Invariance-Weighted Compression under Constraint A Foundational Account of Persistent Order and Epistemic Admissibility

This paper establishes the foundational criterion for a four-part research program spanning physics, biology, governance, and epistemology. It advances the thesis that order is not fundamental structure but conditional persistence under constraint, and derives an admissibility condition for descriptive frames: frames that maximize invariance coverage under compression, subject to constraint satisfaction. The thesis is demonstrated through four physics exemplars — Rayleigh–Bénard convection, BCS superconductivity, environment-induced decoherence, and Shannon channel capacity — each showing that persistent order arises where constraint-compatible invariants are retained across anticipated transformation classes. The epistemological corollary is regime-bounded: reality supplies invariants, cognition supplies coarse-graining, and invariance-weighted compression specifies the admissibility condition linking them. The paper grounds three downstream contributions — SHRF (biological implementation of invariance retention through morphological geometry), GASD (governance and authority structure drift as invariance-tracking failure under power asymmetry), and the Trident (minimal decomposition of epistemic coupling as the cognitive analog of physical persistence under constraint). The identity claim between physical and epistemic selection criteria is methodological rather than ontological: structural equivalence of selection criteria, not reduction of epistemic systems to physical systems. Keywords invariance, frame selection, persistent order, constraint satisfaction, epistemic admissibility, compression, coarse-graining, thermodynamics, symmetry breaking, decoherence, Shannon capacity, Rayleigh–Bénard convection, BCS superconductivity, epistemology of science, regime-bounded, transformation classes, foundational framework, morphological computation, governance drift, epistemic coupling