Four Observations, One Exponent

Abstract

GG-Theory derives the laws of open systems from a fixed six-dimensional geometry with no adjustable parameter — a program whose record in particle physics and cosmology is stated with its falsifiers named in advance. This paper extends that program to the phenomena that sit closest to life. Its claim, inherited from the Qi-4 pillars of the boundary law and named Qi-CON: any persisting open system, observed through the finite window every real observation has, carries an effective dynamics with one geometric exponent and no intrinsic scale — and that single exponent forces four signatures at once: power-law scaling, heavy-tailed Lévy steps, fractal geometry, and 1/f spectra bounded by two knees at derivable places.

The claim is put on trial three ways. First, the record: 245 measurements compiled from four literatures that rarely read one another — allometry, movement ecology, fractal geometry, and 1/f noise — every row graded and verified against its primary source, skeptics printed at full size. Second, the arithmetic: on every system where two or more signatures were measured independently, the exponents must satisfy parameter-free lock relations; the cross-consistency audit runs that test across the whole record — seventeen pairs, one identity line, no free parameters. Third, the failure theory: four named modes in which the signatures must degrade, three already exhibited by the record itself.

The verdict is stated at its earned strength: the relations fail nowhere, hold exactly where the physics is exactly understood, hold loosely at honest error bars everywhere else — interesting, and not proof — and the paper closes with the measurements that could kill it, and with why scale-free dynamics is what the geometry of openness offers a world that must explore, adapt, and persist.