landscape over the non-spatial directions, not of any 4D field
configuration. There is no self-energy to regulate because the mass was
never self-energy. The Poincar\'e stresses are not explained; they are
\emph{unemployed}. We flag the claim's status precisely: this is a
dissolution (the problematic quantity is shown never to arise), not a
calculation of radiative corrections within QED, whose renormalized
perturbation theory remains the correct effective description on the
boundary and is untouched here.

\paragraph{Spin without spinning.}
The spin paradox assumed that $\hbar/2$ of angular momentum must be
carried by rotation of a spatial mass distribution. Equation
\eqref{eq:spin15} replaces the picture: the electron's spin label is the
quaternionic double-cover label of $\mathrm{Spin}(1,5)$ acting on the
boundary --- group-theoretic data of the bulk readout, not kinematics of
a body. Nothing rotates, so no surface speed exists to exceed $c$. The 4D
observer who insists on a rotation finds exactly the paradox history
records, because the rotation was never there: spin is the boundary shadow
of a bulk algebra whose ``$\tfrac12$'' counts the double cover, not a
revolution rate. Status: the group identification is A2's theorem; the
``shadow'' reading is interpretive language for the boundary projection of
\AEight{}, and we mark it as such.

\section{The pointlikeness theorem and its observable shadow}
\label{sec:formfactor}

\subsection{What must be proved --- and what merely follows}
The question of this Part is geometric --- does the electron have
spatial structural support beyond a point? --- and its answer, built
in \S\ref{sec:ggep-particle}--\S\ref{sec:mass-spin}, is
constitutional. Experiment, however, accesses that geometry through
one interface: a scattering experiment measures the charge form factor
$F(q^2)$, and ``pointlike'' reaches the laboratory as
$F(q^2) = 1$ at all accessible spacelike momentum transfers, equivalently
the vanishing of every structural radius moment, beginning with
$\langle r^2 \rangle = -6\,\hbar^2\, dF/dq^2|_{q^2=0} = 0$. (Throughout,
$F$ denotes the \emph{structural} form factor: the Standard-Model
radiative dressing of a point vertex --- vacuum polarization, the
anomalous moment $a_e$ --- is calculable, observed, and not at issue; a nonzero $a_e$ is not
substructure, which is why Dehmelt's $g-2$ radius argument needed a
compositeness \emph{model} to convert precision into femtometers
\citep{Dehmelt1988}.) Compositeness models predict $F(q^2) = 1$ only below
their binding scale $\Lambda$, with deviations of order $q^2/\Lambda^2$
appearing at the scale of the constituents
\citep{EichtenLanePeskin1983}. The \GGTheory{} claim must therefore be:
$F \equiv 1$ \emph{identically, at every scale, forever}.

\paragraph{Physics intuition.} A form factor is a ruler made of
wavelength. Rutherford's point-charge cross-section is dressed, for an
extended target, by $F(q^2)$ --- in the static limit the Fourier
transform of the charge distribution --- so scattering at momentum
transfer $q$ asks: does the target look different at resolution
$\hbar/q$? The proton answers \emph{yes}, with a slope at $q^2 = 0$
giving its $\approx 0.84$~fm charge radius; nuclei answer \emph{yes}
with diffraction minima; the electron, probed to scales more than four orders of
magnitude below the proton's, has only ever answered \emph{no}.
Theorem~\ref{thm:pointlike} is the claim that nature's answer is
\emph{no} at every $q$ there will ever be --- the experimental record
to date promoted from streak to law.

\subsection{The derivation, and the constitutional step that closes it}
\label{ssec:derivation-attempt}
Proposition~\ref{prop:nonspatial} gives the bulk-side fact: the electron
configuration carries no structural data along $\cM_4$. The missing step
is boundary-side: the form factor is a property of the \emph{readout} ---
the \OGGEP{} bulk-to-boundary projection (= the operational form of the
geometry--gauge equivalence principle: the map by which bulk
configurations register as 4D boundary events; \AEight{}'s framework). If the readout map itself
smeared bulk configurations over a 4D length scale $\ell$ (an instrumental
resolution of the bulk--boundary correspondence, so to speak), scattering would
measure $F(q^2) \ne 1$ at $q \sim \hbar/\ell$ \emph{even though the
electron has no spatial structure}, and conversely. The derivation
therefore requires a locality property of the readout map. The
constitution supplies it. AX-1 (LC: Locality and Causality) of \AOne{}
is formulated, by explicit constitutional clarification, for open
systems --- LC ``must hold for open evolution maps and measurement
instruments, not only for closed unitary dynamics'' --- and its
microcausality clause attaches admissible observables to \emph{points}
of the manifold, excluding fundamental extended structure. Imposed
strictly on the registration channel, AX-1 yields the required property
as a lemma:

\begin{lemma}[RL --- Readout Locality; status: derived from AX-1]
\label{post:RL}% label kept from v1.0 for cross-reference stability
The \OGGEP{} bulk-to-boundary readout map introduces no 4D length scale:
the registration of a bulk configuration at a boundary point is local in
the boundary coordinates, with any apparent extension of the readout
bounded by the wavelength of the probe, not by any property of the
registered configuration.
\end{lemma}

\begin{proof}[Proof (channel level; full version in
Appendix~\ref{app:formfactor}, Step 2)]
AX-1 binds the readout itself: its constitutional statement quantifies
over ``every admissible boundary intervention protocol'' and requires
registered boundary records to depend only on data in the causal past,
with acausal effective kernels inadmissible; its constitutional
clarifications extend this to open evolution maps and measurement
instruments, and attach admissible observables to points
(microcausality) \citep{ArisakaA1Constitution}. A registration kernel
carrying an intrinsic 4D length $\ell_{\rm hol}$ must place support
either at spacelike separation --- barred directly by the constitutional
statement --- or along the causal past, as retarded memory. Retarded
memory is admissible but generates no equal-time spacelike profile:
causal response disperses in frequency, while the static structural
form factor probes equal-time spacelike correlations only. Hence no
admissible readout supplies a spacelike scale; and the probe-wavelength
clause of the statement is then the operational restatement of
scale-freedom --- with the registration scale-free, the only length
present in a registration event is the probe's own. The formalization
of the static-limit step in the \OGGEP{} channel formalism is
registered as open problem D-P3-1.
\end{proof}

One honesty note accompanies the lemma. AX-1 is an axiom, and a reader
who rejects the constitution receives Theorem~\ref{thm:pointlike} in
conditional form --- exactly as every theorem of this cohort is
conditional on its declared axiom system. What a reader may \emph{not}
conclude is that pointlikeness has thereby been answered by fiat:
Appendix~\ref{app:formfactor} (Step 2, first Remark) prices precisely
what AX-1 contributes (point-attachment of observables), what it cannot
contribute alone (the dissolution of the self-energy crisis, and the
permanence of structurelessness at every scale --- which require
Proposition~\ref{prop:nonspatial} and the lemma jointly), and why the
result differs in observable content from the Standard Model's
``pointlike by construction.''

\begin{theorem}[Pointlikeness; status: theorem, by AX-2 coupling
completeness, Proposition~\ref{prop:nonspatial}, and
Lemma~\ref{post:RL} from AX-1 (T-Electron-4)]
\label{thm:pointlike}
The electron's structural support in the boundary spatial directions
is exactly a point: no structural length exists anywhere in the
chain that registers it --- not in the matter coupling (AX-2,
Eq.~\ref{eq:ggep-worldline}, which has no profile slot), not in the
structural data (Proposition~\ref{prop:nonspatial}: all of it lies
along $\Ir$ and $\Stheta$), and not in the readout
(Lemma~\ref{post:RL}). Consequently --- as pure Fourier bookkeeping,
the transform of a point being flat by definition --- the structural
form factor is identically unity, $F(q^2) = 1$ at every momentum
transfer however large: every structural radius moment vanishes
exactly, and no substructure exists at any spatial scale.
\end{theorem}

\begin{remark}[On the status of the form factor]
\label{rmk:ff-status}
The reader should be clear about what role $F$ plays in this paper,
because it is \emph{not} the role it has played for forty years of
compositeness searches. In a framework with no first-principles
account of pointlikeness, the form factor is the primary object ---
all one can do is measure bounds and push $\Lambda$ upward. In the
present framework the logic runs the other way: the point is a
constitutional theorem, and once both its sides are closed --- the
object by AX-2 and Proposition~\ref{prop:nonspatial}, the
registration by Lemma~\ref{post:RL} (the one step the ``flat by
definition'' shorthand silently assumes) --- the flat form factor
carries no further physics. We retain $F$ for exactly one reason:
falsification must name an observable, and experiment speaks $F$.
It is the theorem's shadow on the laboratory wall, and kill criterion
F2 watches that shadow; the theorem itself lives upstream, in the
geometry.
\end{remark}

\begin{proof}[Proof sketch]
By \S\ref{sec:ggep-particle}, the structural vertex is already the
point vertex of Eq.~\eqref{eq:ggep-worldline}: AX-2's matter coupling
has no slot for a profile (constitutional Step 0). What remains, for
the Fourier corollary to be licensed, is to exclude scale generation
by kinematics or by the readout.
A deviation $F(q^2)\ne1$ requires a length scale: $F$ is dimensionless in
$q^2\,\ell^2$ for some $\ell$ characterizing either the probed object or
the probing channel. By Proposition~\ref{prop:nonspatial} the electron
supplies no such $\ell$ (its structural scales $2^J$, depth, winding are
dimensionless coordinates along non-spatial directions, and the basin
level $m_e$ enters kinematics, not structure); by Lemma~\ref{post:RL} the readout supplies none. A function of $q^2$ with no scale and the normalization $F(0)=1$
(charge seen whole at zero momentum, which is charge quantization,
\S\ref{ssec:value-charge}) is identically 1. The full argument, including
why the scale profile of the canonical metric cannot smuggle in a scale and
the comparison with the Kaluza--Klein case (where genuinely
\emph{spatial} extra dimensions do produce form-factor towers), is Appendix~\ref{app:formfactor}.
\end{proof}

\subsection{The sharp edge}
\label{ssec:sharp-edge}
Theorem~\ref{thm:pointlike} has a falsifiable edge that no compositeness
model shares and no agnosticism can blur, and we pre-register it in the
strongest available form: \emph{no substructure will ever be found, at any
spatial scale, by any probe, at any energy}. Every compositeness model
predicts a scale at which structure appears; \GGTheory{} predicts that the
present experimental situation --- structurelessness to the limit of every
probe --- is exact and permanent. \figref{fig:formfactor} draws the
contrast: every rival picture owes structure at \emph{some} scale; this
one owes structurelessness at \emph{all} of them.

\begin{figure}[ht]
\centering
\resizebox{0.676\textwidth}{!}{%
\begin{tikzpicture}[
 yscale=1.45,
 font=\small,
 arr/.style={->, line width=0.80pt, draw=black!70},
 lab/.style={font=\footnotesize, align=left}
]
%% axes
\draw[arr] (0, 0) -- (0, 5.2) node[anchor=south] {$|F(q^2)|$};
\draw[arr] (0, 0) -- (12.6, 0);
\node[font=\footnotesize\itshape, anchor=north east] at (12.4, -0.42)
 {momentum transfer $q$ (schematic, logarithmic) --- resolution $\hbar/q$ sharpens $\to$};
\node[anchor=east, font=\footnotesize] at (-0.08, 4.0) {$1$};
\draw[black!40, dashed] (0, 4.0) -- (12.2, 4.0);
%% experimental reach band
\fill[black!12] (6.3, 0) rectangle (6.55, 4.0);
\node[anchor=east, font=\footnotesize] at (-0.08, 0) {$0$};
%% proton curve (dipole-like fall)
\draw[line width=1.0pt, draw=black!55] plot[smooth, samples=80, domain=0:7.5]
 (\x, {4.0/((1+(\x/1.6)^2)^2)});
\node[lab, text=black!55, anchor=west, align=left] at (2.8, 2.5)
 {proton: $F$ falls ---\\ structure at $\langle r^2\rangle^{1/2} \approx 0.84$ fm};
\draw[-{Stealth[length=2mm]}, draw=black!55] (2.75, 2.3) -- (1.8, 1.25);
%% composite-electron curve (flat then falls at Lambda)
\draw[line width=1.0pt, draw=red!70!black, dashed] plot[smooth, samples=80, domain=0:12.0]
 (\x, {4.0/((1+(max(\x-8.2,0)/0.9)^2)^2)});
\node[lab, text=red!70!black, anchor=west, align=left] at (9.6, 2.9)
 {composite electron:\\ structure appears at\\ \emph{some} scale $\Lambda$};
\draw[-{Stealth[length=2mm]}, draw=red!70!black] (9.55, 2.5) -- (9.05, 1.7);
%% GG line: F == 1 forever
\draw[line width=1.6pt, draw=blue!60!black] (0, 4.0) -- (12.2, 4.0);
\node[lab, text=blue!60!black, anchor=south west] at (2.6, 4.22)
 {\textbf{\GGTheory{}: $F \equiv 1$ at every scale, forever} (the Pointlikeness Theorem)};
\node[lab, anchor=west, text=black!60, align=left] at (2.6, 1.15)
 {experimental reach to date\\ (contact-interaction scales $\mathcal{O}(10)$ TeV)};
\draw[-{Stealth[length=2mm]}, draw=black!60] (5.95, 1.15) -- (6.32, 1.05);
\node[lab, text=black!70, anchor=west, font=\scriptsize] at (3.6, 3.5)
 {every probe to date: no deviation from $1$};
\end{tikzpicture}%
}
\caption[Structural form factors compared, and the prediction $F \equiv 1$.]{The falsification interface of the pointlikeness theorem, drawn --- the theorem's ground is constitutional (\S\ref{sec:ggep-particle}); this figure shows its shadow on the laboratory wall. A structural form factor $F(q^2)$ answers the question ``does the target look different at resolution $\hbar/q$?'' The proton (gray) answers yes, with the fall-off encoding its $\approx 0.84$~fm charge radius. Every compositeness model (red, dashed) answers ``yes, eventually'': flat until its binding scale $\Lambda$, then structure --- the scale may be pushed up, but the model owes one. \GGTheory{} (blue) answers \emph{no at every scale, forever}: with the electron's structure entirely along the non-spatial directions and the readout scale-free by Lemma RL (from AX-1), $F \equiv 1$ identically. The gray band marks the current experimental reach; all curves are schematic. The first confirmed structural deviation, at any $q$, kills Part V outright (F2).}
\label{fig:formfactor}
\end{figure} Each extension of the contact-interaction
reach is a test; the first confirmed structural deviation in any electron
form factor kills this Part outright, with no parameter to retreat to
(Part~\ref{part:VIII}, F2). Q4, historically the question on which theories
of the electron died, is on this account the question on which the present
theory has agreed to die.

%% ===================================================================
%%  PART VI -- SENSING AS GFF DESCENT (Q5)
%% ===================================================================

\section[Part~VI in plain English]{Part~VI in plain English: how the electron can have structure and still be a point}
Of the six, this is the only question that was a crisis rather than a gap. A point charge has infinite field energy; a charge of finite size flies apart unless something holds it together. Abraham, Lorentz and Poincar\'e each tried, and each traded one problem for another. Renormalization made the infinity manageable without making it go away, and every graduate student is taught the subtraction and asked not to look at it too hard.

The proposal here is that the electron has structure and that none of it is in space. It is a point along the three spatial directions and extended along the two that are not --- the scale direction and the phase circle. That is not a rhetorical dodge, because it has a consequence any experiment can test: a form factor measures whether a target looks different at finer resolution, and a particle with no spatial extent must return a constant. The Part derives that constant and states the reach at which it would be falsified.

The reason the crisis was a crisis is that everyone assumed structure meant spatial structure. Drop the assumption and the mass needs no self-energy and the spin needs nothing spinning.

\GGPart[Why the electron moves]{Why the Electron Moves}{The phase fiber, the equivalence principle for charge, and force as geometry (Q5)}
\label{part:VII}

\section{The sixth dimension is the electromagnetic fiber: a circle over every point}
\label{sec:fiber}

Before any machinery, we state Q5's answer in the form a student can
carry out of the room, because the deepest part of it requires nothing
the reader does not already own.

Every graduate student knows that electromagnetism is a $\mathrm{U}(1)$
gauge theory: the phase of a charged field can be chosen freely and
independently at each point of spacetime, and the textbook
formalization of that freedom is a \emph{fiber bundle} --- over every
point of spacetime hangs a circle, and the electron's wavefunction
carries, at each point, a position on that circle. In the Standard
Model this circle is scrupulously ``internal'': an abstract
bookkeeping space, drawn in every textbook figure as a little ring
over spacetime and then immediately disclaimed as not really being
anywhere.

The constitutional move of \GGTheory{} --- AX-2, the Geometry--Gauge
Equivalence Principle \citep{ArisakaA1Constitution} --- is to stop
disclaiming the picture. The circle the textbooks draw is the sixth
dimension: $\Stheta$ \emph{is} the $\mathrm{U}(1)_{\rm EM}$ fiber,
attached to every point of $\cM_4$ exactly as gauge theory always
drew it (\figref{fig:bulk-cross-section}, the green circle).
Electromagnetism then needs nothing added to the world: the gauge
potential $A_\mu$ is the rule for comparing phase between neighboring
points --- the \emph{connection} of the bundle --- and the field
strength $F_{\mu\nu}$ is the failure of a phase to come home after
transport around a small loop --- the \emph{curvature}. A student who
has computed an Aharonov--Bohm phase has already measured this
geometry once, without being told that is what the measurement was.

Charge follows at once: the electron is charged because it
\emph{winds} around the fiber, and winding around a circle comes only
in integers --- charge quantization is the compactness of the sixth
dimension (\S\ref{sec:coupling}), Klein's century-old insight
\citep{Klein1926} promoted from curiosity to constitution.

Now the step that answers Q5, and it is Einstein's step taken a second
time. General relativity retired the question ``what pulls the
apple?'': nothing pulls it; mass-energy curves the stage, and the
apple follows the straightest available path. The equivalence
principle is what makes this possible --- the geometry is one geometry
for all bodies. AX-2 extends the very same principle from the metric
sector to the gauge sector: spacetime and the phase circle are not a
stage plus a decoration but \emph{one connected geometry}, described
by one composite connection. Consequently a winding particle's
straightest path through the \emph{combined} geometry bends in space
wherever the phase sector is curved, in proportion to its winding
number $q$ --- and an external electric field is precisely such a
curvature, whose spatial direction the bend inherits. The electron
``senses'' the field's direction because the local $\mathrm{U}(1)$
phase over its position is geometrically linked, through \GGEP{}, to
the phases over neighboring points: a proton nearby curves that
linkage, and the electron's geodesic leans toward it. Falling toward
a proton and falling toward the Earth are one phenomenon read on the
two sectors of one geometry --- which is exactly what the unified
equation of motion, derived in \S\ref{ssec:two-chains} and reproduced
in full in Appendix~\ref{app:Q5}, says with symbols:
$m(\ddot x^\mu + \Gamma^\mu_{\nu\lambda}\dot x^\nu\dot x^\lambda) =
q\,F^\mu{}_\nu\,\dot x^\nu$, metric curvature on the left, fiber
curvature on the right, no force anywhere.

\paragraph{Physics intuition.} Picture every point of space carrying a
small clock dial --- the fiber. The electron, being charged, reads the
dials as it travels: its quantum phase advances according to the
settings it passes. A proton nearby sets the neighboring dials
systematically askew, and that pattern of mis-setting \emph{is} the
electric field --- there is nothing else to it. The electron's
``straight'' path is the one along which its accumulated phase is
stationary (the reader who knows the path integral knows this is not
a metaphor but the classical limit of $e^{iS/\hbar}$ with the
minimal-coupling term $q A_\mu \dot x^\mu$ in $S$), and through the
askew dial field the stationary-phase path bends toward the proton.
No message is sent; no force is transmitted; the electron does the
only thing matter ever does --- it follows the geometry --- and its
charge merely sets how strongly its path attends to the dial sector.
After all, Einstein taught us in 1915 that ``force'' is what geometry
looks like when we forget to count a dimension; \GGTheory{}'s claim
is that electricity was the same lesson, waiting for the sixth.

\section{Existence, quantization, and value of the coupling}
\label{sec:coupling}

With the fiber picture of \S\ref{sec:fiber} in hand, Q5's bookkeeping
questions answer themselves in order, and the citations below are
records of where each step is proved rather than the argument itself.
The parts of the answer that
\GGTheory{} owns outright begin with the existence, the quantization, and the
value of the coupling. Existence: the boundary $\mathrm{U}(1)_{\rm EM}$ is
not postulated; it descends from the derived bulk gauge group of \ATwo{}
(its Theorem~3), and the photon's masslessness --- the reason the force is
long-range at all --- is the commutant statement of \ANine{}'s identity
section. Quantization: the winding-integer origin of charge
(\S\ref{ssec:value-charge}) is why every source couples in integer units --- in Chain (B)'s language (\S\ref{ssec:two-chains}), electric charge is the integer-quantized holonomy momentum on the compact phase circle, the Kaluza--Klein integer made constitutional. The force law itself follows in \S\ref{ssec:two-chains}.
Value: Eq.~\eqref{eq:alpha} --- $\alphainv(M_Z) = 2^{J} = 128$, completed
at zero momentum to the CODATA $137.036$ --- is the dyadic-closure
attractor coordinate: the number Sommerfeld introduced as an input in
1916 \citep{Sommerfeld1916}, the century's most famous unexplained
constant, produced by the same ledger that produced the mass. Status: codebook-level
(A9), with the non-primitivity of $e$ at theorem level (A4, T-Euclid-4).
We note for completeness that the two most precise atom-interferometric
determinations of $\alpha$ currently disagree at $>5\sigma$ (Rb:
\citealp{Morel2020}; Cs: \citealp{Parker2018}); the QD-completed
prediction is registered against CODATA 2022, and Part~\ref{part:VIII}
phrases the corresponding kill criterion so that the experimental dispute
cannot be mistaken for a fence of ours.

\section{The force law as composite geodesic motion}
\label{sec:force}

\S\ref{sec:fiber} stated the principle; this section shows it is not
a picture but a derivation. Both classical force laws descend,
step by checkable step, from the one bulk action --- the content of
\AFive{}'s Part~VI, reproduced in digest in Appendix~\ref{app:Q5} so
the reader can run every line without leaving this paper. The
foundation is \S\ref{sec:ggep-particle}'s AX-2 worldline.

\subsection{Two chains, one bulk}
\label{ssec:two-chains}
\AFive{}'s Part~VI derives, in deliberate parallel and in full
pedagogical detail, the two iconic inverse-square laws from the same
six-dimensional bulk. \emph{Chain (A)}: integrating the 6D
Einstein--Hilbert action over the phase circle (a factor $2\pi$) and
then over the scale interval (the scale-profile integral
$\int_0^K e^{-2r}dr$) yields four-dimensional general relativity \citep{Einstein1915} with
$M_{\rm Pl}^2 = \pi M_6^4 (1 - e^{-2K})$; the weak-field limit gives
Newton's potential \citep{Newton1687}, and the geodesic equation gives $F = ma$.
\emph{Chain (B)}: the gauge connection on the phase circle descends to
the 4D Maxwell action \citep{Maxwell1865}; minimal coupling
(Eq.~\ref{eq:ggep-worldline}) gives the Lorentz force; the static
Green's function of the 3D Laplacian gives Coulomb's law. The two
chains have the same starting point, the same number of steps, and
the same kind of endpoint --- and they converge on the single unified
equation of motion \eqref{eq:unified-eom}. Newton's law and Coulomb's
law are the same equation read on the two curvatures of one geometry:
this is the precise, derived realization of Einstein's unification
program --- the road Kaluza and Klein opened
\citep{Kaluza1921,Klein1926} --- and the gravity--electricity dictionary of
Appendix~\ref{app:Q5-dictionary} sets the parallel out term by term.

\subsection{The answer to Q5}
\label{ssec:q5-answer}
With the unified equation in hand, the question ``why does the
electron sense the field and move toward the proton?'' receives the
same kind of answer general relativity gave to ``why does the apple
fall?'' Nothing is transmitted to the apple; the apple follows the
metric. Nothing is transmitted to the electron; \emph{the electron
follows the composite connection}, of which the proton's presence has
shaped the gauge sector exactly as a mass shapes the metric sector.
``Sensing'' at the fundamental level is generalized free fall ---
motion on the one geometry that AX-2 says is all there is --- and the
electric force is not an influence the electron detects but the shape
of the electron's world. The three structural ingredients that make
the two laws twins --- a massless mediator protected by unbroken
symmetry, Gauss-law flux conservation in three spatial dimensions
(the same Green's function $-1/4\pi r$ on both sides), and a
conserved Ward-identity current ($T_{\mu\nu}$ for the metric sector,
$J^\mu$ for the gauge sector) --- are reproduced in
Appendix~\ref{app:Q5-ingredients}. Status: theorem-level within the
framework --- both chains are derived end-to-end in \AFive{}'s
Part~VI from the bulk action, with no force postulated anywhere ---
and constitutional at the root, since the unification \emph{is}
AX-2's content. Where the two laws differ (universal coupling to
mass-energy versus quantized coupling to holonomy charge; bulk-set
$G_N$ versus boundary-running $\alpha$) is itself derived, not
modeled.

\subsection{The division of credit, restated exactly}
\label{ssec:credit-restated}
The refined version of this paper's R4 sentence is the following.
\emph{The framework derives the force itself}: the existence,
masslessness, and inverse-square form of both laws; the quantization
of the charge that couples to one of them; the strength $\alpha$
(Appendix~\ref{app:Q1-alpha}); and the unified equation of motion in
which attraction and repulsion reside as the two signs of $q$ in
$qF^\mu{}_\nu\dot x^\nu$ --- the full classical Maxwell--Lorentz
system arrives derived, sign structure included, in Chain~(B).
\emph{QED owns the quantum reading of the sign rule}: that the
attraction of opposites and repulsion of likes is, at the mediator
level, the signature of spin-1 exchange (where spin-0 or spin-2 would
not flip the sign) is a theorem of relativistic quantum field theory
(see, e.g., \citealp{Weinberg1995}), restated inside the framework by
\ANine{}'s forces section, and credited here as before. Nothing in
this sharpened statement blurs the R4 line; it relocates the
boundary honestly --- the classical phenomenology is derived, the
quantum mechanism is QED's, and the framework's boundary theory
\emph{is} QED at accessible energies, so the two statements cohere.

\section{The open-system layer: what descends, and where}
\label{sec:sensing}

What remains of Q5 after \S\ref{ssec:q5-answer} is the open-system
question: where, in the physics of a charged particle, is there an
arrow of time? The answer requires a precision this paper initially
blurred, and we state it now in the form the two non-spatial
dimensions themselves dictate. \emph{The phase sector moves the
electron; the scale sector transmutes it.} Motion in space is the
$\theta$-sector geodesic of \S\ref{sec:fiber} --- conservative,
reversible, dissipating nothing: an external field curves the phase
connection over \emph{position space}, and the bend it produces is
not a descent of anything. Genuine \GFF{} gradient descent ---
\GRIPin{}, dissipative and irreversible --- lives in the
\emph{scale} sector: its landscape is the family stratum, not
position space; it transmutes its occupant ($\tau \to \mu \to e$,
Part~\ref{part:IV}) at a point, and it transports nothing. An
earlier reading of this paper identified spatial drift with \GFF{}
descent on a ``tilted landscape''; we withdraw that identification
here as mis-sectored --- the \textbf{INT} tag exists precisely so
that readings can be corrected without damage to theorems, and
nothing downstream depended on it.

\begin{remark}[Reading: the dissipative channel of motion is
radiation; status: interpretive; supersedes a withdrawn earlier reading]
\label{rmk:sensing}
Where, then, does open-system language properly attach to
\emph{motion}? At the one place energy actually leaves: radiation.
An accelerated charge sheds energy (Larmor's law,
\citealp{Larmor1897}; the classical reaction force of
\citealp{Dirac1938}), and it is this --- not the
conservative geodesic bend --- that gives the trajectory of a charged
particle its arrow: the classical orbit decays by radiating, the
excited atom relaxes to its ground state by the same channel, and in
\GDOS{} terms this radiative loss is the open boundary doing to
motion what \GRIPin{} does to particle identity --- carrying the
system downhill, here in orbital energy, there in basin level.
``Sensing,'' at theorem level, is \S\ref{sec:fiber}'s statement:
to be continuously registered against the local fiber geometry. The
open-system layer adds only the arrows, each in its own sector:
radiation for motion, \GRIPin{} descent for decay.
\end{remark}

\paragraph{Physics intuition.} Read a bubble-chamber photograph of a
muon with the two sectors in mind, and the whole of this Part is in
the picture. The track \emph{curves}: that is the sixth dimension ---
the phase fiber's curvature bending a conservative geodesic, no
energy lost to the bend. The track \emph{tightens} as it spirals:
that is dissipation --- radiation and ionization, energy leaving
through the open boundary. And the track \emph{ends} in a kink with
an electron flying on: that is the fifth-dimension sector ---
\GRIPin{} descent through a gate, at a point, transmuting the
occupant. Three phenomena, three readings, one geometry: the sixth
dimension bends the track, dissipation shrinks it, the fifth-dimension
descent ends it. The electron's own track differs in exactly one way
--- it has no endpoint (Theorem~\ref{thm:stability}) ---
\figref{fig:sensing-regimes} draws the two sectors side by side.

\begin{figure}[ht]
\centering
\resizebox{0.716\textwidth}{!}{%
\begin{tikzpicture}[
 font=\small,
 arr/.style={->, line width=0.80pt, draw=black!70},
 lab/.style={font=\footnotesize, align=center}
]
%% ---- left panel: drift within a basin --------------------------
\begin{scope}
\draw[line width=1.2pt, draw=black!80] plot[smooth, samples=60, domain=0:5.4]
 (\x, {0.30*(\x-2.4)*(\x-2.4) - 0.22*\x + 1.85});
\fill[blue!60!black] (1.45, {0.30*(1.45-2.4)*(1.45-2.4) - 0.22*1.45 + 1.85}) circle (2.2pt);
\draw[-{Stealth[length=2.4mm]}, line width=1.0pt, draw=blue!60!black]
 (1.7, 1.65) to[bend right=18] (2.9, 1.30);
\node[lab, text=blue!60!black, anchor=west] at (0.0, 2.85) {the geodesic bends\\ toward the source};
\draw[-{Stealth[length=2mm]}, draw=black!55] (4.6, 3.4) -- (3.9, 2.4);
\node[lab, text=black!65, anchor=south] at (4.6, 3.45) {the field curves the\\ phase fiber ($\theta$-sector)};
\node[lab, anchor=north, font=\footnotesize\bfseries] at (2.7, -0.45)
 {Response to a field: geodesic motion ($\theta$-sector)};
\node[lab, anchor=north, text=black!60] at (2.7, -0.95)
 {conservative, reversible --- the Lorentz force;\\ moves the electron, dissipates nothing};
\end{scope}
%% ---- right panel: hop through a gate ----------------------------
\begin{scope}[xshift=7.6cm]
\draw[line width=1.2pt, draw=black!80] plot[smooth, tension=0.8] coordinates {
 (0.0, 2.6) (0.9, 1.45) (1.8, 1.7) (2.6, 2.45) (3.6, 0.7) (4.6, 0.95) (5.4, 2.9)};
\fill[black!75] (0.95, 1.46) circle (2.2pt);
\node[lab, below=2pt] at (0.95, 1.4) {$\mu$};
\fill[blue!60!black] (3.7, 0.72) circle (2.2pt);
\node[lab, below=2pt, text=blue!60!black] at (3.7, 0.66) {$e$ (\GGA{})};
\draw[draw=red!70!black, line width=0.9pt] (2.6, 2.57) -- (2.6, 2.33);
\node[lab, text=red!70!black, anchor=west] at (2.85, 2.55) {gate, toll $S$};
\draw[-{Stealth[length=2.4mm]}, line width=1.0pt, draw=black!70, dashed]
 (1.15, 1.7) to[bend left=35] (3.4, 1.1);
\node[lab, text=black!70, anchor=east] at (1.9, 3.5) {hop through the pass,\\ rate $\propto e^{-S}$};
\node[lab, anchor=north, font=\footnotesize\bfseries] at (2.7, -0.45)
 {Decay: \GRIPin{} descent (scale sector)};
\node[lab, anchor=north, text=black!60] at (2.7, -0.95)
 {dissipative, local, exponentially tolled ---\\ transmutes the occupant; transports nothing};
\end{scope}
\end{tikzpicture}%
}
\caption[Two sectors of one geometry: $\theta$-sector geodesic motion (force) and scale-sector \GRIPin{} descent (decay).]{Q5 and Q3 as the two sectors of one geometry. \emph{Left ($\theta$, the sixth dimension):} an external field curves the phase connection over position space, and the electron's geodesic bends toward the source --- conservative motion that transports the particle and dissipates nothing (\S\ref{sec:fiber}). \emph{Right ($I_r$, the scale sector):} \GRIPin{} --- genuine \GFF{} gradient descent --- acts on the family stratum, not on position space: it transmutes its occupant through a gate at exponential cost $e^{-S}$, at a point, transporting nothing. A muon's bubble-chamber track shows both at once, plus the dissipative channel between them: the sixth dimension bends the track, radiation and ionization shrink it, the fifth-dimension descent ends it. The electron's track differs in exactly one way: no endpoint (Theorem~\ref{thm:stability}).}
\label{fig:sensing-regimes}
\end{figure}

\paragraph{The canonical worked example: the synchrotron --- and its
gravitational twin.} Nature runs the partition as a standing
demonstration in every electron storage ring, and \AFive{}'s Part~VI
now carries the full treatment as its radiative completion
\citep{ArisakaA5GDOS}; we import the result in digest. The stored
electron does three separable things. It \emph{bends}: the cyclotron
orbit is the $\theta$-sector geodesic of \S\ref{sec:fiber} made
hardware --- the magnetic field does no work, and the bend descends
nothing. It \emph{radiates}: the energy loss
(\citealp{Larmor1897}; enhanced by the famous $\gamma^4$ for
relativistic circular motion) is precisely the dissipative channel of
Reading~\ref{rmk:sensing}, and the beam cools toward its equilibrium
emittance. And it \emph{never ends}: no gate
(Theorem~\ref{thm:stability}), so the descent runs out of energy, not
of electron. \AFive{}'s radiative section sorts these into the
canonical \GDOS{} current sector by sector --- the orbit is the
divergence-free circulation, the radiation damping is the gradient
drift, the photon shot noise is the diffusion --- and the
monotonicity lemma makes beam cooling an H-theorem statement realized
in hardware. The status discipline travels with the import: the field
equations, power formulas, and current decomposition are
theorem-level; the sector \emph{identification} is now itself
derived --- \AFive{}'s closure subsection traces out the field
(Feynman--Vernon) and obtains the drift as the retarded flux, the
mobility in closed form with the Larmor and Peters coefficients
exact, and the diffusion with the universal storage-ring constant
$C_q$ --- and, completing the chain, the covariant kernel itself: a
closed-form spectral sum over the derived lock tower, causal
manifestly and runaway-free by passivity, with the classical
obstruction dissolved by this paper's own Q4 doctrine (the mass is a
basin level, not a self-energy ledger). \AFive{}'s Open Problem~O7
is thereby Resolved, and the status arrives with the example.

