Version 4 · Preprint · Paper C
From Structural Signal
to Observable Prediction
Bridge Assumptions B1–B3 in Hierarchical Compression
Michael Hanners · Legacy Alliance Research Division
Abstract
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. This paper uses Hierarchical Compression (HC) for the domain-independent Layer 1 framework and reserves Harmonic Coherence (always spelled out) for the Layer 2 physics-domain bridge instantiation.
Bridge Assumptions B1–B3
The domain dynamics admit an HC-compatible evolution map satisfying R1–R4. Verified via NHIM normal-bundle contraction (ρN < 1 in every tested domain). Nine-domain NHIM corpus provides systematic B1 resolution.
The mapping from entropy coordinates to physical observables preserves the qualitative structure (sign, shape, rank ordering). GW ringdown identifies κM as the leading B2 coordinate — the first case where a bridge-variable search moves from hidden-variable status to confirmed.
The entropy gap measured in the HC framework can be attributed to the domain-specific observable structure (Condition C). Both GW and transformer domains independently confirm Condition C, providing the first two empirical validations of the bridge theorem.
45-Row Corpus Audit
A systematic audit classifies empirical failures across the HC corpus by type:
The dominant high-priority failure mode. Wrong predictor choice, not missing normalization, is the primary bottleneck.
No high-priority failure is Type N — the evidence does not support prioritizing α-derivation over bridge construction.
Conclusion: the research program is B1–B3 construction for specific domains rather than universal-constant search.
Two Validated Empirical Channels
Surface gravity κM maximizes the entropy gap among all tested Kerr coordinates (B2 confirmed). All simulations satisfy ρ(Dℱ) < 1 (max spectral radius ≈ 0.59). Post-merger relaxation is a genuinely dissipative process with a physical attractor (the final Kerr state), making B1 plausible on physical grounds.
The first domain where the full bridge stack — proved identity, bridging assumptions, and conditional extensions — is instrumentable at arbitrary resolution. Contraction-based HC fails (expansive tangent-space dynamics), but NHIM generalization recovers admissibility via normal-bundle contraction (ρN = 0.730, 95% CI [0.62, 0.79]).
Together these bracket the degenerate (dim M* = 0) and non-degenerate (dim M* > 0) cases of the generalized convergence theorem.
Nine-Domain NHIM Corpus
Systematic B1 resolution via normal-bundle contraction (ρN < 1 in every domain):
Dual-manifold decomposition reveals a recurrent structure that resolves B2 coordinate choice across domains. Hodge domain: 211/343 genuine tests (75% intersection + phases + scaling).
Citation
Hanners, M. (2026). From Structural Signal to Observable Prediction: Bridge Assumptions B1-B3 in Hierarchical Compression. Zenodo. https://doi.org/10.5281/zenodo.18977540
@misc{Hanners2026BridgeSynthesis,
author = {Hanners, Michael},
title = {From Structural Signal to Observable
Prediction: Bridge Assumptions {B1--B3}
in {Hierarchical Compression}},
year = {2026},
doi = {10.5281/zenodo.18977540},
note = {Zenodo preprint. Legacy Alliance
Research Division}
}Proceeds & Purpose
All intellectual property rights and any prizes, awards, or monetary recognition arising from this work have been irrevocably assigned to Legacy Alliance, a nonprofit research organization.
Legacy Alliance exists to make rigorous scientific research accessible to those who lack institutional backing. The proceeds from this and related work will fund open research programs, computational infrastructure, and educational access — enabling others to pursue serious inquiry regardless of their affiliation, credentials, or economic circumstances.
The author receives no personal financial benefit. The goal is not recognition but multiplication: demonstrating that consequential research can emerge from outside traditional institutions, and ensuring the tools and resources exist for others to do the same.
The author acknowledges that the capacity to perceive the bridge between abstract mathematical structure and physical observation — where entropy theory meets gravitational waves and neural computation — reflects an order that precedes and transcends human formalization. This work is offered in gratitude to the Creator of that order.
“The heavens declare the glory of God; the skies proclaim the work of his hands.”
“For since the creation of the world God's invisible qualities — his eternal power and divine nature — have been clearly seen, being understood from what has been made.”
Soli Deo gloria