Bridge Note: From Hanners Theorem to Harmonic Coherence via Nested Temporal Layering

Formalizes a dependency-safe path from the proved Hanners Theorem to broader HC modeling claims within the Hierarchical Compression framework. Structures claims as proved (Layer 1), assumed (Layer 2), and conditional (Layer 3), with a claim-status ledger and quantitative falsifiability tests. Layer 1 states the entropy identity and identifies the exact gain term I(X;Ψ). Layer 2 introduces explicit bridging assumptions for nested temporal layering. The contribution is methodological: theorem-stack structuring and quantitative falsifiability rather than a new entropy identity. Terminology. The foundational publications developed the framework under the name Harmonic Coherence, reflecting its origin in physics domains where phase-locked resonance and coherent-structure formation are the operative bridge mechanisms. As the framework extended to number theory, complexity theory, and algebraic geometry—domains with no physical harmonic content—the name became a source of friction. This paper uses Hierarchical Compression (HC) for the domain-independent Layer 1 framework and reserves Harmonic Coherence (always spelled out, never abbreviated) for the Layer 2 physics-domain bridge instantiation. The abbreviation HC refers exclusively to the framework. Companion documents: CER Foundation | Hanners Theorem | Fixed-Point Theorem | Bridge Synthesis