The gravitational twin seals the one-geometry claim. A binary star
is the metric-sector synchrotron: the Kepler orbit is circulation;
the quadrupole radiation is the dissipative channel; and the Peters
drift --- the slow shrinkage of the orbit --- is the gradient sector
on the $(a,e)$ state manifold. The Hulse--Taylor binary pulsar has
tracked that prediction for five decades to a few parts in $10^3$
\citep{HulseTaylor1975}, and LIGO now records the final seconds of
the same descent directly \citep{Abbott2016}. One structural
difference is itself instructive: the binary's landscape has no
normalizable equilibrium --- the inspiral terminates at the merger
--- whereas the synchrotron beam settles into its equilibrium
emittance. The synchrotron relaxes; the inspiral exits; the electron,
alone among the three, simply persists.

A muon in the same storage ring would do all of the above \emph{and}
decay: drift, cool, and then end at a kink, the scale-sector
\GRIPin{} descent acting at a point. The electron only drifts and
cools (\figref{fig:sensing-regimes}). That asymmetry, visible in any
bubble-chamber photograph and now in any light source, is the
two-sector partition of this section drawn by nature itself.

We close the Part by registering where Q5 now stands. Its kernel is
answered at theorem level by the fiber geometry of \S\ref{sec:fiber}
and the parallel chains of \S\ref{ssec:two-chains}: the electron
moves because the one composite geometry is curved, and its charge
sets how strongly its path attends to the phase sector. The
open-system layer adds the arrows, each in its proper dimension ---
radiative dissipation for motion, scale-sector \GRIPin{} for decay
--- both priced as interpretive readings, neither carrying any
theorem. The sentence to keep is the partition itself: \emph{the
phase sector moves the electron; the scale sector transmutes it; and
only what actually sheds energy descends.}
%% ===================================================================
%%  PART VII -- PREDICTIONS AND KILL CRITERIA
%% ===================================================================
%%  PART VII -- DISCUSSION (v1.8 restructure, author plan of June 11:
%%  19 Significance / 20 Uniqueness / 21 SUSY-string contrast /
%%  22 Prediction for Falsification / 23 Open problems / 24 Objections)
%% ===================================================================

\section[Part~VII in plain English]{Part~VII in plain English: the force law as geometry, and the circle that was never abstract}
Every graduate student knows that electromagnetism is a $\mathrm{U}(1)$ gauge theory: over every point of spacetime hangs a circle, and the electron's wavefunction carries a position on that circle. Every textbook draws the circle and then explains that it is not really anywhere.

This Part takes it literally. If the circle is a direction of the world rather than a bookkeeping device, then charge is a winding number \citep{ArisakaW2Holonomy}, its quantization is a counting statement rather than an assumption, and the force law is what a free trajectory looks like after it is projected back into four dimensions. Electricity and gravity become the same kind of statement about two different directions --- one the scale interval, one the phase circle --- and the dictionary between them is written out term by term.

Whether a reader finds this compelling will turn on whether the two extra directions are believed, which is a fair place for the argument to rest and where the falsification program points. What the Part does not do is derive the coupling's value: that is fixed by the integer ledger, and imported.

\GGPart[Discussion]{Discussion}{Significance, uniqueness, the contrast with strings and supersymmetry, falsification, open problems, and objections}
\label{part:VIII}

\section{Significance: summary of the solutions for the six questions}
\label{sec:significance}

The technical work of the paper is complete; this Part steps back. We
first state, in plain terms, what has actually been established for
each of the six questions and what each solution buys
(\S\ref{sec:significance}); we then locate the result against every
prior approach known to us (\S\ref{sec:prior}) and against the two
dominant frameworks of beyond-Standard-Model physics
(\S\ref{sec:susy-string}); we consolidate the falsification program
(\S\ref{sec:predictions}); we lay out the open problems at full length
(\S\ref{sec:open}); and we close with the objections a critical reader
should raise, and our answers (\S\ref{sec:objections}) --- the
triumph-before-triage ordering this cohort uses deliberately, so that
the defensive case is read after the positive one, not instead of it.

\subsection{The six solutions, one by one}
\label{ssec:five-solutions}

\paragraph{Q1 (Identity) --- solved at two layers, within the declared
axiom system.} The sameness layer: every electron is the readout of
the \emph{same} unique ground attractor of the \emph{same} boundary
stratum (Theorem~\ref{thm:identity}); sameness stops being a
convention of the formalism and becomes a uniqueness theorem of a
landscape. The content layer: the values themselves are no longer
inputs --- $y_e = 3/1{,}024{,}000$ from five integers, $m_e$ at the
declared $1.9\times10^{-4}$ residual, charge quantized by winding with
$\alphainv = 2^J + N^2$, and spin-$\tfrac12$ forced by
$\mathrm{Spin}(1,5)\cong\SLtwoH$ rather than chosen from Wigner's
menu. What it buys: the only complete answer we know of to ``why is
every electron the same, \emph{and the same as what}?'' --- the second
half of which no field ontology can address.

\paragraph{Q2 (Stability) --- solved as ground-state-ness, with the
textbook argument recovered as a consistency check.} The electron
cannot decay because its basin is the global minimum and possesses no
exit gate (Theorem~\ref{thm:stability}); the lightest-charged-particle
argument survives \emph{inside} the framework, with charge
conservation now derived rather than postulated. What it buys:
``absolute'' stability stops being an accident of an input spectrum
and becomes the defining property of a terminus --- and it yields a
sharper experimental posture, since even charge-violating channels are
forbidden by the landscape, not merely by bookkeeping.

\paragraph{Q3 (Copies) --- solved by import, with the fences carried
visibly.} The muon and tau are the depth-1 and depth-0 basins of the
electron's own landscape --- excited states in the literal,
spectroscopic sense --- and the ladder ends at three by the budget
arithmetic of \PaperPTwo{}, conditional exactly on its declared inputs (CP violation observed; the coupling clause; the integrality theorem
L-INT with residue R-INT). What it
buys for \emph{this} paper: the unification of Q2 with Q3 --- the same
finite resource that stops the ladder guarantees the terminus is
reachable --- and the honest division of labor that lets the electron
paper stand on the count without re-proving it.

\paragraph{Q4 (Pointlikeness) --- solved by dissolution, the one
genuinely new derivation of this paper.} The electron appears as a
point in space because, under AX-2, a particle's entire interface with
the world is two charges on one composite connection --- there is no
slot in which a size could be written (\S\ref{sec:ggep-particle}) ---
and because none of its structure is \emph{in} space: every
structural datum lives along the scale direction $\Ir$ and the phase
direction $\Stheta$ (Proposition~\ref{prop:nonspatial}); the mass is a
basin level, so the self-energy crisis never starts; the spin is a
double-cover label, so nothing spins; and the readout cannot smuggle a
length back in, because AX-1 binds measurement instruments themselves
(Lemma~\ref{post:RL}) --- the flat form factor then following as pure
Fourier bookkeeping, retained only as the falsification interface
(Theorem~\ref{thm:pointlike} and Remark~\ref{rmk:ff-status}). What it buys: the first statement in
the cohort --- to our knowledge, the first anywhere --- that converts
``why pointlike?'' from an experimental streak into a scale-free
theorem with a kill criterion.

\paragraph{Q5 (Sensing) --- solved at constitutional depth, with the
open-system gloss priced.} The force law itself is derived: Newton's
and Coulomb's laws descend in parallel from the same bulk, converging
on the unified equation of motion in which gravity and electricity are
the two curvatures of AX-2's single composite connection --- so that
responding to a field is generalized free fall
(\S\ref{ssec:q5-answer}; \AFive{}'s Part VI, reproduced in
Appendix~\ref{app:Q5}). The coupling's existence, quantization
(holonomy momentum on $\Stheta$), and strength ($\alphainv = 137$,
QD-completed) are derived; the open-system arrows are priced in
their proper sectors --- radiative dissipation for motion,
scale-sector \GRIPin{} for decay --- as interpretive readings; the
quantum reading of the sign rule is QED's theorem, credited. What it
buys: Einstein's unification realized at exactly the point a student
first meets electricity --- the electron and the apple obey one law
--- together with the three-phenomena reading of a bubble-chamber
track: the sixth dimension bends it, dissipation shrinks it, the
fifth-dimension descent ends it.

\paragraph{Q6 (The twin) --- solved by import at theorem grade, with
the same-basin reading priced and its promotion registered.} The
origin of antiparticles is imported from \PaperPFive{}: the twin is
forced in the real bulk, before quantization, by the agreement of two
independently forced real structures --- the circle's $i$ and the
clock's $i$ --- with the charge flip definitional for fermions
(Part~\ref{part:positron}). The positron is then read as the
conjugate readout of the electron's one basin: mass equality trivial
rather than enforced, and the sixth question collapsing into the
first. What it buys: the only account we know of in which ``why does
the electron have a twin?'' and ``why is every electron identical?''
are the same question --- answered once, by counting objects
correctly. The reading's promotion to a proved spinor-level corollary
remains registered as D-P3-4, deliberately open.

\subsection{The conjunction, and the solutions at a glance}
\label{ssec:conjunction-significance}

Table~\ref{tab:solutions} compresses the Part into one view. The
significance of the paper is not any single row; rows have appeared
before, in fragments, throughout a century of literature. The
significance is the \emph{column}: one fact --- the electron is the
unique ground state of its stratum --- generating all six rows at
once, each with a named status, each with a declared failure mode.
Remarkably, the six questions turn out to have needed each other: the
values of Q1 are basin data, the stability of Q2 is basin topology,
the copies of Q3 are the basin's neighbors, the twin of Q6 is the
basin's conjugate orientation, the pointlikeness of Q4
is the basin's orientation relative to space, and the sensing of Q5 is
the basin's response to tilt. No fragment-by-fragment program could
have found that structure, because the structure \emph{is} the
conjunction.

\begin{table}[ht]
\centering
\caption[The six solutions at a glance, each with its grade.]{The six solutions at a glance. Status tags as in
\S\ref{sec:status-table}; the full per-step ledger is
Appendix~\ref{app:ledger}. One row per question and one sentence per answer, meant to be read before the derivations rather than after them. The status column is the honest half of the table: it records the grade at which each sentence is held, and the grades are not uniform across the six.}
\label{tab:solutions}
\small
\renewcommand{\arraystretch}{1.3}
\begin{tabular}{@{}lp{0.42\textwidth}p{0.30\textwidth}@{}}
\toprule
\textbf{Q} & \textbf{The solution, in one sentence} & \textbf{Status} \\
\midrule
Q1 & One deepest basin, one readout --- and the basin's data are the
measured values & THM (\GDOS{}) + codebook; spin THM \\
\addlinespace
Q2 & The ground basin has no exit gate; nothing is downhill from the
bottom & THM given \GFF{}-ST7 \\
\addlinespace
Q3 & $\mu, \tau$ are the higher basins; the budget pays for exactly
three & Imported (EMP + coupling clause + L-INT/R-INT) \\
\addlinespace
Q4 & A particle is two charges on one connection (AX-2) --- no slot
for a size; readout adds no length; $F \equiv 1$ forever & THM via
Lemma RL from AX-1 + AX-2 coupling \\
\addlinespace
Q5 & Force = composite geodesic motion (Newton \& Coulomb, one bulk);
coupling, $\alpha$ derived; arrows: radiation (motion), \GRIPin{}
(decay) & THM (\AFive{} Part VI) + codebook; arrow readings INT \\
\addlinespace
Q6 & The twin is forced in the real bulk; the positron is the same
basin read in the conjugate orientation & THM (imported: T-P5-A/B/C,
C2) + INT (named); D-P3-4 \\
\bottomrule
\end{tabular}
\end{table}

\subsection{What the solutions change}
\label{ssec:what-changes}

Three ledgers move. For the Standard Model: of the quantities the
electron contributes to the input list --- $m_e$, the charge unit, the
representation choice, the family count --- none remains a pure input
within the framework; each is now a theorem, a codebook entry, or a
fenced conjecture with a declared status. For the cohort: the electron
becomes the charter case of the \GGA{} principle --- the simplest
stratum on which identity-and-stability-as-ground-state-ness can be
exhibited end to end --- and Parts III--VII of this paper are, in
effect, the worked example that \AEleven{}'s cascade generalizes
through eighteen layers. For method: Q4's resolution demonstrates that
the open-system, non-spatial commitments are not philosophical
luxuries; they are load-bearing --- remove either, and the six
solutions collapse back into six mysteries (\S\ref{sec:why-century}).
After all, the test of a foundation is not how much it explains on a
good day, but how much stops being explainable the moment you take it
away.

\subsection{The electron on the two fibers}
\label{ssec:electron-two-fibres}

The six solutions sort, and the sorting is the cohort's recent
campaign made local (\textsf{GG-W1-Symmetry};
\citealp{ArisakaP5CPT}; \citealp{ArisakaA8QM}). The campaign's
instrument is one exact statement: \emph{holonomy requires closed
loops, and an interval has none.} The compact circle \Stheta{} is
nothing but closed loops --- everything on it is holonomy,
quantized and protected, its transport a group; the scale interval
\Ir{} can hold no holonomy at all --- its transport composes only
forward, a semigroup. Sorted on this anatomy, the electron divides
cleanly in two. Everything about it that is \emph{identical and
permanent} is circle-side data: the charge (a winding number), the
spin, the representation, identity itself --- holonomy classes on
the fiber that remembers. That is Q1's solution said
topologically: every electron is the same because every electron
is the same \emph{class}, and classes do not age, do not wear, and
admit no continuous deformation for any boundary operation to
apply --- sameness needs no enforcement mechanism because the
fiber it is written on has nothing that could enforce a
difference. Everything about the electron that is \emph{placed and
priced} is interval-side: the mass --- the address of the ground
basin at the descent's terminus --- the muon's descent rate (a
\GRIPin{} event along the one-way fiber,
\S\ref{sec:lifetime}), and stability itself, Q2's no-exit
reading: the semigroup below the ground basin has nowhere further
to carry the state, and cannot re-ascend, because ascent would be
the inverse transport the fiber does not possess. The positron,
Q6, is the same circle-side class read in the mirror orientation
--- which is why it shares the mass to the last digit while
negating every charge: the interval's address is
orientation-blind; the circle's labels are not.

In one sentence: \emph{an electron is a holonomy class wearing a
mass --- the class is the circle's, the mass is the interval's.}
The six questions stayed open for a century in part because the
two halves were misfiled --- the first half mistaken for a
convention of the formalism (identity as bookkeeping), the second
half for an input (the mass as a measured constant). The campaign's
anatomy files them correctly: one half is topology, the other is
dynamics, and the electron is the simplest object in nature on
which both fibers have signed their work.

\section{Uniqueness: comparison with prior approaches}
\label{sec:prior}

No prior approach known to us answers more than one of the six
questions, and each pays for its single answer with a commitment the
present framework does not need. We review them at full strength ---
the reader should hear each at its best before the comparison is
scored.

\paragraph{Wheeler's one-electron universe.} The most celebrated
previous attempt to explain electron identity is Wheeler's 1940
suggestion, relayed in Feynman's Nobel lecture \citep{Feynman1966},
that all electrons are one electron weaving forward and backward
through time, positrons being the backward strands. It is the correct
\emph{kind} of answer --- identity explained by uniqueness of an
underlying object --- and it remains, eighty-six years later, the most
imaginative one-line proposal in the subject. It failed empirically
(the universe is not positron-balanced, and the worldline bookkeeping
has no answer for net lepton number) and conceptually (it explains
sameness but neither the values, nor stability, nor the generations,
nor pointlikeness). The present account preserves Wheeler's insight in
a form that survives: what is unique is not the particle's worldline
but the attractor it reads out --- one basin, many readouts, no
positron bookkeeping required. And the replacement of a worldline by an
attractor is precisely what lets the account reach across the sky.
Wheeler's mechanism is \emph{causal}: one particle threads every
electron's place, so identity is carried by a shared trajectory. That is
exactly the kind of explanation that cannot survive the second horizon
problem of \ATen{} \citep{ArisakaA10Cosmos} --- electrons in causally
disconnected regions share no trajectory, and a worldline that must visit
them all is no more available than a signal that must reach them all. The
attractor account is \emph{acausal}: identity is a property of one
landscape read out everywhere at once, requiring no shared history and no
shared worldline (Corollary~\ref{cor:horizon-independence}). Where
Wheeler's picture needs the electrons to have been connected, the \GGA{}
needs only that they be boundaries of the same bulk --- which is why the
one-basin reading answers across the horizon where the one-worldline
reading cannot. The differences are auditable: \GGA{}
uniqueness is a theorem within a stated framework rather than a
picture; it derives the values; it covers all six questions; and it
is falsifiable on five declared criteria. Wheeler's question to
Feynman --- ``why do all electrons have the same charge and the same
mass?'' --- is, we believe, answered here in the spirit in which it
was asked.

\paragraph{Compositeness and preon models.} The structural tradition
--- the electron as a bound state of more elementary constituents ---
is the conservative bet on Q4, and its best versions were genuinely
economical: in the rishon model \citep{Harari1979,Shupe1979}, the summit of the lineage Pati and Salam opened \citep{PatiSalam1974}, two
constituents and their anti-partners generate the entire fermion
spectrum of one family, an arithmetic elegance the codebook reader
will recognize as kindred in spirit. The tradition answers Q3 by
construction (generations as excitations of the bound system) and
promises Q1's values as binding-energy calculations. What it could
never do is reconcile the promise with the point: compositeness at
scale $\Lambda$ predicts form-factor deviations of order
$q^2/\Lambda^2$ and a spectroscopy of excited states at $\Lambda$
\citep{EichtenLanePeskin1983}, while the electron's mass sits five
orders of magnitude \emph{below} any allowed binding scale --- the
notorious mass paradox: a bound state light compared to its own
inverse size requires extreme fine-tuning, precisely what 't~Hooft's
anomaly-matching analyses formalized \citep{tHooft1980}. Forty years of contact-
interaction searches have pushed $\Lambda$ upward without limit in
sight. The present framework keeps the tradition's two real insights
--- the electron \emph{does} have structure, and the generations
\emph{are} excitations --- and relocates both where the searches
cannot refute them: along directions that are not space.

\paragraph{The geometric-electron tradition (Kerr--Newman).} A quieter
lineage sought the electron in general relativity itself. Carter's
analysis of the Kerr--Newman solution \citep{Carter1968} noted the
remarkable fact that a KN source with the electron's mass, charge, and
spin has gyromagnetic ratio $g = 2$ --- Dirac's value, from pure
geometry --- and a tradition of ``electron as KN geometry'' models
followed. The instinct --- electron properties are geometric data ---
is exactly the present framework's instinct, and the $g = 2$
coincidence deserves more respect than it usually receives. The
obstacles are structural: the KN geometry at electron parameters has
a naked ring singularity of Compton-scale extension in \emph{space}
(colliding with Q4 rather than solving it), no quantization of charge
or spin, no second and third generation, and no stability statement.
The lesson we draw: geometry was the right language but 4D spacetime
was the wrong manifold --- the electron's geometry lives in the bulk
directions, where rings, dials, and singularities are replaced by
windings, integers, and basins.

\paragraph{QFT identity, stated at its strongest.} The field-theoretic
treatment of indistinguishability (permutation symmetry of the quanta
of one field; see, e.g., \citealp{Weinberg1995}) is the standard
professional answer to Q1 and is engaged at full strength in
\S\ref{ssec:qft-identity}: it is correct, it is exact, and it is the
reason no working physicist loses sleep over electron identity. It is
also bookkeeping --- sameness is automatic once one field is posited,
and the posit (which field, which values, which representation) is
where the question lives. We emphasize what the present paper does
\emph{not} claim: it does not claim QFT is wrong about identity; it
claims QFT's answer has a second half, and derives it. The boundary
effective theory of the framework \emph{is} a quantum field theory;
the field ontology survives as the boundary description of the basin
readout.

\paragraph{Anthropic and landscape treatments of the values.} The
remaining modern position on Q1's values is environmental: $m_e$ and
$\alpha$ vary across a multiverse of vacua, and we observe values
compatible with observers \citep{Susskind2003}. Stated honestly, this
is not an answer to ``why these values'' but a principled argument
that the question has no answer --- a position consistent, hard to
falsify by design, and corrosive to the codebook program: if the
values are environmental, a formula like $\alphainv = 2^J + N^2$ can
only be numerology. The present framework makes the opposite bet, and
the bet is testable: the codebook either continues to survive
ever-sharper measurement at its declared precision (P5) or it breaks.
One of the two research programs is wrong, and unusually for
foundational disputes, the data will eventually say which.

\paragraph{The classical extended electron.} Abraham, Lorentz, and
Poincar\'e sought the electron's structure in space and met the
self-energy crisis; Dirac formalized the point limit and met runaways
\citep{Abraham1903,Lorentz1909,Poincare1906,Dirac1938}. Their failure
was instructive in a way the present paper finally makes precise: they
were right that the electron has structure, right that the structure
is physical, and wrong only about the manifold it inhabits. Part
\ref{part:VI} locates their impasse exactly --- structure in space
costs self-energy and spin paradoxes; structure along scale and phase
costs nothing in space at all.

\paragraph{The sister derivation, and the division of labor.} All
comparisons regarding the family count (Dobrescu--Poppitz bounds,
modular flavor symmetry, NCG, division algebras, anthropics applied
to $N$) are owned by \PaperPTwo{} (its \S11) and not duplicated here.
What is unique to the present paper, against every entry above, is
the conjunction: no prior approach attempted all six questions as
one object, because no prior framework had the one fact of which the
six are faces. That --- not any single ingredient --- is the
uniqueness claim, and \S\ref{sec:objections} defends it against the
strongest objections we could construct.

\section{Sharp contrast with supersymmetry and string models}
\label{sec:susy-string}

The two dominant frameworks of beyond-Standard-Model physics deserve
more than a paragraph in \S\ref{sec:prior}, because the contrast with
them is uniquely sharp and uniquely instructive: \GGTheory{} shares
most of its technical machinery with string theory --- and commits to
the opposite answer on every question this paper is about. This
section adapts, for the electron, the full treatment given in
\ATwo{}'s comparison Parts \citep{ArisakaA2GG6}.

\subsection{Same machinery, opposite commitments}
\label{ssec:same-machinery}

A reader trained in string theory will recognize nearly every tool in
this paper's upstream chain: anomaly cancellation by a modified
Bianchi identity (the Green--Schwarz mechanism
\citep{GreenSchwarz1984}, of which \BIsix{} is the six-dimensional
descent), warped throat geometry (the Randall--Sundrum lineage
\citep{RandallSundrum1999}), holographic projection from bulk to
boundary \citep{Maldacena1998}, and instanton actions counting tunneling between vacua. The
machinery is shared; the constitutional commitments are opposite, and
they are exactly two. String theory takes the extra dimensions to be
\emph{spatial} and the fundamental objects to be \emph{extended};
\GGTheory{} takes the extra dimensions to be \emph{non-spatial} (a
scale direction and a phase direction) and the fundamental excitations
to be \emph{point-like} (AX-1's microcausality clause). Everything
this paper says about the electron flows from those two commitments
--- and everything testably different between the frameworks flows
from them too.

\subsection{Spatial dimensions carry moduli; the landscape follows}
\label{ssec:moduli-landscape}

A spatial extra dimension is a Riemannian direction with an intrinsic
length, and an intrinsic length is a dial. The Kaluza--Klein circle
has a radius; the Calabi--Yau manifolds of superstring
compactification \citep{Candelas1985} carry continuous K\"ahler and
complex-structure moduli --- shapes and sizes that nothing in the
theory fixes. The structural consequence is the landscape: the moduli
space of compactifications supports $\sim 10^{500}$ vacua \citep{KachruKalloshLindeTrivedi2003}
\citep{Susskind2003}, and the values of the low-energy constants ---
including $m_e$ and $\alpha$, the subjects of Q1 --- become
environmental selections rather than predictions. \GGTheory{}'s two
further directions carry no dials at all: $\Ir$ is the
renormalization-group coordinate $r = \ln(E_{\mathrm{seam}}/\mu)$ with
$E_{\mathrm{seam}} = M_{\mathrm{Pl}}/2$, dimensionless,
with an \emph{integer} endpoint $K = 35$ fixed by the Diophantine
ledger; $\Stheta$ is a topological circle whose metric component is
fixed to unity by the canonical-metric theorem --- a phase, not a
shape. Where the string construction has continuous moduli, the
\GG{} construction has five integers; where the landscape has
$10^{500}$ vacua, the ledger has exactly one solution (\ATwo{},
Theorem~6). For the questions of this paper the consequence is direct:
in a landscape, Q1's values are unanswerable in principle; in a
ledger, they are theorems or they are false.

\subsection{Supersymmetry: the partner answer and the basin answer}
\label{ssec:susy-contrast}

Supersymmetry is the other great structural bet, and its logic is
worth stating fairly: pair every boson with a fermion so that
quadratic divergences cancel, stabilizing the Higgs hierarchy; embed
in a GUT and the couplings unify; add R-parity and the lightest
superpartner is dark matter. It is a beautiful architecture --- and
for the six questions of this paper it adds nothing structural (on the
sixth it inherits quantum field theory's formal answer unchanged). SUSY
does not
explain why electrons are identical (the selectron is a new field,
not an explanation of the old one); it does not explain electron
stability (still lightest-charged bookkeeping); it does not predict
three generations (the family count is as free in the MSSM as in the
SM); it makes the pointlikeness question \emph{harder} (every SM
point now has a partner point, doubling the unexplained); and it adds
its own unanswered identity question (why is every selectron
identical?). Meanwhile its sharp prediction --- superpartners at the
electroweak-to-TeV scale --- has met four decades of null results.
The \GG{} alternative spends nothing on partners: stability is
topology (no exit gate), the hierarchy is carried by the integer scale
depth ($M_{\rm lock} = \tfrac12 M_{\rm Pl}e^{-35}$), and the electron
needs no superpartner for any of its five properties to be theorems.
The two bets are cleanly separable by experiment: a selectron
discovery would be a triumph for one and an embarrassment for
neither's electron sector --- but a confirmed electron substructure
or a fourth family would kill this framework while merely
re-parameterizing SUSY. Asymmetric falsifiability is the deliberate
posture here (\S\ref{sec:predictions}).

\subsection{The electron as the cleanest discriminator}
\label{ssec:discriminator}

Table~\ref{tab:contrast} scores the three pictures against the six
questions and their observables. One row deserves emphasis, because it
is decisive in principle: a string electron is an extended object with
a scale ($\ell_s$), and at that scale --- wherever it lies --- its
form factor departs from unity and a Regge tower of excitations
exists. The departure may sit at experimentally hopeless energies;
the point is structural: \emph{string theory owes structure at some
scale, supersymmetry owes a partner at some scale, and \GGTheory{}
owes the absence of both at every scale.} The flat blue line of
\figref{fig:formfactor} is this paper's signature in a single stroke:
any confirmed structure kills it (F2), while every null result that
disappoints a compositeness or string-scale search is, for this
framework, another passed test.

\begin{table}[ht]
\centering
\caption[The electron in three frameworks, and what each one owes.]{The electron in three frameworks. ``Owes'' marks what each
framework predicts must exist at some scale; the verdicts are this
paper's declared kill criteria (\S\ref{sec:predictions}). The three columns are three frameworks answering the same questions about the same particle, so the comparison is like for like. The \emph{owes} row is the one that decides anything: it records what each framework requires to exist that has not been seen, which is the axis along which any of the three can be retired.}
\label{tab:contrast}
\small
\renewcommand{\arraystretch}{1.3}
\begin{tabular}{@{}p{0.20\textwidth}p{0.24\textwidth}p{0.22\textwidth}p{0.24\textwidth}@{}}
\toprule
 & \textbf{Superstring} & \textbf{SUSY (MSSM)} & \textbf{\GGTheory{}} \\
\midrule
Extra dimensions & six--seven, \emph{spatial}, with moduli & none
required & two, \emph{non-spatial} (scale, phase), zero moduli \\
\addlinespace
Electron extension & string scale $\ell_s$: $F \ne 1$ there; Regge
tower & point by construction & $F \equiv 1$ at every scale (Thm.,
via Lemma RL) \\
\addlinespace
Identity (Q1) & field convention; values environmental (landscape) &
field convention; values free & uniqueness theorem; values from five
integers \\
\addlinespace
Stability (Q2) & bookkeeping & bookkeeping & no-exit-gate theorem \\
\addlinespace
Generations (Q3) & topology-dependent (e.g.\ $|\chi|/2$); not forced
& free parameter & forced at $N=3$ (P2, fenced) \\
\addlinespace
Antiparticle (Q6) & inherited from QFT, formal & inherited from QFT,
formal & forced in the real bulk, pre-quantization; positron =
conjugate readout (P5 import, fenced) \\
\addlinespace
Owes at some scale & string excitations & superpartners & nothing ---
forbidden forever \\
\bottomrule
\end{tabular}
\end{table}

\subsection{Honest credits}
\label{ssec:string-credits}

Three credits, stated without reluctance. String theory remains the
most developed candidate for a UV-complete quantum theory of gravity,
and nothing in this paper addresses quantum gravity at that depth;
the Green--Schwarz machinery this cohort's anomaly structure descends
from was a string-theoretic discovery \citep{GreenSchwarz1984,
GSW1987}; and the scale-geometry intuition that makes
\figref{fig:bulk-cross-section} natural entered physics through the
string-adjacent literature \citep{RandallSundrum1999}. The honest
statement of the contrast is therefore not ``strings wrong, \GG{}
right''; it is that the two frameworks bought different things with
the same machinery. String theory bought mathematical depth and
UV-completeness, and paid with moduli, the landscape, and the
permanent deferral of every question this paper is about.
\GGTheory{} bought the six answers and zero dials, and pays by
standing permanently in front of the experimental gun
(\S\ref{sec:predictions}) --- with quantum gravity delegated to the
cohort's bulk papers rather than solved. A reader may reasonably
prefer either purchase; what the reader can no longer do, after this
section, is regard them as the same kind of theory that differs only
in taste. After all, the deepest difference between two frameworks is
never what they explain --- it is what they are willing to be killed
by.

