From Structural Signal to Observable Prediction: Bridge Assumptions B1-B3 in Hierarchical Compression

This paper formalizes the bridge assumptions B1–B3 that connect the proved Hierarchical Compression (HC) entropy identity to domain-specific observables, conducts a 45-row cross-domain audit of the existing corpus, and identifies bridge incompleteness as the dominant failure mode. Two empirical channels are validated: gravitational-wave ringdown (surface gravity κM confirmed as B2 bridge coordinate across 382 NR simulations) and transformer inference (NHIM admissibility confirmed with normal-bundle contraction ρN=0.730). Together these bracket the degenerate and non-degenerate cases of the generalized convergence theorem. 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.