The Saturation Theorem: Axiomatic Constraints on Quantum Gravity from Cosmological Relaxation

DRAFT version. Subject to revisions. We formulate four minimal axioms — finite geometric capacity (A), cooperative reinforcement with antisymmetric extension (B/B'), monotone cosmic control (C), and renormalization-group composition with boundary regularity (D) — that any quantum theory of gravity must satisfy if its macroscopic limit reproduces general relativity with a bounded cosmological relaxation mechanism. The corrected Saturation Theorem is two-step. Axioms A--D determine a one-dimensional Abel-coordinate / boundary-collar structure for cosmological saturation dynamics. The hyperbolic tangent profile follows only after adding the projective boundary-quotient normalization D', namely that the quotient…