\section{Prediction for falsification}
\label{sec:predictions}

We consolidate the paper's entire empirical exposure in one section,
in the cohort's pre-registration discipline: each prediction is
stated with its current anchor, its experimental future, and its
\emph{live falsifier} --- the specific observation that would kill it.
The anchor table with sources is Appendix~\ref{app:anchors};
Table~\ref{tab:predictions} summarizes with declared classes.

\paragraph{P1 --- The electron never decays.}
\emph{Prediction:} no electron decay, in any channel, at any rate ---
including charge-violating channels that bookkeeping arguments cannot
address; the basin has no gate (Theorem~\ref{thm:stability}).
\emph{Anchor:} $\tau_e > 6.6\times10^{28}$~yr at 90\% C.L.
\citep{Borexino2015}, more than eighteen orders of magnitude beyond
the age of the universe. \emph{Future:} every next-generation
low-background liquid-scintillator program (the Borexino lineage,
including JUNO-class detectors) extends the reach; the prediction is
that the bound improves forever, without limit. \emph{Live falsifier
(F1):} observation of electron decay in any channel. No appeal to
conditioning is available: Theorem~\ref{thm:stability}'s
\GDOS{}-internal status would not survive its empirical
falsification.

\paragraph{P2 --- No substructure at any scale, ever.}
\emph{Prediction:} the structural form factor is identically unity
(Theorem~\ref{thm:pointlike}); contact-interaction and form-factor
searches return null at every energy, with no compositeness scale
$\Lambda$ anywhere \citep{EichtenLanePeskin1983}. \emph{Anchor:}
$\mathcal{O}(10)$~TeV contact-interaction reach (model-dependent);
$g-2$ consistency at the $10^{-13}$ level. \emph{Future:} FCC-ee /
ILC / CLIC-class $e^+e^-$ programs push effective compositeness
scales toward and beyond $10^2$~TeV; precision M{\o}ller and Bhabha
scattering sharpen the low-$q^2$ slope. Every extension is a test
this paper has agreed in advance to face. \emph{Live falsifier (F2):}
a confirmed structural deviation of any electron form factor from
unity, at any energy --- which kills Part~\ref{part:VI} outright with
no parameter to retreat to, and, under Lemma~\ref{post:RL}, reaches
the constitution itself: confirmed substructure falsifies AX-1's
point-locality within the framework.

\paragraph{P3 --- $a_e$ remains pure Standard-Model dressing of a
structureless point.} \emph{Prediction:} the measured anomalous
moment continues to agree with the Standard-Model computation (QED to
high order, plus the small hadronic and electroweak terms) for a
point fermion, using an independently measured $\alpha$; no
\emph{structural} contribution ever appears. \emph{Anchor:} $g/2$
measured to 0.13~ppt \citep{Fan2023}, superseding
\citealp{Hanneke2008}, against the tenth-order computation
\citep{Aoyama2012}; the SM test currently limited
by the $>5\sigma$ Rb/Cs disagreement in $\alpha$
\citep{Morel2020,Parker2018}. \emph{Future:} next-generation Penning
traps and the resolution of the $\alpha$ dispute promote this to a
test at the few-$10^{-13}$ level. We register the scope honestly:
this paper engages $g-2$ qualitatively, as the empirical anchor of
structurelessness; a quantitative \GGTheory{} statement is open
problem D-P3-3. \emph{Live falsifier:} an $a_e$ anomaly that survives
the $\alpha$-dispute resolution and the SM-theory error budget would
indicate structure and trigger F2's logic.

\paragraph{P4 --- No fourth charged lepton.} \emph{Prediction:} the
ladder ends at three --- imported from \PaperPTwo{} with its complete
conditioning (\S\ref{sec:conditioning}), and therefore carried here
as a \emph{conditional} class. \emph{Anchor:} LEP lepton counting
$N_\nu = 2.9963 \pm 0.0074$ \citep{ALEPH2006}. \emph{Future:} a
Tera-Z run at FCC-ee would sharpen $N_\nu$ by an order of magnitude;
direct fourth-generation searches continue at hadron colliders.
\emph{Live falsifier (F3):} a fourth sequential charged lepton (or a
fourth light neutrino at multi-$\sigma$). As \S\ref{sec:conditioning}
records, Q2's no-exit-gate statement would survive unless the new
state were charged and lighter than the electron --- in which case
everything falls.

\paragraph{P5 --- The values hold at declared precision.}
\emph{Prediction:} $m_e$ agrees with the QD-completed codebook value
at the declared $1.9\times10^{-4}$ residual, and $\alphainv$ with its
QD completion, as \ANine{} reports, against CODATA
\citep{CODATA2022,PDG2024}. This is a \emph{postdiction audit}: the
numbers were known before the codebook existed, and the class label
says so. \emph{Future:} the residual itself is the open frontier ---
D-P3-5 records what sharpening the QD layer would mean, and what
breaking it would mean. \emph{Live falsifier (F4):} once the Rb/Cs
dispute is resolved, a settled $\alphainv$ incompatible with the
QD-completed prediction at its declared precision, or an $m_e$
determination outside the declared residual. The experimental dispute
is not a fence of ours, and we do not hide behind it.

\paragraph{F5 --- the theoretical falsifier.} A demonstrated flaw in
the AX-1 derivation of Lemma~\ref{post:RL} --- for instance, an
admissible \OGGEP{} registration kernel carrying a spacelike scale
consistently with AX-1 --- would demote
Theorem~\ref{thm:pointlike} to conditional status and reopen the
fence this paper closed. The lemma's proof is registered precisely so
that it remains under audit; \S\ref{sec:objections}, Objection~15,
hosts the strongest version of the attack we could construct.

\paragraph{F6 --- the mirror falsifier.} A \emph{confirmed} electron--positron
asymmetry --- in mass (current bound $|m_{e^+}-m_{e^-}|/m <
8\times10^{-9}$, 90\% C.L.), in charge magnitude
($|q_{e^+}+q_{e^-}|/e < 4\times10^{-8}$), or in $g$-factor
($(g_{e^+}-g_{e^-})/g = (-0.5\pm2.1)\times10^{-12}$)
\citep{Fee1993, Hughes1992, VanDyck1987}. For the standard account
such an asymmetry would violate the CPT theorem; for this paper it is
sharper --- it would falsify the conjugate-readout reading of
Part~\ref{part:positron} (there is no pair whose members could
differ) \emph{before} it falsified CPT. Permanent, two-sided
exposure, running now.

\medskip
Table~\ref{tab:predictions} summarizes with each entry's class
declared in the cohort's pull-table discipline: a \textbf{Forward}
prediction risks something not yet measured; a \textbf{Postdiction
audit} checks consistency against numbers already known; a
\textbf{Conditional} entry inherits named fences.

\begin{table}[ht]
\centering
\caption[The predictions of this paper, with their declared classes.]{The predictions of this paper, with declared classes (cohort
pull-table convention). Anchors as of June 11, 2026
(Appendix~\ref{app:anchors}). Each row is a prediction, the measurement that currently bounds it, and the class it is declared in, so that a falsifiable commitment can be told from a consistency check without reading another line. The anchors carry a date because they move, and the class is what a null result would retire.}
\label{tab:predictions}
\small
\begin{tabular}{@{}lp{0.36\textwidth}p{0.22\textwidth}p{0.30\textwidth}@{}}
\toprule
\textbf{ID} & \textbf{Prediction} & \textbf{Current anchor} & \textbf{Class} \\
\midrule
P1 & Electron never decays; bound improves forever & $\tau_e > 6.6\times10^{28}$ yr & \textbf{Forward} \\
\addlinespace
P2 & No substructure at any scale, ever ($F\equiv1$) & no deviation to $\mathcal{O}(10)$ TeV reach & \textbf{Forward} \\
\addlinespace
P3 & $a_e$ stays pure SM dressing of a point & $g/2$ at $0.13$ ppt & \textbf{Forward} (qualitative) \\
\addlinespace
P4 & No fourth charged lepton & LEP $N_\nu = 2.9963(74)$ & \textbf{Conditional} (P2 fences, \S\ref{sec:conditioning}) \\
\addlinespace
P5 & $m_e$, $\alphainv$ at declared QD precision & CODATA 2022 & \textbf{Postdiction audit} ($1.9\times10^{-4}$ declared) \\
\addlinespace
P6 & Electron--positron equality exact, forever (one basin, two
readouts) & mass $8\times10^{-9}$; charge $4\times10^{-8}$; $g$
$2.1\times10^{-12}$ & \textbf{Forward} (kills via F6) \\
\bottomrule
\end{tabular}
\end{table}

\paragraph{What would \emph{not} falsify this paper.} Pre-registration
cuts both ways: we state the negative space, so that no future
accommodation can be smuggled in as if it had been intended. A
resolution of the Rb/Cs $\alpha$ dispute in \emph{either} direction
within the declared QD tolerance does not falsify P5. New heavy
states that are not sequential leptons --- vector-like fermions,
sterile neutrinos, exotic scalars --- do not trigger F3, which is
about a fourth copy of the family pattern; they would bear on the
cohort elsewhere. An anomaly in the \emph{muon's} $g-2$ does not
trigger F2 (the muon is a non-ground basin, and its physics carries
additional structure imported from \PaperPTwo{}); only electron-side
structure does. And precisely this has occurred: \PaperPTwo{}'s rigidity lemma proves the budget underivable from the bulk data alone, sharpening D-P3-2 exactly as anticipated without killing Q3's import, which is conditional by declaration. What
remains, after the negative space is drawn, is a paper that can be
shot in six specific places --- and nowhere else without first
proving it said what it did not say.

\paragraph{The asymmetry, restated.} Every rival picture in
\S\ref{sec:susy-string} owes something at some scale; this paper owes
absences --- no decay, no structure, no fourth copy, forever. An
absence can never be verified, only tested again; this is sometimes
raised as a Popperian complaint, and \S\ref{sec:objections}
(Objection~14) answers it in full: a universal absence is the
\emph{most} falsifiable kind of claim there is, refutable by a single
event at any energy, in any decade, by any experiment. The paper's
posture is maximal exposure, deliberately chosen. After all, the six
questions waited a century for an answer; the least the answer can do
is stand where it can be shot.

\section{Open problems}
\label{sec:open}

Seven problems are open, listed in increasing order of how much of
the paper they could move. For each we state the problem, why it
matters, and what would count as a solution --- the cohort's
convention for keeping its to-do list as auditable as its claims.
Each entry is registered as \textsf{D-P3-$N$} --- ``D'' for
registered debt --- since the cohort-wide \textsf{O-Suffix-$N$}
convention is reserved for the numbered objections
(\S\ref{sec:objections}).

\paragraph{D-P3-1: Formalize the static limit of Lemma RL.}
\emph{Problem:} the channel-level derivation of Lemma~\ref{post:RL}
(Appendix~\ref{app:formfactor}, Step 2) contains one step stated at
physicist's rigor --- that retarded registration memory contributes
nothing to the elastic, zero-energy-transfer structure function.
\emph{Why it matters:} this is the only step of the paper's one new
derivation that is not yet theorem-grade; F5 lives here. \emph{What
counts as a solution:} a theorem in the \OGGEP{} open-channel
formalism of \AEight{} --- kernel $\mathcal{K}(t,t')$ retarded,
output: the equal-time structure function of the registered record
equals that of the registered configuration --- or a counterexample,
which would trigger F5. We judge this formalization rather than
missing physics; the judgment is itself part of what a referee should
audit.

\paragraph{D-P3-2: The inherited fence (the coupling clause and
R-INT).} \emph{Problem:} the capacity of the family stratum rests on
the coupling clause together with the integrality theorem L-INT of
\PaperPTwo{}, whose single topological residue R-INT is discharged on
the benchmark background by the $\kappa$-bridge theorem of that
paper's Appendix~H and remains
open off it, exactly as recorded in \PaperPTwo{} (its
\S12) and \ASix{} (M10). \emph{Why it matters:} Q3's upper bound ---
and with it the ``exactly two copies'' half of the conjunction ---
carries this conditioning at every layer. \emph{What counts as a solution:} closure of the residue across the
intended class --- the warped and relative refinements that
appendix declares --- everything else is settled: the induced
connection is constructed (Berry transport, forced at Born-grade by
\PaperPTwo{}'s adiabatic theorems), the $\lfloor J/2\rfloor$ question
is dissolved by the form-robustness classification, the bulk-only
route is closed by the rigidity lemma, and the benchmark case of the
residue is closed by the $\kappa$-bridge theorem. Resolution upstream
automatically
sharpens Part~\ref{part:IV}; nothing in this paper can shortcut it.

\paragraph{D-P3-3: A quantitative \GGTheory{} statement for $a_e$.}
\emph{Problem:} this paper predicts the electron's structural
contribution to $a_e$ is exactly zero, qualitatively. Can the
framework say more --- either a proof that the \GDOS{} readout
contributes nothing to all orders, or a computed bound? \emph{Why it
matters:} $g-2$ is the most precisely measured property of any
particle; a framework statement at the $10^{-13}$ level would convert
P3 from qualitative to sharp. \emph{What counts as a solution:} a
boundary-channel computation with declared status at every step ---
and we state plainly that this is new physics requiring its own
paper and its own fences; done carelessly it would be numerology, and
the cohort would rather leave it open than do it carelessly.

\paragraph{D-P3-4: The positron, as a theorem.} \emph{Problem:}
the \emph{origin} of the twin is no longer owed --- it is
imported at theorem grade in Part~\ref{part:positron} (T-P5-A/B/C and
the fermionic factorization T-P5-C2 of \PaperPFive{}). What remains
owed is exactly one step: nothing in this paper distinguishes the
electron from the positron except readout orientation, and the CPT
mirror of every statement of Part~\ref{part:III} should follow from
the bulk spinor structure (Eq.~\ref{eq:spin15}) applied to the
conjugate readout. \emph{Why it matters:} the same-basin reading is
the one interpretive row left in the Q6 status table
(Table~\ref{tab:q6-status}); its promotion would close the sixth
question at theorem grade end to end. \emph{What counts as a
solution:} a short companion statement --- conjugate winding, same
basin level, same absence of exit gates --- promoted from
\S\ref{sec:q6-readout} to a proved corollary of A2's quaternionic
structure and A8's projection, composing T-P5-C2 with \GFF{}-ST7.

\paragraph{D-P3-5: Sharpening the $m_e$ residual.} \emph{Problem:}
the codebook reproduces $m_e$ at $1.9\times10^{-4}$; CODATA knows it
at $3\times10^{-10}$. Six orders of magnitude of unexplained residual
stand between the QD layer and the data. \emph{Why it matters:} this
is the paper's most exposed number (\S\ref{sec:objections},
Objection~5): the framework's wager is that the residual is the next
QD order, not a breakdown. \emph{What counts as a solution:} an
upstream (\ANine{}) derivation of the next correction layer with a
declared precision target --- agreement at $10^{-5}$ would be a
spectacular postdiction audit; a derived next order that \emph{moves
away} from CODATA would be a quiet form of F4, and we say so now so
that it cannot be reframed later.

\paragraph{D-P3-6: Pointlikeness for the non-ground basins.}
\emph{Problem:} Theorem~\ref{thm:pointlike} is stated for the
electron; the muon and tau occupy basins of the same non-spatial
landscape, and the same argument should give $F \equiv 1$ for them
too. \emph{Why it matters:} muon substructure searches are an active
experimental program, and the framework should say in advance what
it owes there. \emph{What counts as a solution:} a one-page corollary
extending Proposition~\ref{prop:nonspatial} and Lemma~\ref{post:RL}
basin-by-basin --- with the one new subtlety (the non-ground basins'
finite lifetimes and gate couplings) handled explicitly rather than
waved through.

\paragraph{D-P3-7: The gravitational form factors.} \emph{Problem:}
this paper's $F \equiv 1$ concerns the electromagnetic structural
form factor. The electron also has energy-momentum (gravitational)
form factors; does the non-spatial-structure argument extend?
\emph{Why it matters:} a framework that derives Newton and Coulomb
from one geometry (\ANine{}'s forces section) should speak with one
voice about the matter side of both. \emph{What counts as a
solution:} the analogue of Appendix~\ref{app:formfactor} for the
stress-tensor vertex --- including an honest treatment of what
``mass as basin level'' implies for the $D$-term, where we
genuinely do not yet know the answer.

\medskip
These seven problems are the paper's to-do list, and F1--F5 are its
standing offer to be wrong. After all, a review that aims to clear
the reader's mind owes the reader one thing above all: an exact map
of where the clearing ends.

\section{Common objections and responses}
\label{sec:objections}

We close the Discussion with the objections a critical reader should
raise --- the strongest versions we could construct, including
several sharpened by the hostile-referee pass this paper underwent
before shipping. The format follows the cohort convention
(\ATwo{}'s closing objections section): each objection is stated at
full force, and each response begins by conceding whatever the
objection gets right.

\paragraph{Objection 1 (O-P3-1): ``QFT already explains identity; this paper
redescribes it.''} The field answer is real and exact
(\S\ref{ssec:qft-identity}), and any account that pretended otherwise
would be wrong. But the objection conflates two questions. QFT
explains why excitations of one field are alike; it cannot say why
\emph{this} field exists with \emph{these} values --- those are free
inputs, and ``free input'' is not an explanation but a place where
explanation stops. The present paper derives the inputs: $y_e$ from
five integers, charge from winding, spin-$\tfrac12$ from the bulk
group. A reader who holds that deriving the content of identity adds
nothing to asserting its form is invited to apply the same standard
to the hydrogen atom: Bohr did not ``redescribe'' Balmer.

\paragraph{Objection 2 (O-P3-2): ``Pointlike by axiom --- AX-1 assumes what Q4
asks.''} Partially right, and the paper says so before the objector
can (Appendix~\ref{app:formfactor}, Step 2, first Remark). AX-1
contributes point-attachment of observables --- an axiomatic input,
exactly as stated. What AX-1 alone cannot do is dissolve the
self-energy crisis (the SM's point electron still needs
renormalization's subtraction) or exclude hidden compositeness (``by
construction'' is silent about deeper scales --- that is why
compositeness searches exist). The new content is the conjunction:
Proposition~\ref{prop:nonspatial} makes point-locality
\emph{consistent} (the structure exists, elsewhere than space), and
Lemma~\ref{post:RL} makes it \emph{permanent} (no scale hides in the
readout). An axiom plus two theorems that make the axiom tenable is
not the axiom alone.

\paragraph{Objection 3 (O-P3-3): ``Theorems `within \GDOS{}' just relocate the
mystery into your axioms.''} We accept the criticism in the form
stated: every theorem in this paper is conditional on the declared
axiom system, and a reader who rejects the constitution receives
conditionals. Two replies. First, relocation \emph{with compression}
is what explanation is: five independent mysteries became
consequences of one axiom system that also derives the Standard-Model
parameter sheet, the cosmological inventory, and the family count
elsewhere in the cohort --- the mystery count went down, sharply.
Second, the axioms are not freely adjustable refuges: AX-1 through
AX-4 are fixed cohort-wide, and this paper added no axiom of its own
--- its one new assumption-shaped object (RL) was \emph{derived}, and
its honest residue is a formalization step (D-P3-1), not a new
postulate.

\paragraph{Objection 4 (O-P3-4): ``The coupling clause and an open integrality lemma carry Q3; an axiom-plus-lemma cannot close a century-old question.''} Correct as stated, and the paper never claims otherwise: Q3's upper bound is conditional on the coupling clause and L-INT at every layer, including the abstract --- though the residue is now one topological check (R-INT), discharged
on the benchmark background in \PaperPTwo{}'s Appendix~H, with two
obstruction theorems showing why nothing weaker can replace the
clause. What the objection underweights is what is
\emph{unconditional}: the lower bound (given observed CP violation),
the basin ontology, the codebook cross-check at four significant
figures, and the dynamical reading. The honest position is that
``why exactly three'' is nine-tenths closed with the last tenth named
--- which is a different epistemic state from ``open,'' and a
century better than ``who ordered that?''

\paragraph{Objection 5 (O-P3-5): ``The $m_e$ residual is a $10^{5}\sigma$
discrepancy --- the codebook is already falsified.''} This is the
sharpest arithmetic objection available, and we state it with full
force: CODATA knows $m_e$ to $3\times10^{-10}$; the codebook misses
by $1.9\times10^{-4}$; measured against experimental uncertainty,
that is astronomically many standard deviations. The response is
about what the codebook claims to be: a \emph{first-order-plus-QD}
structural calculation with a declared precision of its own, not a
prediction with experimental-grade error bars. The correct comparison
is between layers: first-order misses by $\sim10^{-3}$; the QD layer
improves this to $1.9\times10^{-4}$; the wager (D-P3-5) is that the
next layer continues the pattern. The framework is falsified at this
number only if its declared precision is violated --- which F4
registers --- or if the layer-by-layer convergence breaks, which we
have committed in advance to report as failure rather than
re-parameterize.

\paragraph{Objection 6 (O-P3-6): ``The open-system readings are unfalsifiable
decoration --- why are they in a physics paper?''} Honestly stated as
readings rather than results, priced so in the text --- and, in one
case, corrected: this paper's earlier tilted-landscape reading of
spatial drift was withdrawn as mis-sectored
(\S\ref{sec:sensing}), which is the INT discipline working exactly
as designed. It is
included for the same reason interpretations of quantum mechanics
appear in serious papers: Q5's ontological kernel is a real question,
the formalism's silence on it is a real silence, and a framework that
\emph{can} formulate an answer should display it with its status tag
rather than suppress it. Nothing downstream depends on it; deleting
Reading~\ref{rmk:sensing} would cost the paper one insight and zero
theorems --- which is exactly what the INT tag tells the reader.

\paragraph{Objection 7 (O-P3-7): ``Calling a dimension `scale' is relabeling;
any compact direction can be renamed.''} The difference is in the
symmetry algebra and in the observables, not the vocabulary. A
spatial circle has a radius (a continuous dial), translations along
it generate momenta, and its existence produces a Kaluza--Klein tower
and form-factor structure at $\hbar/R$ --- the experimental signature
of \emph{space}. The \GG{} directions have no dials (dimensionless
$r$ with integer endpoint; $G_{\theta\theta} = 1$), their generators
are a dilatation and a compact charge, and they produce \emph{no}
tower --- the absence being P2/F2's testable content
(\S\ref{ssec:kk-contrast}). A relabeling with different observable
consequences is not a relabeling.

\paragraph{Objection 8 (O-P3-8): ``A unique ground state seems to forbid the
positron --- yet positrons exist.''} A fair reading of an imprecise
phrase, and the precision matters: the \GGA{} is unique \emph{per
stratum and per readout orientation}. The positron is the conjugate
readout of the same basin --- same level (mass), opposite winding
eigenvalue (charge) --- exactly as CPT requires; what the framework
forbids is a \emph{second basin}, not a second orientation. This is
no longer a fence but a chapter:
Part~\ref{part:positron} houses it as the sixth question, with the
origin of the twin imported at theorem grade from \PaperPFive{} and
the same-basin reading priced in Table~\ref{tab:q6-status}. The
spinor-level promotion remains owed and registered (D-P3-4); the
observation that PET scanners work is not in tension with this paper
--- it is Part~\ref{part:positron}'s daily-life anchor.

\paragraph{Objection 9 (O-P3-9): ``\,`No exit gate' must secretly violate the
completeness of QFT's decay analysis --- in the SM the electron is
stable for a reason already.''} It is, and the paper keeps the
reason: within the framework the standard argument (charge
conservation + lightest charged state) survives intact, with its
premise --- the derived $\mathrm{U}(1)$ and the spectrum termination
--- now supplied rather than assumed (\S\ref{ssec:gg-stability}). The
no-exit-gate statement does not compete with the SM argument; it
explains the SM argument's premises, and adds one thing the SM
cannot: the forbiddance of charge-violating channels is structural,
not statistical, which is why P1 covers the Borexino channel at all.

\paragraph{Objection 10 (O-P3-10): ``These are pseudo-questions --- `why' lies
outside physics.''} The century's working position, engaged at length
in \S\ref{sec:why-century}, and not a foolish one: insisting on
``why'' without a deeper layer yields numerology, and the discipline
was right to refuse. But the demarcation is empirical, not
principled: a why-question becomes physics the moment a framework
exists in which its answer is a theorem with kill criteria.
That moment is what this paper claims has arrived for these six
questions. The reader need not agree that the claim succeeds; the
reader can no longer say the questions are unanswerable \emph{in
kind} --- Part~\ref{part:VIII} lists the experiments.

\paragraph{Objection 11 (O-P3-11): ``Calling $a_e$ `pure QED dressing' is
wrong --- the SM value includes hadronic and electroweak loops.''}
Acknowledged, and corrected where it appeared: the accurate statement
is \emph{Standard-Model} dressing of a structureless point --- QED to
high order plus the small hadronic and weak terms, all of them
vacuum and probe physics rather than electron structure
(\S\ref{sec:predictions}, P3). The paper's claim concerns the
structural contribution: exactly zero, at every order, forever. The
objection improves the paper's wording and leaves its content
unchanged --- the most useful kind.

\paragraph{Objection 12 (O-P3-12): ``Basins, gates, landscapes --- metaphors
that explain everything explain nothing.''} The vocabulary is
metaphorical; the objects are not. The landscape is a Morse function
on a specified stratum; the basins carry indices (0, 2, 4), levels
(the measured masses), and tolls ($2\pi$, $\pi$ --- actions in
measured lifetime exponents); the gate count is the family number,
checked against LEP. Every metaphor in this paper has a number
attached, and the numbers have falsifiers (F1--F5). The fair test of
``explains everything'' is whether anything could refute it;
\S\ref{sec:predictions} is the refusal of that charge in advance.

\paragraph{Objection 13 (O-P3-13): ``A single-author preprint cohort,
self-citing its own theorems --- why should anyone trust this?''}
The honest answer is: no one should \emph{trust} it, and the paper is
engineered so that no one has to. Every load-bearing step carries a
status tag; every import names its source and its fences; the
arithmetic reproduces programmatically; the references were verified
against the literature; the kill criteria are pre-registered; and
the intended reader (\S\ref{sec:preface}) is invited to audit, not
believe. Single-author programs have been right before and wrong
before; the only protection either way is exactly the discipline of
exposure this cohort practices. The sociology is a reason for
caution; it is not an argument, and the paper asks to be met with
arguments.

\paragraph{Objection 14 (O-P3-14): ``\,`No substructure ever' is unfalsifiable
--- you can never verify `ever'.''} The objection inverts Popper. A
universal negative can never be \emph{verified}; it is for precisely
that reason the most \emph{falsifiable} kind of statement in science
--- refutable by one event, at any energy, in any decade, by any
experiment, with no parameter to absorb the blow. Compare the
alternatives honestly: a compositeness model with floating $\Lambda$
is the unfalsifiable party here, retreating one decade per decade.
This paper's claim stands still and waits.

\paragraph{Objection 15 (O-P3-15): ``Lemma RL's `derivation' is a verbal
argument, not a proof.''} The strongest form of the paper's most
important objection, and the response has three parts. First, the
derivation is not verbal: it is a two-branch case analysis on the
support of the registration kernel, each branch closed by an explicit
constitutional clause (spacelike support barred by AX-1's statement;
causal support scale-confined by the equal-time-slice argument), with
the scope stated. Second, its one genuinely informal step is named,
isolated, and registered (D-P3-1) --- the difference between a
physicist's argument with a declared gap and hand-waving is precisely
that the gap has a name and a falsifier (F5). Third, the cohort's
record on such steps is the relevant evidence: every previously
declared gap in this lineage was either closed or honestly reported
as open in the successor paper, never silently absorbed. We accept
the demand the objection encodes --- D-P3-1 is the paper's principal
debt --- and we decline the implication that naming a debt is the
same as defaulting on it.

\medskip
Fifteen objections, fifteen responses, several conceding real ground
--- which is how it should be. After all, a paper that can state its
opponents' best arguments more sharply than they would is a paper
that has earned its conclusions twice.


%% ===================================================================
%%  PART VIII -- THE FIFTY-YEAR ARC
%% ===================================================================

\section[Part~VIII in plain English]{Part~VIII in plain English: what has been shown, what it is worth, and what would kill it}
The technical work is finished and this Part steps back from it. It states in plain terms what has been established for each of the six questions and what each answer buys; it locates the result against every prior approach known to us, and against the two dominant frameworks of beyond-Standard-Model physics; it consolidates the predictions into a falsification program; and it sets out the open problems at their full length rather than in a closing sentence.

The ordering is deliberate. The positive case comes first and the objections come last, so that the defensive material is read after the argument rather than instead of it. The objections are ours, written to be the strongest a critical reader would raise, and where the honest answer is ``not yet'' it is given as that.

The comparison with strings and supersymmetry is the section a skeptical reader should turn to first. It is written to be checkable rather than persuasive: three frameworks, the same questions, and a row recording what each one requires to exist that has not yet been seen. That row is the axis along which any of the three --- this one included --- can be retired.

\GGPart[Conclusions]{Conclusions: The Century, the Closing, and the Fifty-Year Arc}{Why the questions waited, what has been answered, and a word to the wider reader}
\label{part:IX}

\section{Why a century? The structural reasons the questions stayed open}
\label{sec:why-century}

It would be easy --- and wrong --- to read this paper as an indictment
of twentieth-century physics: \emph{five obvious questions, a hundred
years, no answer; what was everyone doing?} What everyone was doing
was, by any standard, the most successful science in human history,
and the century's silence on Q1--Q5 was not blindness --- and its premature
confidence on Q6, answered formally in 1931 and understood structurally
only now, was the same structure wearing the opposite mask. It was
structural. It is worth stating the structure plainly, both because
the questions deserve an account of their own neglect and because the
account explains what had to change before they could be answered.

First, \textbf{the questions had no home}. Q1 lived in the foundations
of quantum field theory, Q2 in particle phenomenology, Q3 in flavor
physics, Q4 in renormalization theory, Q5 --- when it was admitted at
all --- in the philosophy of physics. Five thriving subfields, five
filing cabinets; and the observation that the six questions might be
one question belonged to none of them. A conjunction has no natural
referee. The literature is full of excellent partial treatments of
each fragment; the present paper's bibliography cites the best of
them; what the century never produced is a paper whose \emph{subject}
is the conjunction --- because no framework made the conjunction a
single object that a paper could be about.

Second, \textbf{the deepest question was answered by grammar, and
grammar ends conversations}. Quantum field theory does explain why all
electrons are alike: they are excitations of one field. The answer is
correct, and it is the kind of answer that stops further asking ---
not because it satisfies, but because it relocates. Once sameness is
the grammar of the formalism, ``why this field, with these values?''
sounds like a question about the formalism rather than about the
world, and physicists are rightly wary of those. The question did not
die; it was reclassified --- filed under metaphysics, where working
physicists do not browse. Mermin's famous summary of the prevailing
attitude --- ``shut up and calculate'' \citep{Mermin1989} --- was
coined about quantum foundations, and it applied with full force here:
the calculation worked, so the conversation moved on.

Third, \textbf{the success trap}. The classical electron's self-energy
crisis was a genuine emergency --- it broke theories and careers ---
and renormalization resolved the emergency without answering the
question: the infinity was not explained but absorbed, the point-like
ontology kept by construction. Then QED proceeded to agree with
experiment at parts in $10^{12}$, and a discipline cannot easily keep
treating as open a question whose evasion is confirmed to twelve
digits. Q4 was not answered; it was \emph{outperformed}. The radius
bounds shrank, the precision grew, and ``why is it a point, and why
does that cost nothing?'' came to feel like ingratitude.

