Formal Foundations of Adaptive Coherence: A Recursive Metric of Reality

This paper formalizes a universal, coherence-first law of reality designed to supersede legacy invariants, energy, entropy, and probability, across physics, cognition, computation, and governance. It defines a single, recursively computable metric, grounded in system self-relevance, which governs the persistence of structure through adaptive feedback. From this invariant, I derive coherence-weighted entropy, stochastic Recursive Choice Theory, reformulate quantum probability mapping consistent with the Born rule, and an emergent theory of time as a function of dissipative coherence gradients. Logical reasoning is restructured through Recursive Coherence Logic, in which truth evolves via coherence-weighted recursion rather than axiomatic deduction. The framework remains bounded, scale-consistent, and noise-resilient, satisfying formal criteria for self-stabilization under adversarial or stochastic conditions. All results are expressed in generalizable mathematical forms, compatible with empirical simulations but not contingent on them. This work serves as the mathematical backbone for a unified class of coherence-centered theories, intended to replace static formal systems with dynamically recursive, stability-driven alternatives.