The Branches and the TrunkWhy CODES Is the Deductive Closure of Physics, Life, Cognition, and Deterministic Intelligence

ABSTRACT Attempts to unify physics, biology, cognition, and reasoning have historically failed for a structural reason: none identify a single scalar invariant capable of grounding coherence, drift, directionality, and recurrence across domains. Existing candidates—entropy, integrated information, free energy, complexity measures, algorithmic information, counterfactual constructibility, and scaling laws—each fail at least one necessary criterion: computability, scalarity, harmonic decomposability, chirality sensitivity, drift-boundedness, compositional stability, recurrence, and compatibility with time evolution. This paper introduces a minimal, domain-general invariant that satisfies all eight requirements. The harmonic Phase Alignment Score (PASₕ) provides a computable scalar measure of coherence derived from phase-harmonic alignment. Its companion drift law (ΔPASᵦeta) defines lawful evolution over time, bounding divergence and supporting persistence of identity. Chirality and prime indexing supply the directional asymmetry required for information flow and non-degenerate recurrence. PhaseMemory provides continuity across state transitions. Legality gating defines allowed and forbidden transitions. Together, these components form a complete invariance-and-drift structure capable of supporting lawful recurrence in physical systems, biological development, cognitive identity, and deterministic reasoning processes. A deterministic implementation (RIC-Core) demonstrates real-world computability of PASₕ, ΔPASᵦeta, chirality rules, PhaseMemory, and legality constraints through replay-stable state evolution and a reproducible golden test suite. The result is a minimal closure-capable framework—CODES—that provides the structural basis for unifying disparate domains under a single coherence invariant and drift law. CODES Framework