Fourth, \textbf{the inputs culture}. The Standard Model
institutionalized its free parameters: $m_e$ and $\alpha$ are entries
in a data book, maintained with magnificent care, and the professional
slot for ``why these values?'' simply did not exist --- the available
answers were anthropics or numerology, and serious people rightly
avoided both. A culture in which values are measured rather than
derived has no failure mode for Q1's second half; it has only a
silence where the question would go. What was missing was not
curiosity but a framework in which a value could be a theorem ---
because only against derived values can ``why these?'' even be wrong.

Fifth, and most structurally, \textbf{the closed-system blind spot}.
The answer this paper assembles is built from the vocabulary of
descent: landscapes, basins, gates, relaxation, a ground state that is
\emph{reached}. None of these are concepts of closed-system
fundamental physics. A unitary, time-reversible, closed dynamics has
no descent --- nothing relaxes, nothing is spent, nothing halts (the
exact open-system equations that do descend \citep{Lindblad1976}
were filed under applied decoherence, not foundations) ---
and so the very nouns needed to \emph{state} the answer were absent
from the fundamental level for a century, quarantined in statistical
mechanics and chemistry as ``emergent'' talk. \PaperPTwo{}'s
methodological reflection \citep{ArisakaP2N3} makes the argument in
full for the family number: closed-system methods produce
admissibility conditions, never upper bounds; the budget that stops
the ladder at three is an open-system resource. The same diagnosis
covers all six questions at once. Ground-state-ness is an
open-system fact. A physics that treats openness as an approximation
cannot say what the electron is, for the same reason a grammar with no
past tense cannot say what happened.

None of this required anyone to be wrong. The deferral was honest
discipline: without a layer beneath the inputs, insisting on ``why''
yields numerology, and the century's refusal to indulge it protected
the subject's integrity. The cost was only that the questions aged
into furniture --- present in every room of physics, sat upon daily,
and no longer seen. What changed, on the present account, is not that
someone finally thought harder; it is that two ontological commitments
shifted at once. The extra structure of the world was allowed to be
\emph{non-spatial} --- a scale direction and a phase direction, rather
than more space --- and the fundamental dynamics was allowed to be
\emph{open} --- a descent, rather than a reversible flow. On those two
commitments the six questions stop being six metaphysical leftovers
and become one geometric statement with a status table and kill
criteria. Whether the statement is \emph{true} is for experiment ---
Part~\ref{part:VIII} says exactly where to shoot. That it is
\emph{askable} is already the century's lesson: questions do not die
of difficulty; they die of having no language, and they revive the
moment one exists.

\section{The view from the last page: four oldest facts, two formulas,
one geometry}
\label{sec:fourcells}

Before the plain-language close, we look once, panoramically, at
where Part~\ref{part:VII} has actually left the reader --- at a single
table that this paper has earned the right to draw only on its final
pages, because every cell of it is now a derived statement. Consider
the four oldest dynamical facts about matter, the four that every
laboratory and every sky exhibits: charges attract and repel
\citep{Maxwell1865}; masses fall \citep{Newton1687}; accelerated
charges radiate \citep{Larmor1897}; orbiting masses spiral inward
\citep{HulseTaylor1975}. The century inherited these as four separate
literatures. In the present framework they are generated --- not
assembled --- by two derived dichotomies. The \emph{columns} are the
two curvature slices of the one composite connection that AX-2
declares to be the world's whole structural content: the gauge slice
carried by the phase dimension, the metric slice carried by the scale
dimension. The \emph{rows} are the two dynamical regimes of the one
constitution: the closed, conservative dynamics of the bulk
(\GGEP{}), and the open, dissipative dynamics of the boundary
reduction (\OGGEP{} $\to$ \GDOS{} $\to$ \GRIPin{}). And each row is
literally \emph{one equation read twice}.

Row 1 is the unified equation of motion, Eq.~\eqref{eq:unified-eom}.
Its right-hand side, read alone, is cell (1a): the local
$\mathrm{U}(1)$ invariance of the phase fiber forces the connection
$A_\mu$, minimal coupling is the complete gauge-sector coupling AX-2
permits, and the static Green's function delivers Coulomb's law
(\S\ref{ssec:two-chains}, Chain~B). Its left-hand side, read alone,
is cell (1b): the scale-profile reduction along the scale dimension delivers
$M_{\rm Pl}^2$, Einstein's equation, Newton's law, and $F = ma$ as
geodesic bookkeeping (Chain~A). One trajectory, two curvatures, no
force postulated. Row 2 is the canonical \GDOS{} current --- the
gradient-plus-circulation-plus-noise decomposition whose radiative
deployment is \AFive{}'s Part~VI completion and quantitative closure
\citep{ArisakaA5GDOS}. Its gauge-slice reading is cell (2a):
synchrotron damping as the gradient sector, with the mobility derived
in closed form and carrying Larmor's coefficient exactly, halting at
the equilibrium emittance whose universal constant is measured in
every electron storage ring. Its metric-slice reading is cell (2b):
the binary inspiral as the same gradient sector on the orbital
elements, with the mobility carrying Peters' coefficient exactly,
halting at nothing --- the merger --- with five decades of
binary-pulsar timing \citep{HulseTaylor1975} and the directly
recorded waveforms \citep{Abbott2016} as its anchors.
Table~\ref{tab:fourcells} sets the four cells out.

\begin{table}[ht]
\centering
\caption[The four oldest dynamical facts as one geometry.]{The four oldest dynamical facts as one geometry: columns are
the two curvature slices of the composite connection; rows are the
closed (\GGEP{}) and open (\OGGEP{}/\GDOS{}) regimes. Row 1 is one
equation read twice (Eq.~\ref{eq:unified-eom}); Row 2 is one current
read twice (\AFive{}'s canonical \GDOS{} decomposition, radiative
closure included \citep{ArisakaA5GDOS}). Every cell carries measured
numbers at accessible energies.}
\label{tab:fourcells}
\small
\renewcommand{\arraystretch}{1.35}
\begin{tabular}{@{}p{0.26\textwidth}p{0.32\textwidth}p{0.32\textwidth}@{}}
\toprule
& \textbf{Gauge slice ($\Stheta$, 6th)} & \textbf{Metric slice ($\Ir$ scale profile, 5th)} \\
\midrule
\textbf{Closed (\GGEP{}):} one equation, Eq.~\eqref{eq:unified-eom} &
(1a) Coulomb's law; the Lorentz force; $\alpha$ derived, charge
quantized & (1b) Newton's law; $F = ma$ as geodesics; $G_N$ from the
scale-profile integral \\
\textbf{Open (\OGGEP{}/\GDOS{}):} one current, one ledger &
(2a) synchrotron damping; mobility = Larmor-exact; equilibrium
emittance measured & (2b) binary inspiral; mobility = Peters-exact;
Hulse--Taylor, LIGO \\
\bottomrule
\end{tabular}
\end{table}

Two refinements make the table exact rather than evocative.
\emph{First, the row assignment is an energetics statement, not a
field-type statement.} Both fields populate both rows in general: a
charge accelerated by an electric field also radiates, and a charge
in a magnetic field is also conservatively bent. What is exactly true
is that $q\,\vec v\times\vec B$ does no work, so under a pure
magnetic field the \emph{entire} energy budget is radiative --- the
magnetic cell is nature's clean preparation of Row~2, which is
precisely why the synchrotron is the golden case --- while the static
electric field does work conservatively, making the Coulomb cell the
clean preparation of Row~1. The gravity column, elegantly, separates
its rows not by field type but by \emph{timescale}: the same binary
is cell (1b) on any single orbit and cell (2b) secularly.
\emph{Second, the two non-spatial dimensions divide the labor of
Row~2 exactly as \S\ref{sec:sensing}'s two-sector discipline
requires.} The emitted quantum is gauge-sector; what belongs to the
scale dimension is not the emission but the \emph{openness} --- the
\OGGEP{} reduction whose depth coordinate is the scale direction, and
which makes the loss irreversible. The sentence to keep is this:
\emph{the sixth dimension supplies what is emitted; the fifth
dimension supplies why it cannot come back.} Geometrizing
electromagnetism required both: the conservative half of QED is phase
geometry (Row~1), the dissipative half is scale-structured openness
(Row~2), and neither dimension alone completes the geometrization ---
the pair does.

The table also settles a piece of history. Weyl's 1918 attempt
geometrized electromagnetism on the \emph{scale} direction
\citep{Weyl1918} and failed to Einstein's objection that histories
would imprint on atomic spectra; the 1929 repair moved gauge to the
\emph{phase} \citep{Weyl1929}. The present framework diagnoses the
episode rather than merely surviving it: both directions are real,
non-spatial, and employed --- the phase got electromagnetism's
conservative half; the scale got gravity's strength, the
renormalization flow, and the arrow of time. Weyl was not wrong that
scale is geometric; he assigned it the wrong force. Likewise
Kaluza--Klein \citep{Kaluza1921,Klein1926} was not wrong that a fifth
dimension unifies; it was wrong that the dimension is spatial ---
which is where the towers, the moduli, and the invisibility problems
came from. And it locates the contrast that
\S\ref{sec:susy-string} drew at full length: faced with two great
theories, there are exactly two unification strategies --- make
gravity behave like a gauge field theory (\emph{quantize gravity},
moving the unification up to the Planck scale, where no number has
ever been measured), or make the gauge force behave like gravity
(\emph{geometrize the gauge force}, moving it down into the
laboratory). The twentieth century took the first road almost
unanimously; Einstein took the second and failed for a reason the
next section names. The inventory of the second road is now the
table above: cell (1a) carries $\alpha$ and charge quantization,
cell (1b) carries $G_N$, cell (2a) carries the storage-ring constants
that run every light source on Earth, cell (2b) carries the pulsar
timing and the recorded waveforms --- four cells, four empirically
saturated regimes, no adjustable coefficient anywhere in the table.
We state the status of this section with the same care as everywhere
else: every formula in the table is owned where it was derived
(Parts~\ref{part:VI}--\ref{part:VII}; \AFive{}'s Part~VI and closure);
the judgment that this constitutes the \emph{deeper} unification is
the program's reading of its own results, and we price it as such.
What is theorem-grade is the generated structure --- two dichotomies,
two master formulas, four cells --- and the numbers.

\section{The century completed: openness as the missing half of
Einstein's dream}
\label{sec:century-openness}

Section~\ref{sec:why-century} gave five structural reasons the
questions waited; its fifth --- the closed-system blind spot --- is
deeper than the other four, deep enough to rewrite the standard
history of the unification program, and this paper should say so
plainly before it closes. The standard telling of why Einstein's
unified-field program failed is that he ignored quantum mechanics.
The precise telling is that he asked a \emph{closed} theory to do an
\emph{open} system's jobs. The quantum, the arrow of time,
measurement, dissipation, decay --- every phenomenon that defeated
the geometrizers of the 1920s through the 1950s is a boundary
phenomenon, a property of what a reduced observer registers, not of
what the bulk is. Einstein kept trying to build those into the
geometry itself, where they cannot live; the Copenhagen settlement
built a calculus for the boundary and declared the bulk meaningless.
The century-long stalemate was two camps each insisting that its
layer was the only layer. The constitutional split of this program
--- a closed geometric bulk under \GGEP{}, a derived open reduction
under \OGGEP{} --- is, in that sense, the treaty: \emph{Einstein was
right about the bulk} --- it is closed, deterministic, geometric;
\emph{Bohr was right about the boundary} --- it is probabilistic,
irreversible, and cannot help but play dice. The dice are what
determinism looks like through a partial trace. God does not play
dice in the bulk; the boundary has no choice.

There is also a hard historical reason the completion took the
century, and it acquits everyone involved: \emph{the mathematics of
openness did not exist.} The influence functional --- the exact form
of a traced-out sector --- is 1963 \citep{FeynmanVernon1963}, eight
years after Einstein's death. The general open-system generator is
1976 \citep{Lindblad1976}. The gradient-flow formulation of
dissipative dynamics --- the very language in which the descent of
this paper's landscapes is written --- matured only from 1998 onward
\citep{JKO1998}. Einstein failed not only for want of the right
geometry but for want of tools that had not been invented; the second
half of his dream was mathematically inaccessible in his lifetime.
What the present program adds is the recognition that this body of
mathematics is not a phenomenological toolkit for quantum optics and
chemistry but constitutional physics --- the derived law of what any
boundary observer sees (\citealp{ArisakaA5GDOS}; \citealp{ArisakaA6Gi4}).

The author's thesis here --- and the experience of assembling this
paper has confirmed it at every turn --- is that \emph{any system in
nature is an open system}, and that this sentence has an exact formal
expression which inverts the textbook hierarchy. In the traditional
ordering, closed mechanics is fundamental and dissipation is a
correction bolted on. In the structure actually derived, it is the
reverse: the closed, conservative physics of Row~1 is a
\emph{sub-sector} of the open physics of Row~2 --- the unified
equation of motion is the divergence-free circulation piece of the
canonical \GDOS{} current, the part that survives when nothing is
shed (\AFive{}'s closure derives exactly this: the conservative orbit
\emph{is} the circulation sector, by the angle average of the exact
reduced dynamics). $F = ma$ is what the open current does on its
silent sector. Closed physics is the special case; openness is the
law. A century of mechanics was taught in the opposite order, and
that --- more than any single equation --- is the inversion this
program asks its reader to make.

A resonance of dates belongs in the record. This paper is completed
in 2026 --- exactly one century after the boundary calculus was
written down without a derivation: Schr\"odinger's equation
\citep{Schrodinger1926} and Born's rule \citep{Born1926} are both
1926. A hundred years later, the companion papers derive the Born
rule as a theorem of the boundary reduction \citep{ArisakaA8QM}, and
the same reduction, deployed in this paper's Part~\ref{part:VII},
hands back Larmor's and Peters' coefficients and a storage-ring
constant measured to four digits. The centennial framing is not
decoration; it is the actual shape of the history.

One word of method, because the fifty-year questions deserve a claim
that cannot be embarrassed. ``Paradigm shift'' is, in Kuhn's own
terms \citep{Kuhn1962}, a verdict the community renders after a
framework dissolves standing anomalies and survives its falsifiers;
it is not a thing a paper can declare, only a thing a paper can
\emph{qualify for}. What may be written down today, defensibly, is
this: the conceptual inversion is complete and explicit; the
anomalies it dissolves are named --- the measurement problem (dissolved by the always-on \OGGEP{} projection, \AFive{}~\S23), the
radiation-reaction pathologies \citep{Dirac1938}, the six
century-old questions of this paper, the quantize-gravity impasse ---
and the kill criteria are pre-registered
(Part~\ref{part:VIII}, \S\ref{sec:predictions}), with every imported
fence declared. A paradigm shift with declared falsifiers is a
scientific claim; without them it is a mood. This program has the
falsifiers, and the sentence should never be said without them
attached.

Last, the dream itself, in Einstein's own three clauses. He wanted
the forces unified: that is Table~\ref{tab:fourcells}, the two
curvatures of one connection, statics, dynamics, and now dissipation.
He wanted the bulk lawful: that is the treaty above --- determinism
upstairs, derived dice downstairs. And he wanted matter itself to be
field-theoretic --- ``a completely field-theoretic description of
matter,'' particles as aspects of the geometry rather than foreign
bodies placed in it. That third clause is this paper: the electron as
the unique ground state of the geometry, its mass a basin level, its
charge a winding, its spin a double-cover tag, no body anywhere. The
five questions the author has carried for fifty years --- and the sixth,
which he, like everyone, was taught to regard as solved --- turn out to be
the \emph{matter clause} of the same dream --- which is why their
answers arrived together, from one landscape, the moment the
landscape was drawn with both of its halves: the geometry that is
closed, and the observation that is not. Status, one final time:
this section is the program's reading of its own results ---
interpretive by this paper's own tags, resting on theorems owned
elsewhere and on fences declared throughout; the reader who wants
the load-bearing chain will find every link in
Parts~\ref{part:III}--\ref{part:VII} and the status ledger of
Appendix~\ref{app:ledger}. The philosophy is priced exactly like
everything else in this paper. That is the discipline, and we keep
it to the last page.

\section{Conclusions, in plain English}
\label{sec:conclusions-plain}

We close the technical portion of the paper in plain language, for the
reader --- physicist or not --- who wants to know what was attempted
here and what it would mean if it stands.

\subsection{The wider view: what the six answers attempt together}
This paper took the six oldest facts about the electron ---
everywhere identical, absolutely stable, twice copied, exactly
mirrored, perfectly point-like, mysteriously responsive --- and
argued that they are not six facts. They are one fact seen from six
directions: \emph{at the
bottom of the electron's sector of the world there is exactly one
deepest basin, and the electron is what occupying it looks like.}
Identity is the uniqueness of the basin; stability is the absence of
any exit; the muon and tau are the two higher basins of the same
landscape, and their count is the landscape's budget; the
point-likeness is the statement that the basin's structure lies along
directions that are not space; the positron is the same basin read in
the mirror; the sensing is the electron
following the same composite geometry that makes apples fall --- the
open-system layer adding only the arrows, radiation as it moves,
descent where decay is possible (for the electron, nowhere). Around
this one picture stand the companion papers of the program --- the
constitution that fixes the axioms, the bulk theorems, the open-system
runtime, the codebook that turns geometry into the measured numbers,
and the sister paper that counts the basins --- each cited, none
re-derived, every borrowed fence carried along visibly.

\subsection{What this paper is, in one sentence}
This paper is an attempt to move the electron --- the first elementary
particle we ever found, and the one all of chemistry, biology, and
technology runs on --- from the list of things physics \emph{assumes}
to the list of things physics \emph{explains}, and to do it with every
assumption named and every failure mode declared in advance.

\subsection{Why this matters beyond physics}
Three reasons, in widening circles. Within science: ``ground state''
is the single most borrowed concept physics ever lent its neighbors
--- chemistry's stable molecule, biology's folded protein, every
discipline's notion of a configuration things settle into. If the
present account is right, the loan was repayment: the concept was
constitutional all along, and the electron is its charter case. For
the practice of science: this paper is an experiment in a discipline
of candor --- strong claims held together with declared fences,
status tags on every step, kill criteria published before the
referees arrive. We believe ambition and honesty are not rivals, and
that the fences made the thesis stronger, not weaker; readers who
take nothing else from the paper are invited to take the method. And
for anyone at all: the sameness of the electron is the reason the
universe is \emph{reliable} --- the reason a water molecule formed
twelve billion years ago is identical to one formed this morning, the
reason chemistry repeats, the reason memory, inheritance, and
civilization can exist in a world built of particles. And the sameness
holds not only across time but across the sky: the electron in a hydrogen
atom on the far side of the observable universe --- in a region that, but
for inflation, was never in causal contact with our own --- carries the
identical mass and charge, so its Balmer lines are our Balmer lines
(Corollary~\ref{cor:horizon-independence}; the cosmological statement is
the \emph{second horizon problem} of \ATen{}). Temperature could be
smoothed by contact; identity could not, and needed no smoothing --- it
was one attractor all along. To explain that sameness, in time and in
space, is to explain why the universe can be a home rather than merely a
place. The question a child asks --- \emph{why is everything
made of the same stuff?} --- turns out to be the deepest one in the
building, and we have tried to treat it with the seriousness it
always deserved.

\subsection{What we hope a careful reader will take away}
Three convictions, offered for audit rather than assent. \emph{First},
that the six oldest questions about the electron are one
question, and that at least one coherent, quantitative, falsifiable
answer to it now exists --- conditional exactly where its status table
says it is conditional, and nowhere else. \emph{Second}, that the
century of silence was structural, not shameful --- and therefore that
its lesson points forward: where a deep question seems unanswerable,
look first at what the reigning ontology cannot say, for questions die
of missing language, not of difficulty. \emph{Third}, that the
questions you carried out of your first year of physics were the right
questions --- that noticing what the textbook does not pause on is the
beginning of the work, not a distraction from it. If this framework is
right, those questions now have answers you can check. If it is wrong,
the kill criteria of Part~\ref{part:VIII} tell you precisely how to
show it --- and the authors of this program would rather be refuted
sharply than believed vaguely. Either way, the questions are yours
again, with interest.

After all, a universe in which every electron is the same electron is
a universe that keeps its promises --- and a physics that can finally
say \emph{why} has begun, at last, to keep its own.

\section{The fifty-year arc}
\label{sec:arc}

%% Voice author-approved June 11, 2026 (Phase-2 review, J3): kept as
%% drafted at v1.0, at the author's direction.

I met these five questions as a student, fifty years ago, in the form
every physics student meets them: as facts so basic that the textbooks
did not think to flag them as mysteries. The sixth I met differently
--- as a triumph: the positron, predicted by an equation. It took most
of the fifty years to notice that ``the equation predicts it'' names a
mystery rather than solving one. Every electron is the same;
electrons do not decay; there are, inexplicably, three copies; the
electron is a point; charges feel forces. One learns to calculate with
all five before one notices that none of them has a reason. I noticed ---
I have never been able to un-notice --- and for five decades, through a
career spent mostly on other questions, these five kept their place on
the private list a physicist carries of things he would like to
understand before he is done.

What I did not expect, through most of those decades, is that the five
would turn out to be one. The framework assembled across the companion
papers of this program was not built to answer them; it was built to
close the parameter sheet of the Standard Model and the inventory of the
cosmos. That the same geometry, at the point where its cascade halts,
should hand back the electron --- identical because the ground basin is
unique, stable because the ground basin has no gate, copied twice because
the landscape above it holds exactly two more basins, pointlike because
its structure lies along directions that are not space, responsive
because to occupy a basin is to descend its tilts --- was not an
ambition. It was the view from the bottom of the landscape, once the
landscape was drawn.

I have tried to write the paper I would have demanded as a referee at any
point in those fifty years: every fragment of standard physics credited
at full strength; every step that is not a theorem named as what it is;
the kill criteria stated where the paper can be shot. The questions
deserve that discipline. They were patient with me for fifty years; the
least I owe them is a closing that cannot be embarrassed.

After all, the electron was the first elementary particle we ever found,
and it may be the last one we truly understand --- not because
understanding came hard, but because for a century we mistook its six
deepest properties for six separate facts, when they were always one
fact, seen five times: at the bottom of the world there is exactly one
basin, and everything ordinary that exists is what it looks like from
inside.

%% ===================================================================
%%  APPENDICES
%% ===================================================================
\appendix
\GGAppendixPart[Appendices]{Appendices}{Abbreviations, the complete derivations for Q1--Q5 (Q6's derivation is the CPT companion's, imported in Part~V), and reference material}

\section{Summary of Abbreviations}
\label{app:abbrev}

This appendix collects the abbreviations used in the present paper,
following the convention of \ATwo{}'s Appendix~A: program-defined
names are rendered in \emph{sans-serif type} so the reader can see at a
glance which terms belong to the \GGTheory{} program proper; standard
physics abbreviations imported from the wider literature are in plain
uppercase Roman; mathematical objects are in roman or italic in the
usual way. The canonical Dictionary of Program-Defined Acronyms ---
each entry with a full definition and a plain-English physics intuition
--- is \ATwo{}'s Appendix~B and is not duplicated here.

{\small
\begin{longtable}{@{}>{\raggedright\arraybackslash}p{0.155\linewidth} >{\raggedright\arraybackslash}p{0.535\linewidth} >{\raggedright\arraybackslash}p{0.23\linewidth}@{}}
\caption[Summary of abbreviations used in the present paper]{Summary of
abbreviations used in the present paper. Program-defined names are set in sans serif, standard physics abbreviations in plain uppercase roman, and mathematical objects in roman or italic as usual. The third column points at the paper or the section where each name is fixed, so an abbreviation met in the middle of an argument can be resolved without leaving the appendix.}
\label{tab:appA-abbrev}\\
\toprule
\textbf{Symbol} & \textbf{Meaning} & \textbf{Primary link} \\
\midrule
\endfirsthead
\multicolumn{3}{c}{\itshape Table~\ref{tab:appA-abbrev} continued from previous page}\\
\toprule
\textbf{Symbol} & \textbf{Meaning} & \textbf{Primary link} \\
\midrule
\endhead
\bottomrule
\endfoot
\GGTheory{} & Grand Geometric Theory, the program of this cohort & \AOne{} \\
\GG{} & The six-dimensional bulk $\cM_4\times\Ir\times\Stheta$ with geometry--gauge locking & \ATwo{} \\
AX-1 (LC) & Axiom 1: Locality and Causality, binding dynamics \emph{and} measurement instruments & \AOne{}; \S\ref{sec:formfactor} \\
\MSMF{} & Axiom 4: ``Maximum Symmetry, Minimum Freedom'' --- no unforced structure & \AOne{} \\
\GGEP{} / \OGGEP{} & (Operational/Open) Geometry--Gauge Equivalence Principle; \OGGEP{} is the bulk-to-boundary registration & \AOne{}, \AEight{} \\
\BIsix{} & The modified Bianchi identity of the six-force bulk (anomaly closure) & \AThree{} \\
\OGNfive{} & The integer ledger $(M,N,L;J,K) = (1,3,5;7,35)$, Diophantine-unique & \ATwo{}, Thm.~6 \\
\GUfive{} & The five universal constants $\{c,G_N,\hbar;k_B,Q_B\}$ & \AFour{} \\
\GDOS{} & Geometric Dynamics of Open Systems: the boundary law & \AFive{} \\
\GiFour{} & The four geometric pillars (TGG, CCI, \GFF{}, \GRIP{}) & \ASix{} \\
\GFF{} & Geometric Free-energy Functional: the master landscape whose valleys are the stable boundary objects & \ASix{} \\
GFF-ST7 & Structure theorem: each stratum has a unique deepest attractor & \ASix{} \\
\GRIP{} & The cascade runtime $\DGI \to \GSSB \to \GA$ & \ASix{} \\
\GRIPin{} & Fixed-landscape regime: relaxation on the landscape (drift, decay) & \ASix{}, def:GRIPin \\
\GRIPout{} & Landscape-rebuilding regime: transient, out of equilibrium & \ASix{}, def:GRIPout \\
\DGI{} & Dynamical Gauge Invariance: the symmetric top of the cascade & \ASix{} \\
\GSSB{} & Geometric Spontaneous Symmetry Breaking: branch selection at saddles (the gates) & \ASix{} \\
\GA{} & Geometric Attractor: any stable basin & \ASix{} \\
\GGA{} & Ground Geometric Attractor: the unique deepest basin, where \GRIPin{} halts & \ASix{}, def:GGA; \AEleven{} \\
QD & Quantum Descent: the finite transport-correction layer of the codebook & \ANine{} \\
RL & Readout Locality: the registration map carries no 4D length scale & Lemma~\ref{post:RL} \\
$\Ir$, $\Stheta$ & The two non-spatial directions: scale (RG) interval and phase circle & \ATwo{}; \figref{fig:bulk-cross-section} \\
$\Sigma_{\rm fam}$ & The family-projector stratum $\mathbb{C}P^{N-1} = \mathbb{C}P^2$ & \PaperPTwo{}, \ANine{} \\
$F(q^2)$ & The structural (elastic) charge form factor & \S\ref{sec:formfactor} \\
$\JCKM$ & The Jarlskog CP-violating invariant & \PaperPTwo{}; App.~\ref{app:Q3} \\
L-INT & The integrality theorem: Hopkins--Singer quantization of the
descended periods, derived in \PaperPTwo{} with the single topological
residue R-INT (discharged on the benchmark in App.~H) &
\PaperPTwo{}, App.~E, G, H \\
$\SmaxBI$ & The \BIsix{} instanton budget, $3\pi$ = the capacity theorem at $N=3$ & \PaperPTwo{}, T-N3-6 \\
KK & Kaluza--Klein (spatial compactification; the contrast case) & \S\ref{ssec:kk-contrast} \\
RS & Randall--Sundrum (warped-throat lineage) & \citep{RandallSundrum1999} \\
SM / QED / QFT & Standard Model / quantum electrodynamics / quantum field theory & standard \\
CKM / PMNS & Quark / lepton mixing matrices & standard; \PaperPTwo{} \\
MSSM & Minimal Supersymmetric Standard Model (contrast case) & \S\ref{ssec:susy-contrast} \\
CODATA / PDG & Standards bodies for constants / particle properties & \citep{CODATA2022,PDG2024} \\
ppt & parts per trillion ($10^{-12}$) & \citep{Fan2023} \\
\end{longtable}
}


\section{Claim-status ledger}
\label{app:ledger}

Tag vocabulary as in \S\ref{sec:status-table}. ``Location'' names the
companion paper and the labeled environment or section within it. Every
location was verified by direct search in the cited paper rather than from
memory, so each row of the ledger below can be checked the same way.

{\small
\renewcommand{\arraystretch}{1.25}
\begin{longtable}{@{}>{\raggedright\arraybackslash}p{0.30\textwidth}>{\raggedright\arraybackslash}p{0.12\textwidth}>{\raggedright\arraybackslash}p{0.30\textwidth}>{\raggedright\arraybackslash}p{0.17\textwidth}@{}}
\caption[The complete claim-status ledger.]{The complete claim-status ledger. Every load-bearing step of the
paper, its status tag, its verified source, and where it is consumed. This is the table to check a claim against. Every load-bearing step appears exactly once, with the tag that grades it, the place it is established --- here, or in the companion that owns it --- and the section of this paper that consumes it. A step that appears nowhere in this table is not load-bearing.}
\label{tab:ledger}\\
\toprule
\textbf{Load-bearing step} & \textbf{Tag} & \textbf{Source location} & \textbf{Used in} \\
\midrule
\endfirsthead
\multicolumn{4}{@{}l}{\footnotesize\emph{Claim-status ledger, continued}}\\
\toprule
\textbf{Load-bearing step} & \textbf{Tag} & \textbf{Source location} & \textbf{Used in} \\
\midrule
\endhead
\midrule
\multicolumn{4}{r@{}}{\footnotesize\emph{continued on the next page}}\\
\endfoot
\bottomrule
\endlastfoot
6D bulk; $\Ir$, $\Stheta$ non-spatial & THM & A2, Theorem 1 (T-GG6-1) & Parts II, VI \\
\addlinespace
$\mathrm{Spin}(1,5)\cong\SLtwoH$; quaternionic Weyl doublet & THM & A2, magic-square proposition & \S\ref{ssec:value-spin}, \S\ref{sec:mass-spin} \\
\addlinespace
Ledger $(1,3,5;7,35)$ unique & THM & A2, Theorem 6 & \S\ref{ssec:value-mass} \\
\addlinespace
\BIsix{} closure & THM & A3 & Part II \\
\addlinespace
$e$ derived, not primitive & THM & A4, T-Euclid-4 & \S\ref{ssec:value-charge} \\
\addlinespace
\GDOS{} runtime; O3 (Morse-positivity) open & THM/fence & A5; O3 & Parts II, III \\
\addlinespace
\GFF{}-ST7 unique deepest attractor & THM & A6, GFF-ST7 & Thm.~\ref{thm:identity} \\
\addlinespace
def:GGA; def:GRIPin/out & DEF & A6, labels def:GGA, def:GRIPin, def:GRIPout & Parts III, VII \\
\addlinespace
T-GGA-as-Ground-State & THM & A11, Step-3 regime theorem & \S\ref{ssec:gga-statement} \\
\addlinespace
Universal-identity theorem (T-A8.9 = T-QM-9) & THM & A8, theorem T-A8.9 (label thm:TA-9) & Thm.~\ref{thm:identity} \\
\addlinespace
$y_e = N/(L^3 2^{J+L+1})$ & codebook & A9, label sec:lepton-mass & Eq.~\eqref{eq:ye} \\
\addlinespace
$m_e^{\rm QD} = 0.511097845$ MeV; $\mathcal R_e = 641/640$ & codebook & A9, QD-completion section & Eq.~\eqref{eq:meQD}; residual $1.9\times10^{-4}$ declared \\
\addlinespace
$\alphainv(M_Z) = 2^J$; $\alphainv(0) = 2^J{+}N^2$, QD-completed & codebook & A9, dyadic-closure statements & Eq.~\eqref{eq:alpha} \\
\addlinespace
Identity section; forces section; weak as \GRIPin{} & THM/ doctrine & A9: identity \& forces sections (by label); \GRIPin{} doctrine & Parts III, IV, VII \\
\addlinespace
Lepton cascade assignment ($e$ = depth-2 \GGA{}) & THM & A9, label sec:lepton-cascade-depth & Eq.~\eqref{eq:lepton-chain} \\
\addlinespace
$N \ge 3$ from CP violation & THM given EMP & P2, leg L1 & \S\ref{sec:conditioning} \\
\addlinespace
Coupling clause; integrality theorem L-INT & AX; THM (residue
R-INT) & P2, its Axiom AX-B and L-INT; App.~C, F, G & \S\ref{sec:conditioning} \\
\addlinespace
No-exit-gate; reachability reading & THM (\GDOS{}); INT & P2, \S9.3; label ssec:reachability & Thm.~\ref{thm:stability}; \S\ref{sec:conditioning} \\
\addlinespace
Non-spatial support of all electron structure & THM assembly & this paper, Prop.~\ref{prop:nonspatial} (from A2/A4/A9) & Part VI \\
\addlinespace
Readout Locality (RL) & LEMMA from AX-1 & A1, AX-1 (label ax:LC) + constitutional clarifications 2--3; this paper, Lemma~\ref{post:RL} & Thm.~\ref{thm:pointlike} \\
\addlinespace
$F(q^2) \equiv 1$ at all scales & THM (via Lemma RL; D-P3-1 registered) & this paper, Thm.~\ref{thm:pointlike} + App.~\ref{app:formfactor} & Part VI, P2/F2 \\
\addlinespace
Positron = conjugate readout of the same basin (Q6) & THM
(imports) + INT (named) & P5, theorems T-P5-A/B/C, T-P5-C2; this
paper, Part~V & Part~V; D-P3-4 \\
\addlinespace
Open-system arrows (radiation: motion; scale-sector \GRIPin{}: decay) & INT (corrected) & this paper, Reading~\ref{rmk:sensing}; \S\ref{sec:sensing} & Part VII \\
Worldline coupling; unified equation of motion; Newton \& Coulomb parallel chains & THM & A5, Part VI (digest: App.~\ref{app:Q5}) & Parts VI, VII \\
Radiative completion: orbit = circulation, damping = gradient sector; covariant kernel & THM (field-trace closure + covariant kernel); O7 Resolved & A5, radiative-completion, closure and kernel subsections + Open Problem O7 & \S\ref{sec:sensing}, App.~\ref{app:Q5-descent} \\
\addlinespace
$\tau_e$ bound; $a_e$; $\alpha$ anchors; $N_\nu$ & EMP & Borexino 2015; Fan 2023; CODATA 2022; ALEPH 2006 & Parts III, VI, VIII \\
\end{longtable}}

%% ==================================================================
%% APPENDIX C -- Q1 DERIVATIONS (identity and the values)
%% ==================================================================
\section{Derivations for Q1: identity and the values}
\label{app:Q1}

This appendix assembles, in one place and at first-year-graduate level,
the complete derivations behind Part~\ref{part:III}. Everything here is
reproduced from the parent papers with citation --- chiefly \ANine{}'s
charged-lepton codebook sections and \ATwo{}'s group theory --- so that
the student can digest the material on the spot; nothing is new, and
nothing is abbreviated past the point of checkability.

