Anomaly Freedom of BI-6

Abstract

For half a century a quantum anomaly has been described as a flaw that shows up only when a classical symmetry is run through the quantum machine. This paper makes the opposite case: the anomaly is, at bottom, a classical and geometric fact about a higher-dimensional space, and the quantum calculation merely detects it. The lineage is old — Bianchi wrote the geometric ancestor in 1902, and Green and Schwarz, in 1984, modified it for higher dimensions — and it is geometric at every step. We show that the six-dimensional bulk of GG-Theory, built from the four axioms and seven postulates of its constitutional charter, passes the anomaly test completely. The proof has two halves: a local part that closes the usual one-loop consistency in a single line, and a global part that closes it under every large gauge transformation — with no restriction on the topology of the four-dimensional base, because the relevant spin bordism groups of the gauge group's classifying space are shown to vanish. We also show that the five small integers (1,3,5;7,35) that fix every normalization in the theory are locked rather than fitted: the unified block size is forced by single-tensor consistency alone, the color index by the dual-lock closure together with the block embedding, and the remaining two by the same closure identity. No step of the cascade consumes a measured quantity. Read alongside the companion papers, this places BI-6 on the same foundational layer as the 1984 Green–Schwarz mechanism it generalizes — a program, begun with Riemann and Bianchi, of the geometrization of gauge in higher dimensions rather than the quantization of geometry. What makes a theory meaningful is not the cleverness of its calculations but the discipline of its consistency tests, and this is the sharpest one we know how to write down.