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

The Hierarchical Compression (HC) framework produces reliable structural signals correct sign, qualitative shape, rank ordering yet persistently fails at fully normalized quantitative prediction. This paper argues the gap is best understood through a layered architecture separating the abstract formal core from three bridge assumptions: B1 (evolution-map admissibility), B2 (structure preservation under the observable map), and B3 (entropy attribution).

A 45-row corpus audit classifies empirical failures by type and shows that the dominant high-priority mode is wrong predictor choice (Type P), not missing normalization (Type N). The main bottleneck is bridge construction rather than a missing universal constant.

Three empirical anchors:

• Transformers (boundary case): six contraction-based tests uniformly negative; NHIM generalization resolves failure via normal-bundle contraction. Condition C confirmed.
• GW ringdown (positive benchmark): kappa_M confirmed as leading B2 coordinate on 382 NR simulations. Condition C confirmed.
• Nine-domain NHIM corpus: systematic B1 resolution spanning five orders of magnitude. Dual-manifold decomposition resolves B2 coordinate choice.

Version 2 revisions: Restructured abstract; added PRISMA reference (Moher et al.); expanded bibliography to 25 entries; standardized American English; replaced internal test labels; removed temporal framing; added falsifiability criteria; added Appendix A; added audit sensitivity analysis; softened overclaims. 39 pages, zero undefined references.

Companion documents:

• Paper A: Transformer Boundary Case
• Paper B: GW Kerr Ringdown
• Fixed-Point Theorem
• CER Theorem
• Reconciliation
• Bridge Note