\subsection{The uniqueness statement: \texorpdfstring{\GGA{}}{GGA} and GFF-ST7}
\label{app:Q1-gga}

The landscape vocabulary is fixed by \ASix{} \citep{ArisakaA6Gi4}. The
\GFF{} is a Morse functional on each boundary stratum; its index-0
critical points (basins) are the Geometric Attractors (\GA{}); among
them, def:GGA names
\begin{equation}
\GGA(\Sigma) \;=\; \operatorname*{arg\,min}_{x\in\Sigma}\,\FGFF(x),
\label{eq:appC-gga}
\end{equation}
and the structure theorem GFF-ST7 asserts that the minimizer is unique
per stratum: a stratum, like a molecule, has exactly one ground state.
The regime theorem \textsf{T-GGA-as-Ground-State} of \AEleven{}
\citep{ArisakaA11Origin} adds that the cascade \emph{output} is this
ground state --- the descent does not strand permanently in a way
station (within a stratum; the way stations are the metastable
generations of Appendix~\ref{app:Q2}). Identity-as-sameness is then a
two-line argument, which is Theorem~\ref{thm:identity} of the main
text: all electrons are readouts of one attractor (uniqueness:
GFF-ST7); a readout has no degrees of freedom beyond the attractor's
data (universal-identity theorem, \AEight{} T-A8.9
\citep{ArisakaA8QM}); hence no two electrons can differ. The honest
conditioning --- \GDOS{}-internal status; the O3 note --- is stated in
\S\ref{ssec:gga-statement} and not repeated here.

\subsection{The dyadic charged-lepton codebook}
\label{app:Q1-codebook}

We now reproduce the codebook derivation from \ANine{}'s charged-lepton
sections \citep{ArisakaA9SM}, with its own reasoning intact.

\paragraph{Step 1: why the lepton sector is dyadic at first order.}
The compact circle $\Stheta$ supports the Abelian holonomy and the
Wilson-line Higgs, but a field pays a nontrivial \emph{angular}
suppression at first order only if its chirality or charge assignment
distinguishes different angular branches. The color-singlet charged
leptons are the most economical sector in this respect: their
first-order family hierarchy carries zero winding,
\begin{equation}
w_e = w_\mu = w_\tau = 0 ,
\label{eq:appC-w-zero}
\end{equation}
so their hierarchy is \emph{dyadic before it is angular} --- they are
separated not by compact monodromy but by how deeply the boundary
projector must resolve their profiles (\ANine{}, ``why the charged-lepton
sector is purely dyadic''). The angular cascade is reserved for the
quarks and plays no role here.

\paragraph{Step 2: the three Yukawa codes.} The shortest charged-lepton
codebook compatible with the \OGNfive{} ledger
$(M,N,L;J,K)=(1,3,5;7,35)$ and the required family order is
\citep{ArisakaA9SM}:
\begin{align}
y_\tau^{(1)}&=\frac{NJ}{2^{\,J+N+1}}=\frac{21}{2^{11}}=\frac{21}{2048},
\nonumber\\
y_\mu^{(1)}&=\frac{L}{2^{\,J+L+1}}=\frac{5}{2^{13}}=\frac{5}{8192},
\label{eq:appC-yukawas}\\
y_e^{(1)}&=\frac{N}{L^3\,2^{\,J+L+1}}=\frac{3}{5^3\cdot 2^{13}}
=\frac{3}{1\,024\,000}.
\nonumber
\end{align}
The codes are explained, not merely displayed, in \ANine{}; we
reproduce the reasoning. For the \emph{tau}: the third-family lepton is
the least suppressed; the largest admissible numerator available
without a new free integer is $NJ = 21$ (family triplicity times the
dyadic closure index), and the mildest dyadic depth reflecting both the
neutral closure $J$ and the triplicity $N$ is $J+N+1 = 11$. For the
\emph{muon}: one resolution layer deeper --- the depth steps from the
triplicity index to the weak-projection index, $J+L+1 = 13$, with the
single ledger integer $L$ as numerator. For the \emph{electron}: the
lightest mode pays, in addition to the same depth $2^{J+L+1}$, the
\emph{triple boundary re-projection}: each weak projection contributes
a factor $1/L = 1/5$, and three successive projections give $L^{-3}$;
the numerator returns to $N$ because, by the time the lightest mode is
reached, the dominant structure is no longer the dyadic closure but the
persistence of family triplicity through the three projections. Hence
\begin{equation}
y_e^{(1)}=\frac{N}{L^{3}\,2^{\,J+L+1}} = \frac{3}{5^3 \cdot 2^{13}},
\label{eq:appC-ye}
\end{equation}
which is Eq.~\eqref{eq:ye} of the main text.

\paragraph{Step 3: first-order masses.} With the Dirac mass relation
$m = y\,v/\sqrt2$ and the independently derived Higgs vacuum value
$v^{(1)} = 246.331354$~GeV (\ANine{}'s Wilson--Hosotani theorem; no
lepton mass is an input anywhere in this chain), the codebook gives
\begin{align}
m_\tau^{(1)}&=\frac{v^{(1)}}{\sqrt2}\,\frac{21}{2048}
=1.78605~\mathrm{GeV},
\nonumber\\
m_\mu^{(1)}&=\frac{v^{(1)}}{\sqrt2}\,\frac{5}{8192}
=106.3126~\mathrm{MeV},
\label{eq:appC-first-order}\\
m_e^{(1)}&=\frac{v^{(1)}}{\sqrt2}\,\frac{3}{1024000}
=0.5103005~\mathrm{MeV}.
\nonumber
\end{align}
The exact first-order ratios are pure ledger arithmetic,
\begin{equation}
\frac{m_\tau^{(1)}}{m_\mu^{(1)}}
=\frac{NJ}{L}\,2^{\,L-N}=\frac{84}{5}=16.8,
\qquad
\frac{m_\mu^{(1)}}{m_e^{(1)}}=\frac{L^4}{N}=\frac{625}{3}=208.33\ldots,
\label{eq:appC-ratios}
\end{equation}
against the measured $16.817$ and $206.768$: agreement at the
$10^{-3}$ and $8\times10^{-3}$ level \emph{before} any correction
layer. The student should pause on what Eq.~\eqref{eq:appC-ratios}
asserts: two mass ratios that the Standard Model carries as free
inputs are here ratios of small integers and powers of two.

\paragraph{Step 4: the QD completion.} The first-order codebook is the
rigid skeleton, not the final low-energy value; the finite QD
(Quantum-Descent) transport from the idealized seam to the comparison
convention is encoded by the common denominator
\begin{equation}
2^J L = 2^7 \cdot 5 = 640,
\label{eq:appC-640}
\end{equation}
recognized upstream as a Hopkins--Singer descent integrality
coefficient on $\mathbb{C}P^2$ \citep{ArisakaA9SM}. The shortest
allowed rational closures are
\begin{equation}
\mathcal R_\tau = 1-\frac{N}{2^J L}=\frac{637}{640},\qquad
\mathcal R_\mu = 1-\frac{L-M}{2^J L}=\frac{159}{160},\qquad
\mathcal R_e = 1+\frac{M}{2^J L}=\frac{641}{640},
\label{eq:appC-QD}
\end{equation}
giving the transport-corrected masses
$m_\ell^{\rm QD} = \mathcal R_\ell\, m_\ell^{(1)}$:
\begin{equation}
m_\tau^{\rm QD}=1.777680~\mathrm{GeV},\qquad
m_\mu^{\rm QD}=105.64815~\mathrm{MeV},\qquad
m_e^{\rm QD}=0.511097845~\mathrm{MeV}.
\label{eq:appC-QD-values}
\end{equation}
The physical meaning (\ANine{}): the tau shifts slightly down because
the least-suppressed mode still leaks into neighboring dyadic cells;
the muon shifts down by more, sitting one resolution layer deeper; the
electron shifts \emph{up} because, after the triple $L^{-3}$
suppression, the leading correction is a minimal recovery of one
boundary cell rather than a further loss. Comparison with CODATA
$m_e = 0.51099895069(16)$~MeV \citep{CODATA2022} gives the declared
residual $1.9\times10^{-4}$ of \S\ref{ssec:value-mass} ---
the paper's most exposed number (D-P3-5), displayed rather than hidden.

\subsection{Charge: quantization and the value of \texorpdfstring{$\alpha$}{alpha}}
\label{app:Q1-alpha}

Charge quantization is topological: the electron's charge is the
eigenvalue of the fixed, integer-normalized $\mathrm{U}(1)_{\rm EM}$
generator (the commutant of the selected Wilson--Hosotani vacuum) on
the unique stable cascade leg --- an integer times one unit, with no
continuum available (\ANine{}; \S\ref{ssec:value-charge}). The
\emph{strength} is the dyadic-closure attractor coordinate
\begin{equation}
\alphainv(M_Z) = 2^J = 128
\label{eq:appC-alphaMZ}
\end{equation}
(\ANine{}'s electromagnetic dyadic-closure theorem). The first QD
correction is the minimal dyadic self-contraction allowed by the
triplicity sector, $N^2$:
\begin{equation}
\alphainv(M_Z)^{\rm QD} = 2^J - \frac{N^2}{2^J}
= 128 - \frac{9}{128} = 127.9296875,
\label{eq:appC-alphaQD}
\end{equation}
matching the PDG running value $127.930 \pm 0.008$ to measurement
precision \citep{ArisakaA9SM,PDG2024}. At zero momentum the same
integers give
\begin{equation}
\alphainv(0) = 2^J + N^2 = 137.0,
\label{eq:appC-alpha0}
\end{equation}
with the QD-completed prediction matching CODATA's $137.036$, as
\ANine{} reports \citep{CODATA2022}. Finally, the elementary charge
itself is not primitive: with $\alpha$ derived and the \GUfive{}
constants in hand, T-Euclid-4 of \AFour{} \citep{ArisakaA4Euclid}
reads $e$ off as $e = \sqrt{4\pi\epsilon_0\,\hbar c\,\alpha}$ --- a
bookkeeping consequence, not an input.

\subsection{Spin-\texorpdfstring{$\tfrac12$}{1/2}: the quaternionic doublet}
\label{app:Q1-spin}

We reproduce \ATwo{}'s construction \citep{ArisakaA2GG6}. The
six-dimensional Minkowski space is realized as the space of $2\times2$
Hermitian \emph{quaternionic} matrices,
\begin{equation}
\mathbb{R}^{1,5} \;\cong\; \mathrm{Herm}_2(\mathbb{H})
\;=\;\Bigl\{\, X = \begin{pmatrix} t+z & q \\ \bar q & t-z
\end{pmatrix} : t,z\in\mathbb{R},\; q\in\mathbb{H} \Bigr\},
\label{eq:appC-herm}
\end{equation}
on which the Lorentzian quadratic form is the reduced determinant
\begin{equation}
-\det X = -t^2 + z^2 + |q|^2 ,
\qquad |q|^2 = q\bar q = q_0^2+q_1^2+q_2^2+q_3^2 ,
\label{eq:appC-det}
\end{equation}
of signature $(-,+,+,+,+,+)$ with total dimension $1+1+4 = 6$. The
action $X \mapsto gXg^\dagger$ for $g \in \SLtwoH$ preserves $\det X$,
hence the metric; its kernel is $\{\pm\mathbf 1\}$, exhibiting
\begin{equation}
\mathrm{Spin}(1,5) \;\cong\; \SLtwoH
\label{eq:appC-spin15}
\end{equation}
as the double cover of the 6D Lorentz group --- the quaternionic entry
of the magic $2\times2$ sequence over the division algebras
($d=3,4,6,10$ for $\mathbb{R},\mathbb{C},\mathbb{H},\mathbb{O}$;
Hurwitz's 1898 classification underneath). Weyl spinors of the bulk
are two-component \emph{quaternionic} vectors --- equivalently
four-component complex vectors with a quaternionic structure --- and
their boundary projection carries an irreducible doublet. The
half-integer label measured in 4D is the double-cover label of
Eq.~\eqref{eq:appC-spin15}: forced by the dimension and the algebra,
not selected from Wigner's menu \citep{Wigner1939}. This is the
content of \S\ref{ssec:value-spin}, with the dynamical reading (spin
without spinning) in \S\ref{sec:mass-spin}.

%% ==================================================================
%% APPENDIX D -- Q2 DERIVATIONS (the landscape and its gates)
%% ==================================================================
\section{Derivations for Q2: the landscape, the gates, and the absence of an exit}
\label{app:Q2}

\subsection{The family stratum and its Morse skeleton}
\label{app:Q2-skeleton}

The charged-lepton generations live on the family-projector stratum
$\Sigma_{\rm fam} = \mathbb{C}P^{N-1} = \mathbb{C}P^2$ (real dimension
4) (\citealp{ArisakaP2N3}; \citealp{ArisakaA9SM}). By \ASix{}'s Morse-positivity
theorem (T3.1, from CCI), the projected free-energy functional
restricted to $\Sigma_{\rm fam}$ is a perfect Morse function
\citep{Morse1934} with exactly three non-degenerate critical points, of indices $0$, $2$,
$4$ (Lemma~4.2 of \PaperPTwo{}) --- the minimal cell structure of
$\mathbb{C}P^2$. The \GRIP{} cascade chain orders them as
\begin{equation}
\underbrace{[\,\mathrm{ind}=4\,]}_{\text{depth }0}
\;\xrightarrow{\;S_{[4]\to[2]} = 2\pi\;}\;
\underbrace{[\,\mathrm{ind}=2\,]}_{\text{depth }1}
\;\xrightarrow{\;S_{[2]\to[0]} = \pi\;}\;
\underbrace{[\,\mathrm{ind}=0\,]}_{\text{depth }2},
\label{eq:appD-chain}
\end{equation}
with cumulative actions $0, 2\pi, 3\pi$ (Eq.~\ref{eq:lepton-chain} of
the main text; \figref{fig:grip-cascade-cp2}).

\subsection{Basins, not saddles: the spectroscopy argument}
\label{app:Q2-basins}

One precision governs how Eq.~\eqref{eq:appD-chain} must be read
(\PaperPTwo{} \S9.1; \ANine{}'s cascade-depth section): the chain is
the Morse \emph{skeleton} of the stratum, while the physical
generations are the index-0 minima of the depth-$n$ \emph{effective}
landscapes hung on that skeleton --- the index-4 and index-2 critical
points are the \GSSB{} \emph{gates} the descent crosses, not the
particles. All three generations are genuine Geometric Attractors,
and this is not pedantry but spectroscopy: a saddle supports no
sharply defined mass, whereas $m_\tau$ and $m_\mu$ are measured at
the $10^{-4}$ relative level or better --- precisely measurable
masses are the experimental certificate that $\tau$ and $\mu$ are
perfect \GA{}'s. What the higher generations are \emph{not} is the
ground state: only the depth-2 basin is the global minimum, the
\GGA{}.

\subsection{The exit-gate calculus}
\label{app:Q2-gates}

Each non-ground basin possesses an exit gate with a Bogomolnyi toll:
depth 0 exits through the index-4 gate at $S = 2\pi$; depth 1 through
the index-2 gate at $S = \pi$ --- Bogomolnyi-saturating actions
\citep{Bogomolny1976}. In the \GFF{} Morse framework the
partial rate across a gate carries the instanton factor
\begin{equation}
\Gamma \;\propto\; e^{-S},
\label{eq:appD-rate}
\end{equation}
combined with phase-space factors exactly as nuclear lifetime
systematics combine barrier penetrability with phase space; the
quantitative accounting for the $\tau$--$\mu$ lifetime ratio
(including why the $(m_\tau/m_\mu)^5$ phase-space factor dominates)
is \PaperPTwo{}'s \S9.4 and is not duplicated here. The weak
interaction is the physical implementer of every such crossing: within
the boundary gauge group the $\mathrm{SU}(2)_L$ charged current is the
only flavor-connecting channel, so every inter-basin descent observed
in Nature is weak \citep{ArisakaA9SM}.

\subsection{The no-exit-gate statement, assembled}
\label{app:Q2-noexit}

Theorem~\ref{thm:stability} now assembles in four cited steps.
\emph{(i)} The depth-2 basin is the unique global minimum of the
stratum (GFF-ST7; Appendix~\ref{app:Q1-gga}). \emph{(ii)} Its exit-channel
set is empty: there is no critical point below it for a gate to lead
to --- ``No exit gate exists; this is why the electron has never been
observed to decay'' (\PaperPTwo{} \S9.3, verbatim). \emph{(iii)}
Charge conservation, the premise of the textbook stability argument,
is itself derived: the boundary $\mathrm{U}(1)_{\rm EM}$ descends from
the bulk gauge factor (\ATwo{}, Theorem~3), so the standard
lightest-charged argument survives \emph{inside} the framework as a
consistency check (\S\ref{ssec:gg-stability}). \emph{(iv)} The
forbiddance is structural, not statistical: even charge-violating
channels (the Borexino search channel $e \to \nu\gamma$
\citep{Borexino2015}) require an exit from the basin, and there is
none --- which is why P1 covers them. The conditioning --- \GDOS{}
internal; the Q3 import for ``no lighter charged basin'' --- is
declared in the main text and travels with this appendix.

%% ==================================================================
%% APPENDIX E -- Q3 DERIVATIONS (the three legs, digested)
%% ==================================================================
\section{Derivations for Q3: the three legs of \texorpdfstring{$N=3$}{N=3}, digested}
\label{app:Q3}

This appendix reproduces, at full derivational level, the three legs of \PaperPTwo{}'s result \citep{ArisakaP2N3}, so that the
student can check the count without opening the parent paper. The fences travel with the import: leg (L2) is conditional on the coupling clause and the integrality
theorem L-INT (residue R-INT), exactly as in
\S\ref{sec:conditioning}.

\subsection{Leg L1: the CP lower bound \texorpdfstring{$N \ge 3$}{N >= 3}}
\label{app:Q3-L1}

\begin{quote}\small
\textbf{Theorem (\MSMF{} lower bound; \PaperPTwo{} Thm.~3.1).}
\emph{Suppose the boundary observable spectrum admits a non-zero
Jarlskog CP-violating invariant $\JCKM \ne 0$ in the quark sector.
Then under \MSMF{}, $N \ge 3$.}
\end{quote}

\noindent\emph{Proof (reproduced).} After Higgs descent the up- and
down-type mass matrices are general complex $N\times N$ matrices, and
the CKM matrix \citep{Cabibbo1963,KobayashiMaskawa1973}
$\VCKM = U_u^L U_d^{L\dagger}$ is an element of $U(N)$. Counting parameters: $\VCKM$ has $N(N-1)/2$ mixing angles and
$N(N+1)/2$ phases, of which $2N-1$ are removable by independent
rephasings of the up- and down-type flavor eigenstates; the physical
CP-violating phase count is therefore
\begin{equation}
n_{\rm phase}(N) = \frac{(N-1)(N-2)}{2}.
\label{eq:appE-nphase}
\end{equation}
A Jarlskog invariant
$\JCKM = \mathrm{Im}\,(V_{ij}V_{kl}V_{il}^{*}V_{kj}^{*})$ is non-zero
iff at least one physical phase exists, i.e.\ $n_{\rm phase} \ge 1$.
Solving: $(N-1)(N-2)/2 \ge 1 \iff N \ge 3$ --- at $N=2$ the single
complex phase is removable by rephasing; at $N=1$ there is no mixing
matrix at all. Empirically $\JCKM = (3.12^{+0.13}_{-0.12})\times
10^{-5} \ne 0$ \citep{PDG2024}, and \MSMF{} selects the smallest
compatible $N$. Hence $N \ge 3$. \hfill$\square$

\smallskip
The same argument runs in the leptonic sector with the PMNS matrix and
is independently consistent with $N = 3$ (\PaperPTwo{}, with the
global-fit sources cited there). Status: theorem, conditional on one
empirical input (observed CP violation).

\subsection{Leg L2: the budget upper bound \texorpdfstring{$N \le 3$}{N <= 3}}
\label{app:Q3-L2}

\begin{quote}\small
\textbf{Lemma (cascade closure for $\mathbb{C}P^{N-1}$;
\PaperPTwo{} Lem.~4.x, reproduced).}
\emph{The total instanton action accumulated along the chain
$[2(N-1)] \to [2(N-2)] \to \cdots \to [0]$ is}
\begin{equation}
\Stot(N) = \pi \sum_{k=1}^{N-1} k = \pi\,\frac{N(N-1)}{2}.
\label{eq:appE-Stot}
\end{equation}
\emph{Cascade closure requires $\Stot(N) \le \SmaxBI$.}
\end{quote}

\noindent\emph{Proof sketch (reproduced).} The instanton action
between adjacent critical points of indices $2k$ and $2(k-1)$ on
$\mathbb{C}P^{N-1}$ with the Fubini--Study metric is, by direct
integration of the Bogomolnyi-bound-saturating gradient flow,
$S_{[2k]\to[2(k-1)]} = \pi k$ --- the standard Morse--instanton
computation \citep{Witten1982,Helgason1979}. Summing $k = 1,\ldots,
N-1$ gives Eq.~\eqref{eq:appE-Stot}. \hfill$\square$

\smallskip
\noindent\emph{The budget.} The bound is closed by the capacity theorem \textbf{T-N3-6} of \PaperPTwo{}: \begin{equation} \mathrm{Cap}(N) = \pi\,\bigl\langle p_1(T\mathbb{C}P^{N-1}),[\mathbb{C}P^2]\bigr\rangle = \pi N, \qquad \mathrm{Cap}(3) = 3\pi, \label{eq:appE-budget} \end{equation} derived there from the stratum's quantum geometry, conditional on the coupling clause and the integrality theorem L-INT, whose residue R-INT ``is topological
bookkeeping on a specific manifold, of the same kind as checking
orientability, not a conceptual gap'' (\PaperPTwo{}, verbatim; the
$N$-independence demand of \ASix{}'s open problem M10 is met by the same theorem, which consumes neither $K$ nor $J$). Granted its premises,
\begin{equation}
\frac{N(N-1)}{2} \le 3
\;\iff\;
N \le 3,
\label{eq:appE-N3}
\end{equation}
with exact saturation at $N = 3$: $\Stot(3) = 3\pi$. The per-family formulation $\SmaxBI(N) = \pi N$ (the extensive form of T-N3-6; \PaperPTwo{} Appendix~C) gives the equivalent closure $N(N-1)/2 \le N \iff N \le 3$ and
underlies the reachability reading: for $N \ge 4$ the descent's toll
exceeds the stratum's capacity, and a fourth family's ground state
would be \emph{dynamically unreachable} --- a reading that ``inherits the conditioning of the capacity theorem and adds none of its own rigor'' (\PaperPTwo{} \S9.6). The strict-positivity underpinning is dissolved upstream: the bulk-only derivation is closed in the negative (\PaperPTwo{}'s rigidity lemma), the transport geometry is supplied at the Born theorem's own grade by its adiabatic theorems, and the residue is R-INT, of the integrality theorem L-INT ---
discharged on the benchmark background in \PaperPTwo{}'s
Appendix~H. Status:
theorem \emph{conditional} on Eq.~\eqref{eq:appE-budget} with its
stated premises (the coupling clause and L-INT/R-INT).

\subsection{Leg L3: the codebook cross-check}
\label{app:Q3-L3}

The first-order ratio formulas of Appendix~\ref{app:Q1-codebook} are
functions of $N$ once $J = 7$ and $L = 5$ are fixed by \BIsix{}
closure:
\begin{equation}
\frac{m_\tau}{m_\mu}\Big|^{(1)} = \frac{NJ}{L}\,2^{\,L-N},
\qquad
\frac{m_\mu}{m_e}\Big|^{(1)} = \frac{L^4}{N}.
\label{eq:appE-ratioN}
\end{equation}
Evaluating: at $N = 2$ the formulas give $22.4$ and $312.5$ (off by
$33\%$ and $51\%$); at $N = 3$, $16.8$ and $208.3$ (within $10^{-3}$
and $8\times10^{-3}$ of the measured $16.817$ and $206.768$); at
$N = 4$, $11.2$ and $156.25$ (off by $33\%$ and $24\%$)
\citep{ArisakaP2N3}. The empirical ratios select $N = 3$ uniquely at
the four-significant-figure level once the QD layer is applied
(Appendix~\ref{app:Q1-codebook}). Status: consistency check --- L3
validates, it does not independently force.

\subsection{Closure}
\label{app:Q3-closure}

L1 gives $N \ge 3$ (conditional on observed CPV); L2 gives $N \le 3$ (conditional on the coupling clause and L-INT); together $N = 3$ exactly, validated by L3's twelve four-significant-figure
mass agreements. The electron's two excited copies, and only two, are
thereby counted --- and Q2 and Q3 interlock as the main text states:
the same budget that stops the ladder guarantees the terminus is
reachable and final.


\clearpage

\section{Derivations for Q4: the form-factor argument}
\label{app:formfactor}

This appendix expands the proof of Theorem~\ref{thm:pointlike}:
what is derived, from what, and exactly where Lemma~\ref{post:RL} ---
and behind it AX-1 --- enters. Per Remark~\ref{rmk:ff-status}, the
form factor here is the falsification interface, not the ground: the
appendix shows why the interface must read flat once the constitution
has closed both the object and the registration. The constitutional Step 0 --- AX-2's
worldline coupling leaves no slot for a profile --- is
\S\ref{sec:ggep-particle}, presupposed throughout this appendix.

\subsection{Setup}
Operationally, elastic scattering off the electron at spacelike momentum
transfer $q$ measures the matrix element of the electromagnetic current,
parameterized by form factors; ``structure'' means dependence of the
\emph{structural} form factor $F$ on a length scale intrinsic to the
electron, $F = F(q^2\ell_e^2)$ with $\ell_e \ne 0$. The Standard-Model radiative
dressing (Schwinger's $a_e = \alpha/2\pi$ and its successors
\citealp{Schwinger1948}, including the small hadronic and electroweak
terms) is momentum-dependent but carries no new length:
its scales are the probe's and the vacuum's, which is why precision
$g-2$ constrains substructure only through a compositeness model
\citep{Dehmelt1988}. The claim to be established is $F \equiv 1$: no
$\ell_e$ exists.

\subsection{Step 1: the electron supplies no length (theorem-level)}
By Proposition~\ref{prop:nonspatial}, every structural datum of the
electron is either (i) a dimensionless coordinate along $\Ir$ (the dyadic
depth $2^J$, the cascade level), (ii) a winding integer on $\Stheta$, or
(iii) a group label of the bulk spinor action. None is a function on
$\cM_4$; none defines a 4D length. The only dimensionful attribute the
boundary sees is $m_e$ --- the \GFF{} basin level --- and a mass enters
scattering kinematics (propagators, thresholds), not structure: the
Compton wavelength $\hbar/m_ec$ is the scale of the \emph{dynamics} of a
point of mass $m_e$, present identically for a structureless Dirac
particle, and its appearance in cross-sections is already part of the
$F\equiv1$ prediction, not a deviation from it.

A natural worry: the scale profile $e^{-2r}$ of the canonical metric
(\ATwo{}, Theorem 2) relates bulk position along $\Ir$ to 4D scale ---
is the electron's locus on $\Ir$ not, then, secretly a 4D length? It is
a 4D \emph{scale}, which is precisely not a 4D \emph{extension}: the
scale profile maps depth along $\Ir$ to the renormalization-group resolution at
which boundary physics is read, uniformly for all processes, and not to
a profile of the electron in the boundary coordinates. The distinction
is the entire content of A2's statement that $\Ir$ is an RG direction,
not a fifth spatial axis; a Kaluza--Klein theory makes the opposite
choice, and the difference is observable, as \S\ref{ssec:kk-contrast}
records.

\subsection{Step 2: the readout supplies no length (Lemma RL, from AX-1)}
\label{ssec:appB-RL}
What Step 1 cannot exclude is a length scale belonging to the
\emph{registration} itself: if the \OGGEP{} bulk-to-boundary readout smeared
every bulk configuration over some $\ell_{\rm hol}$ in the boundary
coordinates, all boundary particles would exhibit a universal form
factor $F(q^2\ell_{\rm hol}^2)$ regardless of their bulk structure.

The exclusion is constitutional. AX-1 (LC: Locality and Causality) of
\AOne{} \citep{ArisakaA1Constitution} is not a statement about closed
dynamics only. Its constitutional statement quantifies over ``every
admissible boundary intervention protocol'' and requires that registered
boundary records at time $t$ depend only on boundary-accessible data in
the causal past of $t$, with acausal effective kernels inadmissible. Its
second constitutional clarification states that, because \OGGEP{}
defines observation as an open-system projection, LC ``must hold for
open evolution maps and measurement instruments, not only for closed
unitary dynamics.'' Its third attaches admissible observables to
\emph{points} of the manifold (microcausality) and excludes fundamental
extended objects --- noting explicitly that the framework's two further
dimensions are non-spatial. The registration channel is therefore not a
loophole in AX-1's jurisdiction; it is among the named subjects of the
axiom.

