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

This bridge note formalizes a dependency-safe path from a proved information-theoretic result (the Hanners Theorem) to broader Harmonic Coherence modeling claims. Its purpose is scope control: to separate what is proved from what is assumed, conditional, or programmatic. Layer 1 states the proved entropy identity for context-conditioned mixtures. Layer 2 defines explicit bridging assumptions (B1–B3) for mapping nested temporal layering into context variables. Layer 3 derives conditional extension statements under those assumptions, including entropy-gain attribution and model-comparison principles. Version 2 updates (March 2026): Added gravitational-wave ringdown instantiation remark: B2 confirmed via κM coordinate on 382 NR simulations, entropy gap δ = 1.79 bits (Remark: rem:gw-bridge). Updated Condition C bridge remark with two independent empirical confirmations: GW ringdown (δ = 1.79 bits) and transformer language models (δ = 3.28 bits). Expanded transformer instantiation remark with NHIM resolution of B1 boundary case (ρN = 0.730, 95% CI [0.62, 0.79]). Added threshold justification for falsifiability tests (ARI ≥ 0.90 from Hubert–Arabie 1985; TOST equivalence alternative). Enriched SI notation remark with sign-flip motivation for downstream Lyapunov analysis. Fixed citation keys and added 12 bibliography entries for companion papers and foundational references. Companion documents: CER Theorem: 10.5281/zenodo.18668434 Reconciliation Framework: 10.5281/zenodo.18671909 HC Fixed-Point Theorem: 10.5281/zenodo.18978490 Paper A (Transformer Distillation): 10.5281/zenodo.18974716 Paper B (Kerr Ringdown): 10.5281/zenodo.18976467 Paper C (Bridge Synthesis): 10.5281/zenodo.18977541