Coupling Geometry: A General Theory of Systems with Endogenous Assessment

This paper presents a five-axiom foundation for Coupling Geometry as a candidate framework for systems with endogenous assessment (G1 graph substrate, G2 history-dependent architecture, G3 asymmetric coupling cost, G4 endogenous assessment, G5 differential coupling benefit). From specified subsets of these axioms, the paper derives three core theorems — the Involuntary Redistribution Theorem (G1, G5), Hysteresis (G3), and Identity Constraint (G2, G3) — together with three supporting results (a fold-bifurcation existence claim, threshold bounds, and a power-law assessment-gap form), three supporting lemmas, and a role-separation map showing which axiom subset is responsible for which feature. Five necessity propositions establish that no axiom in G1–G5 is removable without losing at least one structural feature, supported by numerical countermodel evidence from an axiom-independence simulation included in this deposit (CG_Axiom_Independence_Simulations.docx and the accompanying Python source files). The general theory is mapped onto six civilisational axioms (A1–A6) familiar from prior cultural-materialist and historical-materialist work, and operationalised through five coupling indicators (I1–I5) for empirical scoring. The framework’s two universality claims — substrate-invariant exponents (strong) and structural-pattern recurrence (weak) — are stated explicitly, and the paper commits to the weak version as the programme’s current evidential position. Empirical evidence for the framework, including the civilisational case portfolio, simulation benchmarks, and cross-domain pilots, is presented in a companion paper currently under submission to Cliodynamics. Manuscript under review at Cliodynamics.