The derivation then has two branches, by where a scale-carrying kernel
would put its support. \emph{(a) Spacelike support} --- registration at
$x$ drawing on configuration data at spacelike-separated points ---
contradicts the constitutional statement directly (the causal
structure of \citealp{Einstein1905}, elevated to an axiom). \emph{(b) Causal
support} --- retarded memory of depth $\ell_{\rm hol}/c$ --- is
admissible under AX-1, but cannot produce the effect at issue: a kernel
supported in the causal past of $x$ has an equal-time slice consisting
of the point $x$ alone, so it generates frequency dispersion (the
analyticity structure of causal response theory), not an equal-time
spacelike profile --- and the static structural form factor of
\S\ref{sec:formfactor} probes equal-time spacelike correlations only.
We make the scope explicit, since the lemma's force depends on it: the
claim concerns the \emph{elastic, zero-energy-transfer} structure
function --- precisely the quantity whose deviation from unity would
constitute substructure --- while frequency-dependent response
generated by causal memory belongs to the dressing layer of
\S\ref{sec:formfactor}, carries the probe's and the vacuum's scales
only, and is not structure. Hence no admissible readout supplies a
spacelike scale: Lemma~\ref{post:RL}. The single step deserving further rigor is the
static-limit factorization in branch (b) --- that retarded channel
memory contributes nothing to the elastic, zero-energy-transfer
structure function in the \OGGEP{} formalism. It is registered as open
problem D-P3-1; we judge it formalization rather than missing physics,
and state the judgment explicitly so that it, too, is auditable.

\paragraph{Remark: what AX-1 does and does not contribute.} A critical
reader will ask whether Q4 has now been answered by axiom --- whether
``pointlike because AX-1 says so'' differs from the Standard Model's
``pointlike by construction.'' It differs in the two places that carry
this Part. First, an axiomatically pointlike field theory neither
dissolves the self-energy crisis (the Standard Model's point electron
still requires renormalization's subtraction) nor excludes that its
pointlike field is the low-energy description of a composite ---
compositeness searches exist precisely because ``by construction'' is
silent about deeper scales. Second, in \GGTheory{} the electron
demonstrably \emph{has} structure --- the codebook integers of its mass,
charge, and depth --- so point-locality could not even be consistent if
that structure were spatial. It is Proposition~\ref{prop:nonspatial}
(structure entirely along $\Ir$, $\Stheta$) that makes AX-1's
point-locality \emph{consistent}, and Lemma~\ref{post:RL} that makes it
\emph{permanent} (no scale can hide in the readout). AX-1 contributes
point-attachment; \ATwo{}'s theorems contribute the consistency; the
lemma contributes the permanence. The conjunction is the answer to Q4,
and no single ingredient is.

\paragraph{Remark: universality, and the experimental texture of F5.}
If, contrary to Lemma~\ref{post:RL}, registration smearing existed, it
would affect every boundary particle identically; an electron
form-factor anomaly accompanied by identical anomalies in every other
species, beyond their known internal structure, would point at the
readout --- that is, at a failure of the lemma's derivation --- rather
than at electron substructure. This is the experimental texture of kill
criterion F5.

\subsection{Step 3: scale-free normalized functions are constant}
Granted Steps 1--2, $F$ is a dimensionless function of $q^2$ alone with
no scale available to nondimensionalize its argument; the only such
functions are constants, and the normalization $F(0)=1$ --- the probe at
zero momentum sees the whole quantized charge, \S\ref{ssec:value-charge}
--- fixes the constant. Hence $F \equiv 1$, all moments vanish, and no
substructure exists at any scale. The logical structure mirrors the
classic scale-argument for the inverse-square law; its strength is
entirely inherited from the two scale-exclusion steps, which is why the
fence sits at Step 2 and nowhere else.

\subsection{Contrast: extra dimensions that are spatial (Kaluza--Klein)}
\label{ssec:kk-contrast}
The argument fails instructively for an electron with structure along
extra dimensions that are genuinely \emph{spatial} --- the Kaluza--Klein
construction, in which the extra circle is a small circle \emph{in
space} of radius $R$. There $R$ \emph{is} a length, boundary physics
sees a Kaluza--Klein tower at $\hbar/R$, and form factors deviate as
$q^2R^2$ --- structure at a scale, the compositeness signature. The empirical absence of any
such tower for the electron is thus not merely consistent with the
\GGTheory{} bulk; it is what the non-spatiality of $\Ir, \Stheta$
predicts, and the contrast is the cleanest observable distinction
between ``two more dimensions of space'' and ``a scale direction and a
phase direction.''

%% ==================================================================
%% APPENDIX G -- Q5 DERIVATIONS (sensing: the derivable parts)
%% ==================================================================
\section{Derivations for Q5: the parallel chains, the unified equation, and the open-system arrows}
\label{app:Q5}

This appendix reproduces, in digest and with citation, the content of
\AFive{}'s Part~VI --- ``Unification of General Relativity and QED''
\citep{ArisakaA5GDOS} --- which is the constitutional foundation of
Q5's answer (and, through the worldline coupling, of Q4's: see
\S\ref{sec:ggep-particle}). The parent treatment is written so that
``a reader meeting gauge theory for the first time can follow every
line''; we compress it to the load-bearing steps and refer the student
to \AFive{} for every omitted manipulation.

\subsection{Chain (A): \texorpdfstring{\GG{} $\to$ 5D GR $\to$ 4D GR $\to$ Newton $\to$ $F=ma$}{GG -> 5D GR -> 4D GR -> Newton -> F=ma}}
\label{app:Q5-chainA}

The gravitational chain descends the two non-spatial dimensions one at
a time, reducing a single geometric object --- the bulk metric ---
with no force postulated anywhere. Start from the six-dimensional
Einstein--Hilbert action on the canonical bulk,
\begin{equation}
S_6 = \frac{M_6^4}{2}\int d^6x\,\sqrt{-g_6}\,R_6,
\qquad
ds_6^2 = e^{-2r} g_{\mu\nu}(x)\,dx^\mu dx^\nu + dr^2 + d\theta^2 .
\label{eq:appG-S6}
\end{equation}
\emph{Step A1 (6D $\to$ 5D):} nothing depends on the phase $\theta$
and the circle is flat, so the $\theta$-integral contributes the
circumference, $M_5^3 = 2\pi M_6^4$ --- reducing on a gauge phase
costs nothing geometrically. \emph{Step A2 (5D $\to$ 4D):} the
determinant scales as $\sqrt{-g_5} = e^{-4r}\sqrt{-g_4}$ and the
four-dimensional curvature as $R_5 \supset e^{+2r} R_4$, so the scale-profile
factors combine to $e^{-2r}$ and the radial integral is elementary:
\begin{equation}
M_{\rm Pl}^2
= M_5^3 \int_0^K e^{-2r}\,dr
= \pi\,M_6^4\,\bigl(1 - e^{-2K}\bigr),
\label{eq:appG-MPl}
\end{equation}
the scale-profile-weighted overlap integral that sets Newton's constant
$G_N = 1/(8\pi M_{\rm Pl}^2)$. \emph{Step A3:} varying the resulting
4D Einstein--Hilbert action gives Einstein's field equation; the
weak-field, static limit gives the Poisson equation
$\nabla^2\Phi_{\rm N} = 4\pi G_N \rho$ and hence Newton's potential
$\Phi_{\rm N} = -G_N M/r$. \emph{Step A4:} the geodesic equation of
the 4D metric, in the same limit, is $F = ma$ with
$\vec F = -m\nabla\Phi_{\rm N}$. Gravitation is, throughout, the
statement that matter follows the geodesics of the reduced metric.

\subsection{Chain (B): \texorpdfstring{\GG{} $\to$ 4D QED $\to$ Maxwell + Lorentz $\to$ Coulomb}{GG -> 4D QED -> Maxwell + Lorentz -> Coulomb}}
\label{app:Q5-chainB}

The electromagnetic chain runs exactly parallel; the geometric object
is now the bulk gauge connection whose holonomy lives on $\Stheta$,
and the electric charge is the integer-quantized momentum of that
holonomy. \emph{Step B1:} a charged field's unobservable local phase
requires a connection $A_\mu$ for its covariant derivative
\citep{Weyl1929} (the non-Abelian generalization being
\citealp{YangMills1954}); the
curvature of that connection is the field strength
$F_{\mu\nu} = \partial_\mu A_\nu - \partial_\nu A_\mu$, and the bulk
gauge action reduces (by the same $2\pi$ and scale-profile integrals as Chain
A) to the 4D Maxwell action. \emph{Step B2:} varying it gives
Maxwell's equations. \emph{Step B3:} the minimally-coupled worldline
\begin{equation}
\mathcal L = \tfrac12\, m\, g_{\mu\nu}\dot x^\mu \dot x^\nu
+ q\,A_\mu \dot x^\mu
\label{eq:appG-minimal}
\end{equation}
--- the complete matter coupling permitted by AX-2
(\S\ref{sec:ggep-particle}) --- yields, on variation, the Lorentz
force. \emph{Step B4:} the static limit of Maxwell's equations is
again a 3D Poisson equation, $\nabla^2\phi = -\rho_e/\varepsilon_0$,
whose Green's function $-1/(4\pi r)$ gives Coulomb's law, attraction
and repulsion arriving as the two signs of $q$. The two chains
converge on the unified equation of motion,
\begin{equation}
m\bigl(\ddot x^\mu + \Gamma^\mu_{\nu\lambda}\dot x^\nu \dot
x^\lambda\bigr) = q\,F^\mu{}_\nu\,\dot x^\nu
\qquad \text{(Eq.~\ref{eq:unified-eom})},
\label{eq:appG-unified}
\end{equation}
one trajectory governed by two curvatures of one composite connection.

\subsection{The gravity--electricity dictionary}
\label{app:Q5-dictionary}

Table~\ref{tab:appG-dictionary} reproduces, in digest, the term-by-term
dictionary of \AFive{}'s Part~VI. The student should read it column
against column: the parallelism is exact in mathematical form, and the
three physical differences (universal vs quantized charge; bulk-set vs
boundary-running coupling; $\mathrm{Spin}(1,5)$ vs
$\mathrm{U}(1)_{\rm em}$) are themselves derived, not modeled.

\begin{table}[ht]
\centering
\caption[The gravity--electricity dictionary, term by term.]{The gravity--electricity dictionary, digested from
\AFive{}'s Part~VI \citep{ArisakaA5GDOS}: one bulk, two curvatures,
term by term. Read across a row and the same geometric object appears twice, once as gravitation and once as electromagnetism; read down a column and each chain stands complete on its own. The reason for setting them side by side is that neither column contains a term the other lacks.}
\label{tab:appG-dictionary}
\small
\renewcommand{\arraystretch}{1.3}
\begin{tabular}{@{}p{0.24\textwidth}p{0.345\textwidth}p{0.345\textwidth}@{}}
\toprule
\textbf{Aspect} & \textbf{Gravitation (Chain A)} & \textbf{Electromagnetism (Chain B)} \\
\midrule
Non-spatial dimension & 5th: scale interval $\Ir$ (scale profile) & 6th: phase circle $\Stheta$ (holonomy) \\
Geometric object & scale-profile metric block $e^{-2r}g_{\mu\nu}$ & gauge connection on $\Stheta$ (Wilson line) \\
Connection & Christoffel $\Gamma^\mu_{\nu\lambda}$ & gauge potential $A_\mu$ \\
Curvature & Riemann $R^\mu{}_{\nu\lambda\sigma}$ & field strength $F_{\mu\nu}$ \\
Test-particle charge & mass--energy $m$ (universal) & electric charge $q = ne$ (holonomy momentum) \\
Charge quantization & none ($m$ continuous) & $q = ne$ from compact $\Stheta$ \\
Massless mediator & graviton $h_{\mu\nu}$ & photon $A_\mu$ \\
Coupling constant & $G_N = 1/(8\pi M_{\rm Pl}^2)$ (bulk) & $\alpha$ (boundary running; App.~\ref{app:Q1-alpha}) \\
Static field equation & $\nabla^2\Phi_{\rm N} = 4\pi G_N \rho$ & $\nabla^2\phi = -\rho_e/\varepsilon_0$ \\
3D Green's function & $-1/(4\pi r)$ & $-1/(4\pi r)$ \\
Conserved current (Ward) & $T_{\mu\nu}$ (translations) & $J^\mu$ ($\mathrm{U}(1)_{\rm em}$) \\
Equation of motion & $m(\ddot x + \Gamma\dot x\dot x) = 0$ & $m(\ddot x + \Gamma\dot x\dot x) = qF\dot x$ \\
\bottomrule
\end{tabular}
\end{table}

\subsection{Why the two laws are twins: the three ingredients}
\label{app:Q5-ingredients}

Both forces are boundary exports of massless sectors of the same
composite connection $\cA_{\rm tot} = \omega \oplus A$, and the
parallelism rests on exactly three shared ingredients
(\AFive{}, Part~VI): \emph{(i)} a massless mediator in the infrared,
protected on each side by an unbroken symmetry (4D diffeomorphism
invariance; unbroken $\mathrm{U}(1)_{\rm em}$); \emph{(ii)} Gauss-law
flux conservation in three spatial dimensions --- the static limits of
both field equations are 3D Poisson equations sharing the Green's
function $-1/(4\pi r)$, which is where the inverse square comes from
on both sides at once; \emph{(iii)} a conserved four-current defined
by a Ward identity --- Noether's theorem \citep{Noether1918} in its
quantum form --- inherited from the bulk through the boundary
reduction and non-anomalous by \BIsix{} ($T_{\mu\nu}$ from boundary
translations; $J^\mu$ from boundary gauge invariance). The
electron-side significance is the answer to Q5 given in
\S\ref{ssec:q5-answer}: with both laws derived as curvatures of one
geometry, ``responding to a field'' is generalized free fall, and the
old picture of a force \emph{transmitted to} the electron is retired
the way ``the pull on the apple'' was retired in 1915.

\subsection{The open-system layer: which sector descends}
\label{app:Q5-descent}

The geodesic statement of this appendix is conservative; the \GDOS{}
layer supplies arrows, and the two non-spatial dimensions assign them
without ambiguity. The \GFF{} monotonicity law
$d\cF_{\GFF}/dt \le 0$ (\ASix{}, GFF-ST6) and the \GRIPin{} regime
(def:GRIPin) are \emph{scale-sector} statements: their landscape is
the family stratum of Appendix~\ref{app:Q2}, their descent is the
gate calculus of Appendix~\ref{app:Q2-gates}, and their action is
local --- a transmutation of the occupant, with no spatial transport.
Nothing in Chains (A) or (B) descends: the unified equation
\eqref{eq:appG-unified} is time-reversal even, and an electron
bending in a static field loses nothing. The dissipative channel of
\emph{motion} is radiation --- Larmor's loss, the reaction force of
\citet{Dirac1938} --- which removes orbital energy through the open
boundary; its \GDOS{} reading (the open boundary doing to motion
what \GRIPin{} does to identity) is this paper's interpretive
Reading~\ref{rmk:sensing}, corrected from an earlier
tilted-landscape formulation that mis-assigned the sector
(\S\ref{sec:sensing} records the withdrawal). The boundary
kinematics remain Newton--Lorentz plus radiation reaction, exactly as
the derived equations say they should;
\figref{fig:sensing-regimes} draws the two sectors. The quantitative
parent of this assignment is the radiative completion of \AFive{}'s
Part~VI \citep{ArisakaA5GDOS}: synchrotron damping and
gravitational-wave inspiral worked side by side as the gradient
sector of the canonical \GDOS{} current, with the conservative orbit
as circulation, and the quantitative closure derived from the field
trace (drift = retarded flux; closed-form mobility; Larmor and
Peters coefficients exact; universal $C_q$) --- \AFive{} Open
Problem~O7 is thereby Resolved --- the covariant kernel itself is
derived there in closed form (causal, passive, Landau--Lifshitz-exact
to $(\hbar\omega/\Mlock c^2)^2$ at laboratory frequencies), with
the classical runaway obstruction dissolved by the Q4 mass doctrine
of Part~\ref{part:VI} (\S\ref{sec:sensing} imports the example and
the status together).

\subsection{What a student should now be able to do}
\label{app:Q5-exercises}

The reader who has worked through
Appendices~\ref{app:Q1}--\ref{app:Q5} can: reproduce all six
first-order charged-lepton numbers and both exact ratios from the five
ledger integers; apply the QD rationals and verify the printed masses
to all digits; count CP phases for general $N$ and rederive
$N \ge 3$; sum the gate tolls and rederive $N \le 3$ given the budget
(saying exactly where the conjecture enters); assemble the
no-exit-gate argument in four cited steps; run both reduction chains
--- the $2\pi$ integral, the scale-profile integral
Eq.~\eqref{eq:appG-MPl}, the minimal coupling, the Green's function
--- and arrive at Newton, Coulomb, and the unified equation of motion
from one bulk action; recite the dictionary; and state which of the
six answers are theorems, which are codebook results, which are
imports, and which are readings --- which is to say: audit this
paper. That, and not assent, is what these appendices are for.

\section{Empirical anchors}
\label{app:anchors}

All values verified against current sources on June 11, 2026; the table is the paper's single point of empirical
reference, and Part~\ref{part:VIII} consumes it.

\begin{table}[ht]
\centering
\caption[Empirical anchors, with sources and verification dates.]{Empirical anchor table, with verification date and sources. Every empirical number this paper leans on, the experiment that supplies it, and the date the value was checked. The anchors are listed apart from the predictions they bound so that the inputs can be re-verified without re-reading the argument, and so that a value which moves has one place to be found and corrected.}
\label{tab:anchors}
\small
\renewcommand{\arraystretch}{1.25}
\begin{tabular}{@{}p{0.26\textwidth}p{0.34\textwidth}p{0.30\textwidth}@{}}
\toprule
\textbf{Anchor} & \textbf{Value} & \textbf{Source} \\
\midrule
Electron lifetime & $\tau_e > 6.6\times10^{28}$ yr (90\% C.L.) &
Borexino \citep{Borexino2015}; still the world's best bound \\
\addlinespace
Electron $g/2$ & $1.001\,159\,652\,180\,559(13)$ (0.13 ppt) &
\citet{Fan2023} \\
\addlinespace
$\alphainv$ (CODATA 2022) & $137.035\,999\,177(21)$ &
\citep{CODATA2022} \\
\addlinespace
$\alphainv$ (Rb, 2020) & $137.035\,999\,206(11)$ & \citet{Morel2020};
$>5\sigma$ from Cs \\
\addlinespace
$\alphainv$ (Cs, 2018) & $137.035\,999\,046(27)$ & \citet{Parker2018} \\
\addlinespace
$m_e c^2$ & $0.510\,998\,950\,69(16)$ MeV & CODATA 2022
\citep{CODATA2022}; cf.\ PDG \citep{PDG2024} \\
\addlinespace
Compositeness reach & contact-interaction scales excluded to
$\mathcal{O}(10)$ TeV (model-dependent) &
\citep{EichtenLanePeskin1983,ALEPH2006} and PDG listings \citep{PDG2024} \\
\addlinespace
Light-neutrino count & $N_\nu = 3$ ($2.9963\pm0.0074$) &
LEP \citep{ALEPH2006} \\
\addlinespace
\GGTheory{} comparators & $m_e^{\rm QD} = 0.511097845$ MeV (residual
$1.9\times10^{-4}$); $\alphainv$: $2^J{+}N^2 = 137.0$, QD-completed &
\citep{ArisakaA9SM}; declared in \S\ref{ssec:value-mass},
\S\ref{ssec:value-charge} \\
\bottomrule
\end{tabular}

\end{table}

%% ===================================================================
%%  ACKNOWLEDGMENTS
%% ===================================================================
\GGAcknowledgments

%% ===================================================================
%%  REFERENCES (inline, annotated with Relevance paragraphs)
%% ===================================================================
\GGBibBegin
\renewcommand{\bibsection}{\vspace{1.2em}}
\section*{References}
\markboth{References}{References}
\noindent The reference list is organized in two sections, in line
with the \GGTheory{} house style. \textbf{Section A} lists the
fourteen sister papers of the \GGTheory{} cohort cited in this
paper, in the canonical order of the program; \textbf{Section B}
lists the external literature, alphabetically by first author.
Every entry carries a \textbf{Relevance} paragraph stating what
the work contributes to this paper and where it enters, followed
by the location of its first citation; the list contains no entry
that is not cited in the text. All cohort preprints are available at \url{https://preprints.arisaka-gg.org/}.

\section*{A.\ Papers by Katsushi Arisaka (the \GGTheory{} cohort)}

\begin{thebibliography}{99}

\bibitem[Arisaka(2026, A1-Constitution)]{ArisakaA1Constitution}
\textbf{Arisaka, K. (2026).} The \GGConstitution{}: Four Axioms and Seven Postulates of the \GGTheory{} Program, From Which \GG{}, \BIsix{}, \OGNfive{}, and \GDOS{} Descend as Theorems. Arisaka-GG-A1-Constitution.
\par\noindent Preprint, available at \url{https://preprints.arisaka-gg.org/a1-constitution/}.
\par\noindent\textbf{Relevance.}
The constitutional charter: the four axioms (including \MSMF{}, ``Maximum
Symmetry, Minimum Freedom'') and seven postulates underlying every
framework element consumed in Part~\ref{part:II}; its axiom AX-1 (LC:
Locality and Causality) --- formulated by constitutional clarification
for open evolution maps and measurement instruments, with
microcausality attaching observables to points --- is the source from
which Lemma~\ref{post:RL} is derived (\S\ref{sec:formfactor};
Appendix~\ref{app:formfactor}, Step 2). First cited in \S\ref{sec:inheritance}.

\bibitem[Arisaka(2026, A2-GG6)]{ArisakaA2GG6}
\textbf{Arisaka, K. (2026).} \GGTheory{} with \GG{}: Geometry--Gauge Locking at the 6D Bulk (\GG{}) at the Heart of Grand Geometric Theory (\GGTheory{}). Arisaka-GG-A2-GG6.
\par\noindent Preprint, available at \url{https://preprints.arisaka-gg.org/a2-gg6/}.
\par\noindent\textbf{Relevance.}
The bulk paper and largest theorem source of Part~\ref{part:VI}: Theorem~1
(the non-spatial directions $\Ir$, $\Stheta$), Theorem~2 (parameter-free
canonical metric), the magic-square proposition
($\mathrm{Spin}(1,5)\cong\SLtwoH$) behind spin-$\tfrac12$, and Theorem~6
(Diophantine uniqueness of the \OGNfive{} ledger). First cited in the Executive Summary.

\bibitem[Arisaka(2026, A3-BI6)]{ArisakaA3BI6}
\textbf{Arisaka, K. (2026).} Anomaly Freedom of \BIsix{}: The Modified Bianchi Identity (\BIsix{}) for the Six-Force, Six-Dimensional Bulk (\GG{}). Arisaka-GG-A3-BI6.
\par\noindent Preprint, available at \url{https://preprints.arisaka-gg.org/a3-bi6/}.
\par\noindent\textbf{Relevance.}
The anomaly paper: \BIsix{} closure and the integer-ledger constraints
consumed via the \PaperPTwo{} import (Part~\ref{part:IV}). The budget value $3\pi$ is \emph{quoted}, not derived, in its ledger; the value itself is the capacity theorem T-N3-6 of \PaperPTwo{}, whose conditioning (the coupling clause and L-INT) this paper inherits. First cited in \S\ref{sec:inheritance}.

\bibitem[Arisaka(2026, A4-Euclid)]{ArisakaA4Euclid}
\textbf{Arisaka, K. (2026).} From Euclid to \GG{}: The Realization of Euclid's Elements in Six Dimensions --- \GUfive{}, \OGNfive{}, and a Parameter-Free Reconstruction of Modern Physics. Arisaka-GG-A4-Euclid.
\par\noindent Preprint, available at \url{https://preprints.arisaka-gg.org/a4-euclid/}.
\par\noindent\textbf{Relevance.}
Source of T-Euclid-4 (the elementary charge derived, not primitive) and
the \GUfive{} constant-absorption lineage by which dimensionful 4D
mysteries become bookkeeping along the scale direction --- consumed in
\S\ref{ssec:value-charge} and Part~\ref{part:VI}. First cited in \S\ref{sec:framework}.

\bibitem[Arisaka(2026, A5-\GDOS{})]{ArisakaA5GDOS}
\textbf{Arisaka, K. (2026).} \GDOS{}: Geometric Dynamics of Open Systems --- 6D \GG{} Bulk Projected to 4D Boundary for Quantum Measurement, General Relativity, and QFT. Arisaka-GG-A5-GDOS.
\par\noindent Preprint, available at \url{https://preprints.arisaka-gg.org/a5-gdos/}.
\par\noindent\textbf{Relevance.}
The open-system framework within which the ground-state theorems of
Part~\ref{part:III} hold. Its open problem O3 records strict \GFF{}
Morse-positivity as unsettled; that fence is restated wherever this
paper's theorems lean on the landscape machinery, and the sensing reading
of Part~\ref{part:VII} is grounded in --- but not asserted by --- this
paper. Its Part-VI radiative completion carries the synchrotron
and binary-inspiral worked examples that \S\ref{sec:sensing} imports in
digest, together with the field-trace closure (Larmor and Peters
coefficients exact) and the covariant kernel in closed form --- its Open
Problem O7 now Resolved, with the no-runaway theorem leaning on this
paper's Q4 mass doctrine. First cited in \S\ref{sec:framework}.

\bibitem[Arisaka(2026, A6-GRIP)]{ArisakaA6Gi4}
\textbf{Arisaka, K. (2026).} The \GRIP{} on \GDOS{} --- \GRIP{}: the Geometric Engine of Symmetry Breaking, from the Big Bang to Mind. Arisaka-GG-A6-GRIP.
\par\noindent Preprint, available at \url{https://preprints.arisaka-gg.org/a6-grip/}.
\par\noindent\textbf{Relevance.}
Source of the \GFF{} landscape and its structure theorem \GFF{}-ST7
(unique deepest attractor), the regime definitions def:GRIPin and
def:GRIPout, and the definition def:GGA on which
Theorems~\ref{thm:identity} and~\ref{thm:stability} stand; its
cascade-closure theorem T4.1 consumes the budget value whose missing
derivation is its open problem M10. First cited in \S\ref{sec:framework}.

\bibitem[Arisaka(2026, A8-QM)]{ArisakaA8QM}
\textbf{Arisaka, K. (2026).} Quantum Mechanics Derived from \GGTheory{} as Projection from 6D Bulk to 4D Boundary. Arisaka-GG-A8-QM.
\par\noindent Preprint, available at \url{https://preprints.arisaka-gg.org/a8-qm/}.
\par\noindent\textbf{Relevance.}
Source of the universal-identity theorem (T-A8.9 = T-QM-9) consumed in
Theorem~\ref{thm:identity}, and of the bulk-to-boundary projection
framework within which Lemma~\ref{post:RL} operates; the remaining
formalization step of the lemma's static limit (D-P3-1) is to be
carried out in its open-channel formalism. First cited in \S\ref{ssec:qft-identity}.

\bibitem[Arisaka(2026, A9-SM)]{ArisakaA9SM}
\textbf{Arisaka, K. (2026).} The Standard Model as Theorem of \GGTheory{}: Its 28 Parameters as Observations of One Six-Dimensional Geometry. Arisaka-GG-A9-SM.
\par\noindent Preprint, available at \url{https://preprints.arisaka-gg.org/a9-sm/}.
\par\noindent\textbf{Relevance.}
The single largest upstream source: the charged-lepton codebook
($y_e$, QD completion, $\mathcal R_e = 641/640$), the dyadic-closure
$\alpha$ theorem, the geometric-origin-of-identity section, the
inverse-square forces section, the weak-as-\GRIPin{} doctrine, and the
lepton cascade-depth assignment ($e$ = depth-2 \GGA{}) --- consumed
throughout Parts~\ref{part:III}, \ref{part:IV} and~\ref{part:VII} at the
locations registered in Appendix~\ref{app:ledger}. First cited in \S\ref{sec:framework}.

\bibitem[Arisaka(2026, A10-Cosmos)]{ArisakaA10Cosmos}
\textbf{Arisaka, K. (2026).} The Standard Cosmology as Theorem of \GGTheory{}: The Cosmic Inventory as Observations of One Six-Dimensional Geometry. Arisaka-GG-A10-Cosmos.
\par\noindent Preprint, available at \url{https://preprints.arisaka-gg.org/a10-cosmos/}.
\par\noindent\textbf{Relevance.}
The cosmological-boundary closure of the program; cited for cohort
context in Part~\ref{part:II} --- the same ledger that fixes the
electron's numbers fixes the cosmic inventory, which is the breadth claim
behind ``ground state of nature.'' First cited in \S\ref{sec:framework}.

\bibitem[Arisaka(2026, A11-Origin)]{ArisakaA11Origin}
\textbf{Arisaka, K. (2026).} The Geometric Inevitability of Cosmos, Life, and Mind: The Self-Referential Closure of the \GGTheory{} Program. Arisaka-GG-A11-Origin.
\par\noindent Preprint, available at \url{https://preprints.arisaka-gg.org/a11-origin/}.
No result of the present paper depends on it.
\par\noindent\textbf{Relevance.}
The capstone: proves the regime theorem \textsf{T-GGA-as-Ground-State}
(the cascade output at each layer is the ground state, not merely a
stable basin) whose deployment on the charged-lepton stratum is
Theorem~\ref{thm:identity}; the regime definitions remain at runtime
level in \ASix{}, per the division of labor recorded in
\S\ref{ssec:gga-statement}. First cited in \S\ref{sec:framework}.

\bibitem[Arisaka(2026, P2-N3)]{ArisakaP2N3}
\textbf{Arisaka, K. (2026).} Why Three Generations: A Three-Leg Derivation of $N_g=3$ from \BIsix{}, \MSMF{}, and \GDOS{} Morse Stability. Arisaka-GG-P2-N3.
\par\noindent Preprint, available at \url{https://preprints.arisaka-gg.org/p2-n3/}.
\par\noindent\textbf{Relevance.}
The sister paper: owns Q3 (the ladder, $N=3$, and the comparisons with
prior approaches), the basins/gates ontology and no-exit-gate statement
deployed in Theorem~\ref{thm:stability}, the reachability reading, and the coupling-clause + L-INT fences that travel verbatim with every Q3 import in Part~\ref{part:IV}. First cited in \S\ref{sec:status-table}.

\bibitem[Arisaka(2026, P4-Real)]{ArisakaP4Real}
\textbf{Arisaka, K. (2026).} The Real Geometry Beneath the Complex Numbers of Physics: Positive Frequency is Holomorphy --- from Cardano's Cubics to Twistor Space, via the Sixth Dimension of \GGTheory{}. Arisaka-GG-P4-Real.
\par\noindent Preprint, available at \url{https://preprints.arisaka-gg.org/p4-real/}.
\par\noindent\textbf{Relevance.}
The origin-of-$i$ member paper of the Foundations Branch: derives the
boundary's imaginary unit --- the $i$ on which the electron's quantum
mechanics runs --- from two real sources, the compact phase circle
and the causal clock, whose forced agreement on the charged sectors
is the shared complex structure that the electron, as the lightest
charged state, carries. Cited at roster level in
\S\ref{sec:inheritance}. First cited in \S\ref{sec:inheritance}.

\bibitem[Arisaka(2026, P5-CPT)]{ArisakaP5CPT}
\textbf{Arisaka, K. (2026).} The Mirrors of Matter: Why Every Particle Has a Twin, Why Nature's Mirrors Break, and Why the Universe Is Made of Matter. Arisaka-GG-P5-CPT.
\par\noindent Preprint, available at \url{https://preprints.arisaka-gg.org/p5-cpt/}.
\par\noindent\textbf{Relevance.}
The CPT member paper of the Foundations Branch: C, P, and T as
orientation reversals of the three real bulk factors, and the
circle--clock handshake whose first receipt is the electron's twin
--- the positron. Cited at roster level in \S\ref{sec:inheritance}. First cited in \S\ref{sec:inheritance}.

\bibitem[Arisaka(2026, A7-Qi4)]{ArisakaA7Qi4}
\textbf{Arisaka, K. (2026).} The \QiFour{} Pillars --- \QiQUA{}, \QiEP{}, \QiCON{}, \QiHAL{}: The Quantum-Information Backbone of \GDOS{}. Arisaka-GG-A7-Qi4.
\par\noindent Preprint, available at \url{https://preprints.arisaka-gg.org/a7-qi4/}.
\par\noindent\textbf{Relevance.}
The quantum-information half of the pair whose geometric half this paper leans on throughout. \ASeven{} supplies the runtime vocabulary in which \GRIPin{} and \GRIPout{} are defined, and the electron's readout --- one basin, read once --- is stated in that vocabulary rather than in a private one. Cited for the vocabulary and for the information charge that partners the baryonic one; no numerical result of this paper depends on it.

\bibitem[Arisaka(2026, C2-Hubble)]{ArisakaC2Hubble}
\textbf{Arisaka, K. (2026).} The Hubble Tension in the Light of \GGTheory{}: The Hubble Constant as One Reading of a Derived Expansion History $H(t)$. Arisaka-GG-C2-Hubble.
\par\noindent Preprint, available at \url{https://preprints.arisaka-gg.org/c2-hubble/}.
\par\noindent\textbf{Relevance.}
The first of the two phenomenology papers on the astrophysical side of the same geometry. It carries no result this paper uses, and the honest description of the relation is that the two are siblings rather than neighbors: the corridor C2 reads along the scale direction is the same direction along which this paper places the electron's structure. Cited at roster level in the cohort map, and named as roster level here.

\bibitem[Arisaka(2026, C3-BH)]{ArisakaC3BH}
\textbf{Arisaka, K. (2026).} Black-Hole Entropy under \GGTheory{}: The \GDOS{} Reading of the Horizon as an \OGGEP{} Port --- with the Exact Bekenstein--Hawking $A/4G_N$ Derived from Induced Gravity. Arisaka-GG-C3-BH.
\par\noindent Preprint, available at \url{https://preprints.arisaka-gg.org/c3-bh/}.
\par\noindent\textbf{Relevance.}
The second phenomenology paper, and the other end of the same open-system reading. Where this paper asks what a projection does to a single particle, C3 asks what it does to a horizon, and both answers are statements about the same boundary law. Nothing in the electron argument turns on the horizon result. Cited at roster level in the cohort map, and the note says so.

\bibitem[Arisaka(2026, P1-KK)]{ArisakaP1KK}
\textbf{Arisaka, K. (2026).} The \GG{} Lock Cluster: A Non-Spatial Kaluza--Klein Resonance near 3.85~TeV as the Standing LHC Falsifier of \GGTheory{}. Arisaka-GG-P1-KK.
\par\noindent Preprint, available at \url{https://preprints.arisaka-gg.org/p1-kk/}.
\par\noindent\textbf{Relevance.}
The collider paper of the Particle Branch, and this paper's sibling in method rather than in subject. Both take the two non-spatial directions literally and both cash that into something a measurement can refuse: P1 into a resonance at a stated mass, this paper into a form factor that must stay flat. The lock cluster says nothing about the electron and the electron says nothing about the lock cluster; what they share is the geometry that produces both, and the willingness to name what would retire it.

\bibitem[Arisaka(2026, P6-Proton)]{ArisakaP6Proton}
\textbf{Arisaka, K. (2026).} The Proton as the Ground Geometric Attractor of Matter: The Eleven Questions of the Proton, Closed and Fenced within \GGTheory{}. Arisaka-GG-P6-Proton.
\par\noindent Preprint, available at \url{https://preprints.arisaka-gg.org/p6-proton/}.
\par\noindent\textbf{Relevance.}
The closest relative of this paper in the whole cohort, and the one worth reading beside it. P6 argues that the proton never decays because baryon number is gauged and its anomaly is canceled; this paper argues that the electron never decays because there is no gate out of the deepest basin. Two particles, two absolute stability claims, one integer ledger underneath both --- and two standing falsifiers that would be lost together. Cited in Part~\ref{part:III} where the electron's own absolute stability is stated.

\bibitem[Arisaka(2026, W1-Symmetry)]{ArisakaW1Symmetry}
\textbf{Arisaka, K. (2026).} Symmetry, Conservation, and Geometry: Seven Steps from Noether, Bianchi, to Hopkins--Singer, and the Ledger the Open-System Turn Pays Out. Arisaka-GG-W1-Symmetry.
\par\noindent Preprint, available at \url{https://preprints.arisaka-gg.org/w1-symmetry/}.
\par\noindent\textbf{Relevance.}
The background this paper's central negative claim needs and does not itself supply. The result in Part~\ref{part:III} is an \emph{absence} --- no exit gate --- and an absence reads as a result only to someone who already accepts that a conservation statement need not descend from a symmetry. W1 is the cohort's survey of exactly that century-long shift. It supplies no number and no theorem this paper uses. Cited at roster level in the cohort map.

\bibitem[Arisaka(2026, W2-Holonomy)]{ArisakaW2Holonomy}
\textbf{Arisaka, K. (2026).} The Circle That Remembers, the Interval That Forgets: \GGTheory{} and the Sixteen Problems of Particle Physics and Cosmology. Arisaka-GG-W2-Holonomy.
\par\noindent Preprint, available at \url{https://preprints.arisaka-gg.org/w2-holonomy/}.
\par\noindent\textbf{Relevance.}
The classification the mechanism of Part~\ref{part:VII} belongs to. The charge quantization argued there is a winding number on a compact phase direction, which is protection by holonomy rather than by symmetry, and that is W2's subject. Cited in Part~\ref{part:VII} where the winding argument is made, and at roster level in the cohort map --- the second because the roster owes it, the first because the mechanism is W2's.

\bibitem[Arisaka(2026, C1-Kaxion)]{ArisakaC1Kaxion}
\textbf{Arisaka, K. (2026).} The Kaxion: Cold Dark Matter as the Non-Spatial Compact-Angle Pseudoscalar of \GG{}. Arisaka-GG-C1-Kaxion.
\par\noindent Preprint, available at \url{https://preprints.arisaka-gg.org/c1-kaxion/}.
\par\noindent\textbf{Relevance.}
The cohort's first deployment of the \GGA{} vocabulary on a companion
stratum (the Kaxion as the deepest stable valley of its landscape);
cited in Part~\ref{part:II} as precedent --- the electron and the dark
sector are ground states of the same constitutional principle. First cited in \S\ref{sec:framework}.

\end{thebibliography}

\section*{B.\ Other references}

\begin{thebibliography}{99}

\bibitem[Abbott et al.(2016)]{Abbott2016}
\textbf{Abbott, B.~P., et al.\ (LIGO Scientific Collaboration and Virgo Collaboration).}
Observation of gravitational waves from a binary black hole merger.
\emph{Physical Review Letters} \textbf{116} (2016) 061102.
\par\noindent\textbf{Relevance.}
The first direct detection of gravitational waves: the final inspiral,
merger, and ringdown of a binary black hole, recorded as the chirp the
quadrupole formula predicts. Cited in \S\ref{sec:sensing} as the
direct observation of the metric-sector twin of synchrotron damping
--- the gradient-sector descent of \AFive{}'s radiative completion,
watched in real time. First cited in \S\ref{sec:sensing}.

\bibitem[Abraham(1903)]{Abraham1903}
\textbf{Abraham, M.}
Prinzipien der Dynamik des Elektrons.
\emph{Annalen der Physik} \textbf{315} (1903) 105--179.
\par\noindent\textbf{Relevance.}
The first dynamical model of an extended electron, opening the classical
self-energy crisis that Part~\ref{part:VI} engages and dissolves. First cited in \S\ref{sec:point-history}.

\bibitem[ALEPH et al.(2006)]{ALEPH2006}
\textbf{ALEPH, DELPHI, L3, OPAL Collaborations \& LEP Electroweak Working
Group.}
Precision electroweak measurements on the $Z$ resonance.
\emph{Physics Reports} \textbf{427} (2006) 257--454.
\par\noindent\textbf{Relevance.}
The empirical bound on the number of light neutrino species,
$N_\nu = 2.9963\pm0.0074$: one of the declared empirical inputs that
travels with the Q3 import (Part~\ref{part:IV}) and the anchor of P4;
also the source of LEP contact-interaction reach quoted in
Appendix~\ref{app:anchors}. First cited in \S\ref{sec:conditioning}.

\bibitem[Anderson(1933)]{Anderson1933}
\textbf{Anderson, C.~D.}
The positive electron.
\emph{Physical Review} \textbf{43} (1933) 491--494.
\par\noindent\textbf{Relevance.}
The discovery of the positron --- Dirac's ``hole'' photographed in a
cloud chamber within a year of the prediction --- and, for this paper,
the protagonist of the sixth question.
Part~\ref{part:positron} asks what the particle in Anderson's
photograph \emph{is}, and answers: the electron's one basin, read in
the conjugate orientation --- with the origin of the twin imported at
theorem grade and the same-basin reading priced
(Table~\ref{tab:q6-status}, D-P3-4). A student should still read
Anderson for the experimental humility of the prose: the most
consequential discovery of 1930s physics is reported in four pages of
careful track analysis. First cited in \S\ref{sec:five-questions}.

\bibitem[Aoyama et al.(2012)]{Aoyama2012}
\textbf{Aoyama, T., Hayakawa, M., Kinoshita, T. \& Nio, M.}
Tenth-order QED contribution to the electron $g{-}2$ and an improved
value of the fine structure constant.
\emph{Physical Review Letters} \textbf{109} (2012) 111807.
\par\noindent\textbf{Relevance.}
The summit of perturbative QED: 12{,}672 tenth-order diagrams,
computed over decades, matching experiment through twelve digits. It
is the precision partner of \citet{Fan2023} in prediction P3
(\S\ref{sec:predictions}) and the sharpest existing statement that the
electron's moment is dressing, not structure. For the student it is
also a methodological landmark: what ``the Standard-Model prediction
for a point fermion'' means, made concrete to five loops. First cited in \S\ref{sec:predictions}.

\bibitem[Bogomolny(1976)]{Bogomolny1976}
\textbf{Bogomolny, E.~B.}
Stability of classical solutions.
\emph{Soviet Journal of Nuclear Physics} \textbf{24} (1976) 449--454.
\par\noindent\textbf{Relevance.}
Source of the Bogomolnyi bound: the energy of a topological
configuration is bounded below by its topological charge, with
equality on first-order (self-dual) solutions. The gate tolls $S =
\pi k$ of the lepton cascade (Eq.~\ref{eq:lepton-chain};
Appendix~\ref{app:Q2-gates}) are Bogomolnyi-saturating instanton
actions, which is why they are exact integers times $\pi$ rather than
landscape-dependent numbers --- the structural reason the budget
arithmetic of Appendix~\ref{app:Q3-L2} can be arithmetic at all. First cited in \S\ref{app:Q2-gates}.

\bibitem[Borexino Collaboration(2015)]{Borexino2015}
\textbf{Agostini, M., et al.\ (Borexino Collaboration).}
Test of electric charge conservation with Borexino.
\emph{Physical Review Letters} \textbf{115} (2015) 231802.
\par\noindent\textbf{Relevance.}
The world's best lower bound on the electron lifetime,
$\tau_e > 6.6\times10^{28}$~yr (90\% C.L.), via the charge-violating
channel $e\to\nu\gamma$: the empirical anchor of Q2 and of prediction P1
/ kill criterion F1. First cited in \S\ref{ssec:standard-stability}.

\bibitem[Born(1926)]{Born1926}
\textbf{Born, M.}
Zur Quantenmechanik der Sto{\ss}vorg\"ange.
\emph{Zeitschrift f\"ur Physik} \textbf{37} (1926) 863--867.
\par\noindent\textbf{Relevance.}
The probability rule of quantum mechanics, postulated in a footnote
in 1926 and never derived within the formalism it completes. Cited in
\S\ref{sec:century-openness}: its derivation as a theorem of the
boundary reduction \citep{ArisakaA8QM} is the centenary's other
bookend --- the dice of the boundary obtained from the determinism of
the bulk. First cited in \S\ref{sec:century-openness}.

\bibitem[Brodsky \& Drell(1980)]{BrodskyDrell1980}
\textbf{Brodsky, S.~J. \& Drell, S.~D.}
Anomalous magnetic moment and limits on fermion substructure.
\emph{Physical Review D} \textbf{22} (1980) 2236--2243.
\par\noindent\textbf{Relevance.}
The classic analysis converting $g{-}2$ precision into substructure
bounds: a composite electron of size $R$ generically shifts $a_e$ by
$\mathcal{O}(m_e R)$, so the measured agreement with QED pushes $R$
far below scattering reach. This is the engine behind Dehmelt's
famous radius bound \citep{Dehmelt1988} and the reason
\S\ref{sec:point-history} calls such bounds model-dependent: the
conversion requires a compositeness ansatz, exactly the assumption
Theorem~\ref{thm:pointlike} renders permanently idle. First cited in \S\ref{sec:point-history}.

\bibitem[Cabibbo(1963)]{Cabibbo1963}
\textbf{Cabibbo, N.}
Unitary symmetry and leptonic decays.
\emph{Physical Review Letters} \textbf{10} (1963) 531--533.
\par\noindent\textbf{Relevance.}
The two-family mixing angle --- the seed of the CKM matrix. Cabibbo's
single parameter became, at three families, the four-parameter matrix
whose single physical phase carries CP violation; the counting that
turns this structure into the lower bound $N \ge 3$ is reproduced in
Appendix~\ref{app:Q3-L1}. For the student: this is what it looks like
when one rotation angle, honestly bookkept, reorganizes the weak
interactions of every quark. First cited in \S\ref{app:Q3-L1}.

\bibitem[Candelas et al.(1985)]{Candelas1985}
\textbf{Candelas, P., Horowitz, G.~T., Strominger, A. \& Witten, E.}
Vacuum configurations for superstrings.
\emph{Nuclear Physics B} \textbf{258} (1985) 46--74.
\par\noindent\textbf{Relevance.}
The seminal Calabi--Yau compactification: the canonical construction in
which the extra dimensions are \emph{spatial} and carry continuous
moduli --- the structural contrast drawn in \S\ref{ssec:moduli-landscape}. First cited in \S\ref{ssec:moduli-landscape}.

\bibitem[Carter(1968)]{Carter1968}
\textbf{Carter, B.}
Global structure of the Kerr family of gravitational fields.
\emph{Physical Review} \textbf{174} (1968) 1559--1571.
\par\noindent\textbf{Relevance.}
Source of the remarkable observation that a Kerr--Newman source with
the electron's parameters has gyromagnetic ratio $g=2$ --- the
geometric-electron tradition engaged in \S\ref{sec:prior}. First cited in \S\ref{sec:prior}.

\bibitem[Christenson et al.(1964)]{CCFT1964}
\textbf{Christenson, J.~H., Cronin, J.~W., Fitch, V.~L. \& Turlay, R.}
Evidence for the $2\pi$ decay of the $K_2^0$ meson.
\emph{Physical Review Letters} \textbf{13} (1964) 138--140.
\par\noindent\textbf{Relevance.}
The discovery of CP violation --- the single empirical input on which
leg (L1) of the $N = 3$ derivation stands
(\S\ref{sec:conditioning}; Appendix~\ref{app:Q3-L1}). A
fifty-seven-event excess in a beamline experiment, and its
consequence, half a century later, is a lower bound on the number of
families of matter: few papers teach more vividly that the count of
fundamental inputs to a framework can hinge on one decisive
measurement. First cited in \S\ref{sec:conditioning}.

\bibitem[CODATA(2022)]{CODATA2022}
\textbf{Mohr, P.~J., Newell, D.~B., Taylor, B.~N. \& Tiesinga, E.}
CODATA recommended values of the fundamental physical constants: 2022.
arXiv:2409.03787 (2024).
\par\noindent\textbf{Relevance.}
Source of the precision anchors $m_e c^2 = 0.51099895069(16)$~MeV and
$\alphainv = 137.035999177(21)$ against which the QD-completed codebook
values are registered, with the $1.9\times10^{-4}$ mass residual
declared in \S\ref{ssec:value-mass}. First cited in \S\ref{ssec:value-mass}.

\bibitem[Compton(1923)]{Compton1923}
\textbf{Compton, A.~H.}
A quantum theory of the scattering of X-rays by light elements.
\emph{Physical Review} \textbf{21} (1923) 483--502.
\par\noindent\textbf{Relevance.}
The electron as point target: X-ray scattering with the kinematics of
a billiard-ball collision, establishing that radiation exchanges
momentum with single electrons. Compton scattering is the ancestor of
every probe in the form-factor story of \S\ref{sec:formfactor} ---
the first experiment to ask, in effect, ``what does the electron look
like at short wavelength?'' and to receive the answer this paper
promotes to law: a point. First cited in \S\ref{sec:five-questions}.

\bibitem[Davisson \& Germer(1927)]{DavissonGermer1927}
\textbf{Davisson, C. \& Germer, L.~H.}
Diffraction of electrons by a crystal of nickel.
\emph{Physical Review} \textbf{30} (1927) 705--740.
\par\noindent\textbf{Relevance.}
The electron as wave: de Broglie's hypothesis confirmed in nickel
diffraction. Together with \citet{deBroglie1925} it fixes the dual
character that any account of the electron must carry --- and it
sharpens Q4: the object that diffracts like a wave nevertheless
scatters, at every accessible $q^2$, like a structureless point
(\S\ref{sec:five-questions}). The tension is resolved in this paper
by relocating structure off the spatial directions entirely. First cited in \S\ref{sec:five-questions}.

\bibitem[de Broglie(1925)]{deBroglie1925}
\textbf{de Broglie, L.}
Recherches sur la th\'eorie des quanta.
\emph{Annales de Physique} (Paris) \textbf{3} (1925) 22--128.
\par\noindent\textbf{Relevance.}
The matter wave: the doctoral thesis that assigned the electron a
wavelength and thereby founded wave mechanics. Cited in
\S\ref{sec:five-questions} as part of the electron's
foundational r\'esum\'e --- the same particle whose wave nature built
quantum mechanics is the particle whose five elementary properties
remained unexplained for the century that followed; this paper's
preface is addressed to exactly that irony. First cited in \S\ref{sec:five-questions}.

\bibitem[Dehmelt(1988)]{Dehmelt1988}
\textbf{Dehmelt, H.}
A single atomic particle forever floating at rest in free space: new
value for electron radius.
\emph{Physica Scripta} \textbf{T22} (1988) 102--110.
\par\noindent\textbf{Relevance.}
The classic $g-2$ argument bounding an electron ``intrinsic radius''
far below scattering reach --- model-dependent, as stated there and in
\S\ref{sec:formfactor}; engaged as the empirical-anchor tradition that
P2/F2 sharpens into a scale-free prediction. First cited in \S\ref{sec:point-history}.

\bibitem[Dirac(1928)]{Dirac1928}
\textbf{Dirac, P.~A.~M.}
The quantum theory of the electron.
\emph{Proceedings of the Royal Society of London A} \textbf{117}
(1928) 610--624.
\par\noindent\textbf{Relevance.}
The relativistic wave equation: spin-$\tfrac12$ and $g = 2$ emerging
unbidden from the marriage of quantum mechanics and special
relativity, with the positron implicit in the negative-energy sea.
For this paper Dirac~1928 is the standard of what ``explaining a
property of the electron'' should mean --- a property falling out of
a structural requirement rather than being fitted --- and
\S\ref{ssec:value-spin} (with Appendix~\ref{app:Q1-spin}) is the
attempt to meet that standard one level deeper: why the world's
spinor algebra is quaternionic in the first place. First cited in \S\ref{sec:five-questions}.

\bibitem[Dirac(1931)]{Dirac1931}
\textbf{Dirac, P.~A.~M.}
Quantised singularities in the electromagnetic field.
\emph{Proceedings of the Royal Society A} \textbf{133} (1931) 60--72.
\par\noindent\textbf{Relevance.}
The founding document of the sixth question: the concession, three
years after the equation, that the negative-energy shadow is ``a new
kind of particle, unknown to experimental physics, having the same
mass and opposite charge to an electron.'' Part~\ref{part:positron}
reads the episode as the century's most successful mis-filing: a
consistency demand mistaken for an explanation. First cited in \S\ref{sec:five-questions}.

\bibitem[Dirac(1938)]{Dirac1938}
\textbf{Dirac, P.~A.~M.}
Classical theory of radiating electrons.
\emph{Proceedings of the Royal Society of London A} \textbf{167} (1938)
148--169.
\par\noindent\textbf{Relevance.}
The definitive classical point-electron dynamics (Lorentz--Dirac
equation), whose runaway and pre-acceleration pathologies close the
classical chapter of Q4's crisis engaged in \S\ref{sec:point-history}. First cited in \S\ref{sec:point-history}.

\bibitem[Dyson(1949)]{Dyson1949}
\textbf{Dyson, F.~J.}
The radiation theories of Tomonaga, Schwinger, and Feynman.
\emph{Physical Review} \textbf{75} (1949) 486--502.
\par\noindent\textbf{Relevance.}
The unification of the three renormalization schemes into one
machine, completing the demonstration that QED's infinities can be
consistently absorbed. In the historical ledger of
\S\ref{sec:point-history} this is the moment the self-energy crisis
was \emph{sidestepped} with full rigor --- the subtraction became a
theory --- and the moment ``why is the electron pointlike?'' stopped
being asked because the question's penalty had been administratively
removed. Required reading for understanding what renormalization does
and does not explain. First cited in \S\ref{sec:point-history}.

\bibitem[Eichten, Lane \& Peskin(1983)]{EichtenLanePeskin1983}
\textbf{Eichten, E., Lane, K. \& Peskin, M.}
New tests for quark and lepton substructure.
\emph{Physical Review Letters} \textbf{50} (1983) 811--814.
\par\noindent\textbf{Relevance.}
The contact-interaction formalism by which compositeness scales are
bounded; the framework of the experimental reach quoted in
Appendix~\ref{app:anchors}, and the standard-physics counterpoint to
Theorem~\ref{thm:pointlike}'s scale-free prediction. First cited in \S\ref{sec:point-history}.

\bibitem[Einstein(1905)]{Einstein1905}
\textbf{Einstein, A.}
Zur Elektrodynamik bewegter K\"orper.
\emph{Annalen der Physik} \textbf{17} (1905) 891--921.
\par\noindent\textbf{Relevance.}
Special relativity: the causal structure --- no influence outside the
light cone --- that AX-1 elevates from property to constitutional
axiom. Lemma~\ref{post:RL}'s branch (a)
(Appendix~\ref{app:formfactor}, Step 2) is, at bottom, Einstein's
prohibition applied to the registration channel itself; the student
tracing the pointlikeness theorem to its roots ends here, in the
paper that made simultaneity local. First cited in \S\ref{ssec:appB-RL}.

\bibitem[Einstein(1915)]{Einstein1915}
\textbf{Einstein, A.}
Die Feldgleichungen der Gravitation.
\emph{Sitzungsberichte der Preussischen Akademie der Wissenschaften}
(1915) 844--847.
\par\noindent\textbf{Relevance.}
The field equations of general relativity --- the original
demonstration that a force can be abolished into geometry. Chain (A)
of \S\ref{ssec:two-chains} (Appendix~\ref{app:Q5-chainA}) descends
exactly these equations from the 6D bulk, and the entire Q5 answer of
this paper is Einstein's move performed a second time, on the gauge
sector: what 1915 did to ``the pull on the apple,'' the composite
connection does to ``the force on the electron.'' First cited in \S\ref{ssec:two-chains}.

\bibitem[Fan et al.(2023)]{Fan2023}
\textbf{Fan, X., Myers, T.~G., Sukra, B.~A.~D. \& Gabrielse, G.}
Measurement of the electron magnetic moment.
\emph{Physical Review Letters} \textbf{130} (2023) 071801.
\par\noindent\textbf{Relevance.}
The most precise property measurement of any elementary particle
($g/2$ to 0.13 ppt): the empirical anchor of structurelessness (P3) and
of the QED-dressing reading of $a_e$ in \S\ref{sec:formfactor}. First cited in \S\ref{sec:point-history}.

\bibitem[Fee et al.(1993)]{Fee1993}
\textbf{Fee, M.~S., Chu, S., Mills, A.~P., Chichester, R.~J.,
Zuckerman, D.~M., Shaw, E.~D. \& Danzmann, K.}
Measurement of the positronium $1\,{}^3S_1$--$2\,{}^3S_1$ interval by
continuous-wave two-photon excitation.
\emph{Physical Review A} \textbf{48} (1993) 192--219.
\par\noindent\textbf{Relevance.}
Positronium spectroscopy as a mass-equality balance: the source of the
$|m_{e^+}-m_{e^-}|/m < 8\times10^{-9}$ bound (90\% C.L.) quoted in the
falsifier face of \S\ref{sec:q6-status} --- for this paper, a bound on
how differently the one basin can read in its two orientations. First cited in \S\ref{sec:q6-status}.

\bibitem[Feinberg \& Goldhaber(1959)]{FeinbergGoldhaber1959}
\textbf{Feinberg, G. \& Goldhaber, M.}
Microscopic tests of symmetry principles.
\emph{Proceedings of the National Academy of Sciences} \textbf{45}
(1959) 1301--1312.
\par\noindent\textbf{Relevance.}
The founding charter of the conservation-law test program: if a
symmetry is exact, prove it by lifetime, and if not, find the decay.
The electron-lifetime searches culminating in
\citet{Borexino2015} descend from this paper's logic, and prediction
P1 (\S\ref{sec:predictions}) is its \GGTheory{} endpoint: the search
must continue forever and must find nothing, forever. First cited in \S\ref{ssec:standard-stability}.

\bibitem[Fermi(1934)]{Fermi1934}
\textbf{Fermi, E.}
Versuch einer Theorie der $\beta$-Strahlen.
\emph{Zeitschrift f\"ur Physik} \textbf{88} (1934) 161--177.
\par\noindent\textbf{Relevance.}
The first theory of the weak interaction --- the four-fermion contact
form that grew into the electroweak gauge sector. In this paper's
ontology the weak interaction is Nature's implementer of \GRIPin{} on
the matter strata (\S\ref{sec:ladder}): every arrow in the
$\tau \to \mu \to e$ descent is a Fermi transition, which makes this
the paper in which the road between the basins was first paved. First cited in \S\ref{sec:ladder}.

\bibitem[Feynman(1949)]{Feynman1949}
\textbf{Feynman, R.~P.}
Space-time approach to quantum electrodynamics.
\emph{Physical Review} \textbf{76} (1949) 769--789.
\par\noindent\textbf{Relevance.}
The diagrammatic formulation of QED --- with \citet{Tomonaga1946} and
\citet{Dyson1949}, the apparatus by which the point electron's
infinities were tamed into the most precise theory in science. Cited
in \S\ref{sec:point-history} at the hinge of the Q4 story: the
formalism that made the point electron \emph{workable} is precisely
what allowed the question of why it is a point to sleep for seventy
years. First cited in \S\ref{sec:point-history}.

\bibitem[Feynman(1966)]{Feynman1966}
\textbf{Feynman, R.~P.}
The development of the space-time view of quantum electrodynamics
(Nobel lecture).
\emph{Science} \textbf{153} (1966) 699--708.
\par\noindent\textbf{Relevance.}
Primary source for Wheeler's one-electron universe (the 1940 telephone
call), engaged in \S\ref{sec:prior} as the closest historical ancestor
of identity-by-uniqueness --- and for the foundational period of QED
whose sign-rule credit Part~\ref{part:VII} states. First cited in \S\ref{sec:prior}.

\bibitem[Feynman \& Vernon(1963)]{FeynmanVernon1963}
\textbf{Feynman, R.~P., \& Vernon, F.~L.}
The theory of a general quantum system interacting with a linear
dissipative system.
\emph{Annals of Physics} \textbf{24} (1963) 118--173.
\par\noindent\textbf{Relevance.}
The influence functional: the exact form of a dynamics from which a
sector has been traced out --- the mathematical key to openness,
published eight years after Einstein's death. Cited in
\S\ref{sec:century-openness} as the first of the tools without which
the second half of the unification dream was inaccessible; its
deployment on the radiation field is \AFive{}'s quantitative closure,
imported in \S\ref{sec:sensing}. First cited in \S\ref{sec:century-openness}.

\bibitem[Green \& Schwarz(1984)]{GreenSchwarz1984}
\textbf{Green, M.~B. \& Schwarz, J.~H.}
Anomaly cancellations in supersymmetric $D=10$ gauge theory and
superstring theory.
\emph{Physics Letters B} \textbf{149} (1984) 117--122.
\par\noindent\textbf{Relevance.}
The original modified-Bianchi-identity mechanism, of which the
cohort's \BIsix{} is the six-dimensional descent --- the shared
machinery acknowledged in \S\ref{ssec:same-machinery} and
\S\ref{ssec:string-credits}. First cited in \S\ref{ssec:same-machinery}.

\bibitem[Green, Schwarz \& Witten(1987)]{GSW1987}
\textbf{Green, M.~B., Schwarz, J.~H. \& Witten, E.}
\emph{Superstring Theory, Vols.~1--2.}
Cambridge University Press, Cambridge (1987).
\par\noindent\textbf{Relevance.}
The standard reference for superstring compactification and anomaly
cancellation; the framework against which \S\ref{sec:susy-string}
draws its contrast, credited there without reluctance. First cited in \S\ref{ssec:string-credits}.

\bibitem[Hanneke et al.(2008)]{Hanneke2008}
\textbf{Hanneke, D., Fogwell, S. \& Gabrielse, G.}
New measurement of the electron magnetic moment and the fine
structure constant.
\emph{Physical Review Letters} \textbf{100} (2008) 120801.
\par\noindent\textbf{Relevance.}
The one-electron quantum cyclotron measurement that held the
record for fifteen years before \citet{Fan2023}: a single electron,
suspended for months, interrogated at the level of parts in
$10^{13}$. Cited in \S\ref{sec:predictions} (P3) as part of the
experimental lineage this paper bets on continuing --- each
generation of traps a fresh chance to find the structural deviation
the framework forbids. First cited in \S\ref{sec:predictions}.

\bibitem[Hughes \& Deutch(1992)]{Hughes1992}
\textbf{Hughes, R.~J. \& Deutch, B.~I.}
Electric charges of positrons and antiprotons.
\emph{Physical Review Letters} \textbf{69} (1992) 578--581.
\par\noindent\textbf{Relevance.}
The charge-sum bound $|q_{e^+}+q_{e^-}|/e < 4\times10^{-8}$, from
Rydberg-energy and cyclotron-frequency ratios, quoted in
\S\ref{sec:q6-status}: in the conjugate-readout picture the charge
flip is definitional (reversed winding), so the bound tests whether
the mirror is exact. First cited in \S\ref{sec:q6-status}.

\bibitem[Harari(1979)]{Harari1979}
\textbf{Harari, H.}
A schematic model of quarks and leptons.
\emph{Physics Letters B} \textbf{86} (1979) 83--86.
\par\noindent\textbf{Relevance.}
The rishon model: the most economical preon construction, engaged in
\S\ref{sec:prior} as the compositeness tradition at its best --- and
the cleanest illustration of the mass paradox that the non-spatial
relocation of structure dissolves. First cited in \S\ref{sec:prior}.

\bibitem[Helgason(1979)]{Helgason1979}
\textbf{Helgason, S.}
\emph{Differential Geometry, Lie Groups, and Symmetric Spaces.}
Academic Press, New York (1979).
\par\noindent\textbf{Relevance.}
Standard reference for the symmetric-space geometry of
$\mathbb{C}P^{N-1}$ underlying the gate-action computation reproduced
in Appendix~\ref{app:Q3-L2} (with \citealp{Witten1982}): the
Fubini--Study metric, the isometry group, and the geodesic structure
between critical points are all standard material here. For the
student, the relevant chapters are those on compact symmetric spaces
--- $\mathbb{C}P^2$ is the simplest non-trivial example, which is
part of why the family stratum's Morse theory is tractable at all. First cited in \S\ref{app:Q3-L2}.

\bibitem[Hulse \& Taylor(1975)]{HulseTaylor1975}
\textbf{Hulse, R.~A., \& Taylor, J.~H.}
Discovery of a pulsar in a binary system.
\emph{The Astrophysical Journal} \textbf{195} (1975) L51--L53.
\par\noindent\textbf{Relevance.}
The binary pulsar PSR B1913+16, whose measured orbital decay has
followed the general-relativistic quadrupole prediction for five
decades to a few parts in $10^3$ --- the first empirical proof that
gravitational radiation drains orbital energy. Cited in
\S\ref{sec:sensing} as the empirical anchor of the inspiral half of
the synchrotron/inspiral worked example imported from \AFive{}. First cited in \S\ref{sec:sensing}.

\bibitem[Jordan, Kinderlehrer \& Otto(1998)]{JKO1998}
\textbf{Jordan, R., Kinderlehrer, D., \& Otto, F.}
The variational formulation of the Fokker--Planck equation.
\emph{SIAM Journal on Mathematical Analysis} \textbf{29} (1998)
1--17.
\par\noindent\textbf{Relevance.}
The discovery that dissipative dynamics is gradient flow --- descent
of a free-energy functional in a geometry on the space of states ---
inaugurating the mathematics in which this paper's landscapes,
basins, and descents are written. Cited in
\S\ref{sec:century-openness}: the language of the answer to the six
questions did not exist until the century was nearly over. First cited in \S\ref{sec:century-openness}.

\bibitem[Kachru et al.(2003)]{KachruKalloshLindeTrivedi2003}
\textbf{Kachru, S., Kallosh, R., Linde, A. \& Trivedi, S.~P.}
de Sitter vacua in string theory.
\emph{Physical Review D} \textbf{68} (2003) 046005.
\par\noindent\textbf{Relevance.}
The KKLT construction --- the technical centerpiece of the string
landscape: metastable de Sitter vacua by the $10^{500}$. Cited in
\S\ref{ssec:moduli-landscape} as the sharpest form of the position
this paper's anti-landscape bet opposes: where moduli are dials,
constants are environmental; where the ledger is five integers,
constants are theorems. One of the two positions will lose to data. First cited in \S\ref{ssec:qft-identity}.

\bibitem[Kaluza(1921)]{Kaluza1921}
\textbf{Kaluza, T.}
Zum Unit\"atsproblem der Physik.
\emph{Sitzungsberichte der Preussischen Akademie der Wissenschaften}
(1921) 966--972.
\par\noindent\textbf{Relevance.}
The original fifth dimension: gravity in five dimensions containing
Maxwell's theory --- the first proof-of-concept that electromagnetism
can be geometry. The \GG{} bulk is this insight with the fatal flaw
repaired: Kaluza's extra dimension was \emph{spatial}, with a radius
nothing fixed; the \GG{} directions are scale and phase, with
integers where the dials were (\S\ref{ssec:moduli-landscape};
Appendix~\ref{app:Q5}). Read it to see how close 1921 came. First cited in \S\ref{ssec:two-chains}.

\bibitem[Klein(1926)]{Klein1926}
\textbf{Klein, O.}
Quantentheorie und f\"unfdimensionale Relativit\"atstheorie.
\emph{Zeitschrift f\"ur Physik} \textbf{37} (1926) 895--906.
\par\noindent\textbf{Relevance.}
The compactification of Kaluza's dimension and the origin of charge
quantization from circular topology: momentum around a compact circle
comes in integers. That single mechanism --- charge as quantized
holonomy momentum --- survives intact into the present framework's
phase circle $\Stheta$ (\S\ref{sec:coupling};
Table~\ref{tab:appG-dictionary}), making Klein's paper the direct
ancestor of this paper's answer to ``why is charge quantized?'' First cited in \S\ref{sec:fiber}.

\bibitem[Kobayashi \& Maskawa(1973)]{KobayashiMaskawa1973}
\textbf{Kobayashi, M. \& Maskawa, T.}
CP-violation in the renormalizable theory of weak interaction.
\emph{Progress of Theoretical Physics} \textbf{49} (1973) 652--657.
\par\noindent\textbf{Relevance.}
The six-quark insight: with fewer than three families the weak mixing
matrix carries no physical CP phase, so observed CP violation demands
a third family --- predicted here four years before the tau and
twenty-two before the top. Leg (L1) of the $N = 3$ derivation
(Appendix~\ref{app:Q3-L1}) is this argument run under \MSMF{}; the
student should read the original to see a family of matter conjured
from one phase that would not go away. First cited in \S\ref{app:Q3-L1}.

\bibitem[Kuhn(1962)]{Kuhn1962}
\textbf{Kuhn, T.~S.}
\emph{The Structure of Scientific Revolutions}.
University of Chicago Press, Chicago (1962).
\par\noindent\textbf{Relevance.}
The account of how frameworks replace one another: by dissolving
standing anomalies and surviving the tests the old framework could
not name. Cited in \S\ref{sec:century-openness} to discipline this
paper's own largest claim --- a paradigm shift is a verdict the
community renders, not a thing a paper declares; what a paper can do
is qualify, by naming its anomalies and pre-registering its
falsifiers, which is what Part~\ref{part:VIII} is for. First cited in \S\ref{sec:century-openness}.

\bibitem[Kusch \& Foley(1948)]{KuschFoley1948}
\textbf{Kusch, P. \& Foley, H.~M.}
The magnetic moment of the electron.
\emph{Physical Review} \textbf{74} (1948) 250--263.
\par\noindent\textbf{Relevance.}
The discovery that $g \ne 2$: the electron's moment exceeds Dirac's
value by a part in a thousand. Together with \citet{Schwinger1948},
which explained the excess as $\alpha/2\pi$, this opened the
dressing-versus-structure distinction on which the entire form-factor
argument of \S\ref{sec:formfactor} rests: the anomaly is the vacuum's
contribution, not the electron's size --- a lesson first taught here. First cited in \S\ref{sec:point-history}.

\bibitem[Lamb \& Retherford(1947)]{LambRetherford1947}
\textbf{Lamb, W.~E. \& Retherford, R.~C.}
Fine structure of the hydrogen atom by a microwave method.
\emph{Physical Review} \textbf{72} (1947) 241--243.
\par\noindent\textbf{Relevance.}
The Lamb shift: the vacuum visibly dressing a bound electron, and the
experimental detonator of modern QED. Cited in
\S\ref{sec:point-history} as the partner discovery to
\citet{KuschFoley1948} --- the pair of 1947--48 measurements that
forced the renormalization program and thereby fixed, for seventy
years, the working answer to Q4: \emph{calculable dressing around an
unexplained point}. First cited in \S\ref{sec:point-history}.

\bibitem[Larmor(1897)]{Larmor1897}
\textbf{Larmor, J.}
On the theory of the magnetic influence on spectra; and on the
radiation of moving ions.
\emph{Philosophical Magazine}, Series 5, \textbf{44} (1897) 503--512.
\par\noindent\textbf{Relevance.}
The original formula for the power radiated by an accelerated charge
--- the oldest quantitative statement that acceleration in the gauge
sector is paid for in radiation. Cited in Reading~\ref{rmk:sensing}
and \S\ref{sec:sensing}: Larmor's loss is the dissipative channel of
motion, the one place open-system language properly attaches to a
moving electron. First cited in \S\ref{sec:sensing}.

\bibitem[Lindblad(1976)]{Lindblad1976}
\textbf{Lindblad, G.}
On the generators of quantum dynamical semigroups.
\emph{Communications in Mathematical Physics} \textbf{48} (1976)
119--130.
\par\noindent\textbf{Relevance.}
The general form of Markovian open-system dynamics --- dissipative
quantum evolution made mathematically exact. Cited in
\S\ref{sec:why-century} as the century's great near-miss: the
machinery of descent existed from 1976, but was filed under applied
decoherence rather than foundations, which is precisely the
closed-system blind spot that kept ground-state-ness unavailable as
an answer to the six questions until the open-system shift of
\GDOS{}. First cited in \S\ref{sec:why-century}.

\bibitem[Jarlskog(1985)]{Jarlskog1985}
\textbf{Jarlskog, C.}
Commutator of the quark mass matrices in the standard electroweak
model and a measure of maximal CP nonconservation.
\emph{Physical Review Letters} \textbf{55} (1985) 1039--1042.
\par\noindent\textbf{Relevance.}
The basis-independent measure of CP violation --- the invariant
$\JCKM$ whose non-vanishing is the empirical input of leg (L1)
(Appendix~\ref{app:Q3-L1}). Jarlskog's construction matters
methodologically for this paper: it converts ``CP is violated'' from
a parameterization-dependent statement into a single number an
experiment can measure and a counting argument can consume. First cited in \S\ref{sec:conditioning}.

\bibitem[Lorentz(1909)]{Lorentz1909}
\textbf{Lorentz, H.~A.}
\emph{The Theory of Electrons and Its Applications to the Phenomena of
Light and Radiant Heat.}
Teubner, Leipzig (1909).
\par\noindent\textbf{Relevance.}
The canonical extended-electron theory whose stability problem
(\S\ref{sec:point-history}) defined Q4's classical crisis. First cited in \S\ref{sec:point-history}.

\bibitem[Maldacena(1998)]{Maldacena1998}
\textbf{Maldacena, J.}
The large $N$ limit of superconformal field theories and supergravity.
\emph{Advances in Theoretical and Mathematical Physics} \textbf{2}
(1998) 231--252.
\par\noindent\textbf{Relevance.}
AdS/CFT: the modern holographic dictionary between bulk gravity and
boundary field theory. Cited in \S\ref{ssec:same-machinery} as shared
machinery --- the bulk-to-boundary projection grammar that \GGTheory{}
deploys with opposite constitutional commitments (non-spatial
directions, zero moduli, an open-system boundary law). The student
who knows AdS/CFT will recognize the radial-direction-as-RG reading;
the framework's departure is to make that reading constitutional. First cited in \S\ref{ssec:same-machinery}.

\bibitem[Maxwell(1865)]{Maxwell1865}
\textbf{Maxwell, J.~C.}
A dynamical theory of the electromagnetic field.
\emph{Philosophical Transactions of the Royal Society of London}
\textbf{155} (1865) 459--512.
\par\noindent\textbf{Relevance.}
The unification of electricity, magnetism, and light --- the first
great field theory, and the system of equations that Chain (B)
re-derives from the bulk gauge connection
(Appendix~\ref{app:Q5-chainB}). In this paper's arc Maxwell plays the
role Newton plays for Chain (A): the classical summit that the
six-dimensional geometry must reproduce exactly before it may claim
anything new --- and does. First cited in \S\ref{ssec:two-chains}.

\bibitem[Mermin(1989)]{Mermin1989}
\textbf{Mermin, N.~D.}
What's wrong with this pillow?
\emph{Physics Today} \textbf{42}(4) (1989) 9--11.
\par\noindent\textbf{Relevance.}
The source of ``shut up and calculate'' (often misattributed to
Feynman; Mermin himself later documented the attribution), quoted in
\S\ref{sec:why-century} as the emblem of the professional attitude
that filed the questions of this paper under metaphysics for a century. First cited in \S\ref{sec:why-century}.

\bibitem[Millikan(1913)]{Millikan1913}
\textbf{Millikan, R.~A.}
On the elementary electrical charge and the Avogadro constant.
\emph{Physical Review} \textbf{2} (1913) 109--143.
\par\noindent\textbf{Relevance.}
The oil-drop measurement: charge comes in integer multiples of one
unit, measured drop by drop. This is Q1's ``and the same charge''
made empirical --- the quantization that \S\ref{ssec:value-charge}
derives from compact holonomy and that \citet{Klein1926} first
explained topologically. The student should notice what Millikan
could not ask: \emph{why} integers? The answer waited for a compact
phase dimension. First cited in \S\ref{sec:five-questions}.

\bibitem[Morel et al.(2020)]{Morel2020}
\textbf{Morel, L., Yao, Z., Clad\'e, P. \& Guellati-Kh\'elifa, S.}
Determination of the fine-structure constant with an accuracy of 81
parts per trillion.
\emph{Nature} \textbf{588} (2020) 61--65.
\par\noindent\textbf{Relevance.}
The rubidium recoil determination of $\alpha$; together with
\citet{Parker2018} defines the $>5\sigma$ experimental discrepancy that
kill criterion F4 is phrased to respect. First cited in \S\ref{sec:coupling}.

\bibitem[Morse(1934)]{Morse1934}
\textbf{Morse, M.}
\emph{The Calculus of Variations in the Large.}
American Mathematical Society Colloquium Publications, Vol.~18,
Providence (1934).
\par\noindent\textbf{Relevance.}
The founding monograph of Morse theory: critical points of a function
encode the topology of the space it lives on. The entire landscape
ontology of this paper --- basins, saddles, gates, the index-0/2/4
skeleton of $\mathbb{C}P^2$ (Appendix~\ref{app:Q2-skeleton}) --- is
Morse's mathematics deployed as physics, with the generations as
critical points and their masses as critical values. First cited in \S\ref{app:Q2-skeleton}.

\bibitem[Neddermeyer \& Anderson(1937)]{NeddermeyerAnderson1937}
\textbf{Neddermeyer, S.~H. \& Anderson, C.~D.}
Note on the nature of cosmic-ray particles.
\emph{Physical Review} \textbf{51} (1937) 884--886.
\par\noindent\textbf{Relevance.}
The muon: a particle with the electron's charge and spin but two
hundred times its mass, found in cosmic rays and wanted by no theory
--- the original ``who ordered that?'' In this paper's terms,
Neddermeyer and Anderson discovered the depth-1 basin
(\S\ref{sec:ladder}) eighty-nine years before the landscape that
houses it was drawn; Q3 begins on these three pages. First cited in \S\ref{sec:ladder}.

\bibitem[Newton(1687)]{Newton1687}
\textbf{Newton, I.}
\emph{Philosophi\ae{} Naturalis Principia Mathematica.}
Royal Society, London (1687).
\par\noindent\textbf{Relevance.}
The inverse-square law of gravitation and the equation of motion ---
the two endpoints of Chain (A) (Appendix~\ref{app:Q5-chainA}). The
\GGTheory{} claim under Q5 is that Newton's law and Coulomb's law are
one law read on two curvatures; the Principia supplies the
gravitational half of that sentence three centuries in advance, and
the parallel-chain derivation is, in a precise sense, the Principia's
$1/r^2$ recomputed from six dimensions. First cited in \S\ref{ssec:two-chains}.

\bibitem[Noether(1918)]{Noether1918}
\textbf{Noether, E.}
Invariante Variationsprobleme.
\emph{Nachrichten von der Gesellschaft der Wissenschaften zu
G\"ottingen, Mathematisch-Physikalische Klasse} (1918) 235--257.
\par\noindent\textbf{Relevance.}
Symmetries make currents: the theorem behind both conserved
four-currents of Appendix~\ref{app:Q5-ingredients} ---
stress--energy from translations, electric current from
$\mathrm{U}(1)$ --- and hence behind ingredient (iii) of the
Newton--Coulomb twinning. Every Ward identity in the cohort is
Noether's theorem boundary-transported; the student should
meet it in the original, where it is purer than in any textbook. First cited in \S\ref{app:Q5-ingredients}.

\bibitem[Okun \& Zeldovich(1978)]{OkunZeldovich1978}
\textbf{Okun, L.~B. \& Zeldovich, Ya.~B.}
Paradoxes of unstable electron.
\emph{Physics Letters B} \textbf{78} (1978) 597--600.
\par\noindent\textbf{Relevance.}
The theoretical anatomy of electron decay: any charge-nonconserving
instability, made consistent with the photon's masslessness, forces
pathological longitudinal-photon emission --- decay is not merely
unobserved but theoretically expensive. Cited in
\S\ref{ssec:standard-stability} as the sharpest standard-physics
companion to the Borexino search: even the loopholes have paradoxes.
The \GGTheory{} statement is stronger still --- no gate exists at all
--- and P1 inherits both lineages. First cited in \S\ref{ssec:standard-stability}.

\bibitem[Parker et al.(2018)]{Parker2018}
\textbf{Parker, R.~H., Yu, C., Zhong, W., Estey, B. \& M\"uller, H.}
Measurement of the fine-structure constant as a test of the Standard
Model.
\emph{Science} \textbf{360} (2018) 191--195.
\par\noindent\textbf{Relevance.}
The cesium recoil determination of $\alpha$; the second pole of the
Rb/Cs discrepancy noted in \S\ref{sec:coupling} and F4. First cited in \S\ref{sec:coupling}.

\bibitem[Particle Data Group(2024)]{PDG2024}
\textbf{Particle Data Group.}
Review of Particle Physics.
\emph{Progress of Theoretical and Experimental Physics} \textbf{2024}
(2024) 083C01.
\par\noindent\textbf{Relevance.}
The standard compilation for lepton properties and compositeness
listings consumed in Part~\ref{part:VIII} and
Appendix~\ref{app:anchors}. First cited in \S\ref{sec:ladder}.

\bibitem[Perl et al.(1975)]{Perl1975}
\textbf{Perl, M.~L., et al.}
Evidence for anomalous lepton production in $e^{+}e^{-}$
annihilation.
\emph{Physical Review Letters} \textbf{35} (1975) 1489--1492.
\par\noindent\textbf{Relevance.}
The tau: the third copy of the electron, found at SPEAR in
anomalous $e\mu$ events. It completed the pattern Q3 asks about ---
and, by being the \emph{last} such discovery despite five decades of
energy frontier since, it wrote the other half of the question:
why does the ladder stop? \S\ref{sec:ladder} houses it at depth 0;
Appendix~\ref{app:Q3} counts why nothing sits above it. First cited in \S\ref{sec:ladder}.

\bibitem[Pati \& Salam(1974)]{PatiSalam1974}
\textbf{Pati, J.~C. \& Salam, A.}
Lepton number as the fourth ``color''.
\emph{Physical Review D} \textbf{10} (1974) 275--289.
\par\noindent\textbf{Relevance.}
The opening of the compositeness era: quarks and leptons unified, with
substructure (``preons'') as the suggested mechanism beneath the
pattern. The tradition it launched --- through
\citet{Harari1979,Shupe1979} --- is the structural bet against which
\S\ref{sec:prior} and Table~\ref{tab:contrast} score this paper's
opposite wager: pattern from connection data rather than from
constituents. First cited in \S\ref{sec:prior}.

\bibitem[Pauli(1925)]{Pauli1925}
\textbf{Pauli, W.}
\"Uber den Zusammenhang des Abschlusses der Elektronengruppen im Atom
mit der Komplexstruktur der Spektren.
\emph{Zeitschrift f\"ur Physik} \textbf{31} (1925) 765--783.
\par\noindent\textbf{Relevance.}
The exclusion principle --- announced before spin itself, as a
``classically non-describable two-valuedness.'' It is the bridge from
Q1 to chemistry: identity plus exclusion equals the periodic table,
which is why \S\ref{sec:conclusions-plain} can say that the sameness
of the electron is the reliability of the world. The two-valuedness
Pauli could not describe classically is the quaternionic double cover
of \S\ref{ssec:value-spin}. First cited in \S\ref{sec:five-questions}.

\bibitem[Pauli(1940)]{Pauli1940}
\textbf{Pauli, W.}
The connection between spin and statistics.
\emph{Physical Review} \textbf{58} (1940) 716--722.
\par\noindent\textbf{Relevance.}
The spin-statistics theorem: half-integer spin forces antisymmetry,
integer spin symmetry, from relativity and positivity alone. Cited in
\S\ref{ssec:qft-identity} as the deepest layer of the standard
identity story --- not only are field quanta identical, the
\emph{way} they are identical is forced by their spin. The present
framework inherits the theorem on the boundary and supplies the layer
beneath it: why spin-$\tfrac12$ was selected at all. First cited in \S\ref{ssec:qft-identity}.

\bibitem[Poincar\'e(1906)]{Poincare1906}
\textbf{Poincar\'e, H.}
Sur la dynamique de l'\'electron.
\emph{Rendiconti del Circolo Matematico di Palermo} \textbf{21} (1906)
129--176.
\par\noindent\textbf{Relevance.}
Source of the Poincar\'e stresses --- the non-electromagnetic glue an
extended classical electron required --- declared ``unemployed'' by the
basin-level reading of the mass in \S\ref{sec:mass-spin}. First cited in \S\ref{sec:point-history}.

\bibitem[Randall \& Sundrum(1999)]{RandallSundrum1999}
\textbf{Randall, L. \& Sundrum, R.}
A large mass hierarchy from a small extra dimension.
\emph{Physical Review Letters} \textbf{83} (1999) 3370--3373.
\par\noindent\textbf{Relevance.}
The warped-throat geometry whose diagram the \GG{} bulk recapitulates
with a different reading of the radial axis (RG scale, not space);
the lineage credited in \S\ref{ssec:same-machinery} and Fig.~1's
visual vocabulary. First cited in \S\ref{ssec:same-machinery}.

\bibitem[Schr\"odinger(1926)]{Schrodinger1926}
\textbf{Schr\"odinger, E.}
Quantisierung als Eigenwertproblem (Erste Mitteilung).
\emph{Annalen der Physik} \textbf{79} (1926) 361--376.
\par\noindent\textbf{Relevance.}
The wave equation of the boundary calculus, written down in 1926
without a derivation from anything deeper. Cited in
\S\ref{sec:century-openness} for the centenary that frames this
paper: one hundred years later the companion papers derive the
boundary calculus --- equation and rule --- as theorems of the
\OGGEP{} reduction. First cited in \S\ref{sec:century-openness}.

\bibitem[Schwinger(1948)]{Schwinger1948}
\textbf{Schwinger, J.}
On quantum-electrodynamics and the magnetic moment of the electron.
\emph{Physical Review} \textbf{73} (1948) 416--417.
\par\noindent\textbf{Relevance.}
The first radiative correction $a_e = \alpha/2\pi$: the founding result
of the QED dressing whose distinction from \emph{structure} carries the
form-factor argument of Appendix~\ref{app:formfactor}, and part of the
sign-rule-era credit stated in \S\ref{sec:force}. First cited in Appendix~\ref{app:formfactor}.

\bibitem[Shupe(1979)]{Shupe1979}
\textbf{Shupe, M.~A.}
A composite model of leptons and quarks.
\emph{Physics Letters B} \textbf{86} (1979) 87--92.
\par\noindent\textbf{Relevance.}
The independent twin of \citet{Harari1979}: the same two-preon
economy discovered simultaneously, which is itself instructive ---
the rishon counting was so natural that two people found it at once.
Cited in \S\ref{sec:prior} as part of compositeness at its best,
before the mass paradox and the null searches closed the road that
this paper's non-spatial relocation reopens at no experimental cost. First cited in \S\ref{sec:prior}.

\bibitem[Sommerfeld(1916)]{Sommerfeld1916}
\textbf{Sommerfeld, A.}
Zur Quantentheorie der Spektrallinien.
\emph{Annalen der Physik} \textbf{51} (1916) 1--94.
\par\noindent\textbf{Relevance.}
The birth of $\alpha$: introduced as the relativistic fine-structure
parameter of hydrogen, it became the dimensionless riddle of the
century --- Feynman's ``magic number.'' Cited in
\S\ref{sec:coupling}: the constant Sommerfeld introduced as an input
is, in Appendix~\ref{app:Q1-alpha}, the dyadic attractor coordinate
$2^J + N^2$, and the century-long question ``why 137?'' receives an
arithmetic answer with a declared status. First cited in \S\ref{sec:coupling}.

\bibitem[Stern \& Gerlach(1922)]{SternGerlach1922}
\textbf{Stern, O. \& Gerlach, W.}
Der experimentelle Nachweis der Richtungsquantelung im Magnetfeld.
\emph{Zeitschrift f\"ur Physik} \textbf{9} (1922) 349--352.
\par\noindent\textbf{Relevance.}
The two spots: space quantization measured three years before spin
was proposed --- the experiment that showed the electron's angular
degree of freedom is binary. In this paper's terms the two spots are
the boundary readout of the quaternionic doublet
(\S\ref{ssec:value-spin}); the student should hold the 1922
photograph next to Eq.~\eqref{eq:appC-spin15} and note that the
number two traveled ninety years to find its algebra. First cited in \S\ref{ssec:value-spin}.

\bibitem[Stoney(1894)]{Stoney1894}
\textbf{Stoney, G.~J.}
Of the ``electron,'' or atom of electricity.
\emph{Philosophical Magazine}, Series 5, \textbf{38} (1894) 418--420.
\par\noindent\textbf{Relevance.}
The naming of the electron --- proposed as the natural unit of
electricity from Faraday's electrolysis, before any particle had been
seen. Cited in \S\ref{sec:five-questions}: the concept preceded the
discovery by a generation, and the unit Stoney abstracted from
chemistry is the same quantized $e$ that
\S\ref{ssec:value-charge} derives from holonomy --- a hundred and
thirty years from electrolysis jars to winding integers. First cited in \S\ref{sec:five-questions}.

\bibitem[Susskind(2003)]{Susskind2003}
\textbf{Susskind, L.}
The anthropic landscape of string theory.
arXiv:hep-th/0302219 (2003).
\par\noindent\textbf{Relevance.}
The canonical statement of the landscape position --- the values of
the constants as environmental selections --- against which
\S\ref{sec:prior} and \S\ref{ssec:moduli-landscape} set the
anti-landscape bet of the integer ledger. First cited in \S\ref{sec:prior}.

\bibitem['t Hooft(1980)]{tHooft1980}
\textbf{'t Hooft, G.}
Naturalness, chiral symmetry, and spontaneous chiral symmetry
breaking.
In \emph{Recent Developments in Gauge Theories} (Carg\`ese 1979),
NATO Advanced Study Institutes Series B59, Plenum Press, New York
(1980) 135--157.
\par\noindent\textbf{Relevance.}
Anomaly matching and naturalness: the consistency conditions any
composite model of light fermions must satisfy, and the formal
statement of why a bound electron far lighter than its binding scale
is unnatural --- the mass paradox cited in \S\ref{sec:prior}. This
paper's escape is structural: with the electron's ``structure''
relocated to non-spatial connection data, there is no binding scale
to be unnatural about. First cited in \S\ref{sec:prior}.

\bibitem[Thomson(1897)]{Thomson1897}
\textbf{Thomson, J.~J.}
Cathode rays.
\emph{Philosophical Magazine}, Series 5, \textbf{44} (1897) 293--316.
\par\noindent\textbf{Relevance.}
The identification of the electron: cathode rays deflected as a
single charged corpuscle with a universal $e/m$, measured the same in
every gas and from every cathode --- the first experimental hint of
Q1, visible in the discovery paper itself. The century this paper's
title counts begins here, and so does the irony its preface
addresses: the particle was identified \emph{by} the very sameness
that then went unexplained for a hundred and twenty-nine years. First cited in \S\ref{sec:five-questions}.

\bibitem[Tomonaga(1946)]{Tomonaga1946}
\textbf{Tomonaga, S.}
On a relativistically invariant formulation of the quantum theory of
wave fields.
\emph{Progress of Theoretical Physics} \textbf{1} (1946) 27--42.
\par\noindent\textbf{Relevance.}
The first covariant formulation of renormalized QED, developed in
wartime isolation. With \citet{Feynman1949} and \citet{Dyson1949} it
forms the trio cited at \S\ref{sec:point-history}'s hinge: the
machinery that made the point electron calculable. The student should
know all three names; the present paper's claim is not that their
construction was wrong but that it answered ``how to live with the
point'' while ``why the point'' waited. First cited in \S\ref{sec:point-history}.

\bibitem[Uhlenbeck \& Goudsmit(1925)]{UhlenbeckGoudsmit1925}
\textbf{Uhlenbeck, G.~E. \& Goudsmit, S.}
Ersetzung der Hypothese vom unmechanischen Zwang durch eine Forderung
bez\"uglich des inneren Verhaltens jedes einzelnen Elektrons.
\emph{Die Naturwissenschaften} \textbf{13} (1925) 953--954.
\par\noindent\textbf{Relevance.}
The proposal of electron spin, whose superluminal-surface paradox for
any spatially spinning model is dissolved by the double-cover reading
of \S\ref{sec:mass-spin}. First cited in \S\ref{sec:point-history}.

\bibitem[Van Dyck et al.(1987)]{VanDyck1987}
\textbf{Van Dyck, R.~S., Jr., Schwinberg, P.~B. \& Dehmelt, H.~G.}
New high-precision comparison of electron and positron $g$ factors.
\emph{Physical Review Letters} \textbf{59} (1987) 26--29.
\par\noindent\textbf{Relevance.}
The Penning-trap comparison $(g_{e^+}-g_{e^-})/g =
(-0.5\pm2.1)\times10^{-12}$ --- among the sharpest null results in
physics, quoted in \S\ref{sec:q6-status}. In the readout picture the
null is not a symmetry holding between two objects but the absence of
a second object; a confirmed asymmetry would kill the reading of
Part~\ref{part:positron} before it killed CPT. First cited in \S\ref{sec:q6-status}.

\bibitem[Weinberg(1995)]{Weinberg1995}
\textbf{Weinberg, S.}
\emph{The Quantum Theory of Fields, Vol.~1: Foundations.}
Cambridge University Press, Cambridge (1995).
\par\noindent\textbf{Relevance.}
The canonical modern treatment of particle identity as field-quantum
indistinguishability and of Wigner's representation classification ---
the standard-physics position on Q1, credited at full strength in
\S\ref{ssec:qft-identity} and \S\ref{sec:prior}. First cited in \S\ref{sec:q6-standard}.

\bibitem[Weyl(1918)]{Weyl1918}
\textbf{Weyl, H.}
Gravitation und Elektrizit\"at.
\emph{Sitzungsberichte der K\"oniglich Preu{\ss}ischen Akademie der
Wissenschaften (Berlin)} (1918) 465--480.
\par\noindent\textbf{Relevance.}
The first attempt to geometrize electromagnetism --- on the
\emph{scale} direction, as a local rescaling invariance --- felled by
Einstein's objection that histories would imprint on atomic spectra.
Cited in \S\ref{sec:fourcells} as the failure the framework
diagnoses rather than merely survives: scale \emph{is} geometric, but
it is gravity's dimension; electromagnetism's is the phase, where
Weyl himself moved it in 1929. First cited in \S\ref{sec:fourcells}.

\bibitem[Weyl(1929)]{Weyl1929}
\textbf{Weyl, H.}
Elektron und Gravitation I.
\emph{Zeitschrift f\"ur Physik} \textbf{56} (1929) 330--352.
\par\noindent\textbf{Relevance.}
The gauge principle in its modern form: local phase invariance
demands the electromagnetic connection --- conceived, fittingly, in a
paper joining the electron to gravitation. Step B1 of Chain (B)
(Appendix~\ref{app:Q5-chainB}) is Weyl's argument verbatim; AX-2's
composite connection is Weyl's program completed in the direction he
pointed: gauge and geometry as one object, with the electron riding
both. First cited in \S\ref{sec:fourcells}.

\bibitem[Wigner(1939)]{Wigner1939}
\textbf{Wigner, E.~P.}
On unitary representations of the inhomogeneous Lorentz group.
\emph{Annals of Mathematics} \textbf{40} (1939) 149--204.
\par\noindent\textbf{Relevance.}
The classification within which spin-$\tfrac12$ is, for the Standard
Model, an unexplained choice --- the precise sense in which Q1's
``why those values'' includes the representation, answered geometrically
in \S\ref{ssec:value-spin}. First cited in \S\ref{ssec:qft-identity}.

\bibitem[Witten(1982)]{Witten1982}
\textbf{Witten, E.}
Supersymmetry and Morse theory.
\emph{Journal of Differential Geometry} \textbf{17} (1982) 661--692.
\par\noindent\textbf{Relevance.}
The classical source for instanton counting between Morse critical
points --- the mathematical machinery behind the Bogomolnyi gate
actions $S = \pi k$ quoted in \figref{fig:grip-cascade-cp2} and
Eq.~\eqref{eq:lepton-chain}, as deployed upstream by \ASix{} and
\ANine{}. First cited in \S\ref{sec:ladder}.

\bibitem[Yang \& Mills(1954)]{YangMills1954}
\textbf{Yang, C.~N. \& Mills, R.~L.}
Conservation of isotopic spin and isotopic gauge invariance.
\emph{Physical Review} \textbf{96} (1954) 191--195.
\par\noindent\textbf{Relevance.}
The non-Abelian gauge field: Weyl's principle generalized to internal
symmetry spaces, the template of the entire Standard-Model gauge
sector. Cited alongside \citet{Weyl1929} in
Appendix~\ref{app:Q5-chainB}: the bulk gauge factor whose unbroken
commutant is this paper's photon is a Yang--Mills object, and the
``two curvatures'' sentence of Eq.~\eqref{eq:unified-eom} is the
Yang--Mills curvature standing beside Riemann's. First cited in \S\ref{app:Q5}.

\bibitem[Zeeman(1897)]{Zeeman1897}
\textbf{Zeeman, P.}
On the influence of magnetism on the nature of the light emitted by
a substance.
\emph{Philosophical Magazine}, Series 5, \textbf{43} (1897) 226--239.
\par\noindent\textbf{Relevance.}
The magnetic splitting of spectral lines --- the electron weighed
inside the atom in the same year Thomson weighed it in the beam, with
Lorentz's analysis extracting the same $e/m$. Cited in
\S\ref{sec:five-questions} as the second leg of the 1897 discovery:
from its first year the electron was \emph{one} particle seen two
ways, a premonition of Q1 that this paper finally converts into a
theorem. First cited in \S\ref{sec:five-questions}.

\end{thebibliography}

\end{document}
