HLV-R-MECH-001: Locked Confirmatory Results for Triangle-Matched Mechanism Testing of the Degree-Preserving Rewire Spectral Residual v0.1.0

Abstract

This record contains the locked confirmatory scientific results of HLV-R-MECH-001, a prospectively frozen mechanism test of the previously observed degree-preserving rewire spectral residual within the Helix–Light–Vortex Framework (HLV), positioned as a Cut-and-Project and Incidence-Spectral Research Programme. The controlling scientific protocol is: Krūger, M. (2026). HLV-R-MECH-001: Prospective Triangle-Matched Mechanism Test of the Surviving Degree-Preserving Rewire Spectral Residual — Pre-Execution Protocol Freeze v0.1.0. Zenodo. DOI: 10.5281/zenodo.22166283 The authoritative corrected implementation freeze is: Krūger, M. (2026). HLV-R-MECH-001: Deterministic One-Click Engine for Triangle-Matched Rewire Mechanism Testing — Corrected Implementation Freeze v0.1.2 [Computer software]. Zenodo. DOI: 10.5281/zenodo.22170307 The v0.1.2 implementation changed only the numerical-runtime bootstrap. The scientific engine remained byte-identical to the prospectively frozen implementation. Frozen scientific engine SHA-256: 317df650991120f686768ffc07d12f044f58e38ce8f2c47c083901bf1d7a8a14 The successful locked scientific execution returned the machine verdict: RMECH001_PASS_TRIANGLE_MATCH_COLLAPSE_PATTERN The experiment contained two fresh prospectively frozen control families. R_DEG: fresh simple connected degree-preserving rewires matched to the target in labelled degree sequence and perturbation depth, with global triangle count unconstrained. R_TRI: fresh simple connected rewires preserving both the exact labelled target degree sequence and the exact global target triangle count T = 6960. Each family contained 31 accepted controls. The frozen family outcomes were: R_DEG: QSPEC PASS RRESP PASS Family PASS R_TRI: QSPEC FAIL RRESP FAIL Family FAIL For the fresh R_DEG family, the previously observed degree-preserving rewire spectral residual reproduced strongly. QSPEC: D_target = 0.008715193283827952 max D_LOO = 0.005181032910966849 median D_LOO = 0.0015059971709314455 robust margin = 5.786991803203511 2 of 3 frozen spectral bands pass. RRESP: D_target = 0.008334776747240381 max D_LOO = 0.0019187166287396942 median D_LOO = 0.0010793384522247884 robust margin = 7.722116014731345 2 of 3 frozen spectral bands pass. Thus the fresh degree-only baseline independently reproduces the earlier R-family spectral separation under the frozen mechanism-test design. For the exact-triangle-matched R_TRI family: QSPEC: D_target = 0.002191501382099135 max D_LOO = 0.0017606104448781759 robust margin = 1.7780654702146463 1 of 3 frozen spectral bands passes. RRESP: D_target = 0.0025511096413481766 max D_LOO = 0.0021234752495009907 robust margin = 2.2593200944928404 1 of 3 frozen spectral bands passes. Both R_TRI signatures therefore fail the complete frozen signature gate because the prospectively required minimum of 2 of 3 passing spectral bands is not reached. The rewiring-depth matching gate passed. Median edge-replacement fraction: R_DEG = 0.42768942937324606 R_TRI = 0.42076707202993446 absolute difference = 0.0069223573433115915 which is below the frozen maximum allowed difference of 0.02. The result therefore cannot be attributed to a substantially weaker perturbation depth in the triangle-matched family. The numerical environment and hard numerical audits also passed. The successful locked execution used: NumPy 2.3.5 SciPy 1.17.0 and completed the prospectively frozen target and selected control eigensolver/identity checks. The central scientific result is: exact preservation of the target's global triangle count collapses the previously robust two-signature, multi-band degree-preserving rewire spectral separation under the frozen HLV-R-MECH-001 gate. This provides prospective evidence that triangle/face organization is a major mechanism contributing to the previously observed R-family spectral residual. The result has a direct analytic basis. For a simple graph Laplacian L = D - A, Tr(L) = sum_i d_i, Tr(L^2) = sum_i d_i^2 + sum_i d_i, and Tr(L^3) = sum_i d_i^3 + 3 sum_i d_i^2 - 6T. Because R_TRI preserves both the complete degree sequence and the exact target triangle count T = 6960, it matches the target exactly in the first three raw Laplacian spectral moments. The observed collapse is therefore consistent with the hypothesis that the earlier degree-preserving R residual was strongly driven by face-triangle and associated short-cycle organization that was destroyed by the original degree-only rewires. However, the result does not prove that global triangle count is the sole causal invariant. Residual differences remain inside the R_TRI family. In particular, although the complete frozen QSPEC and RRESP gates fail, the R_TRI target distances still exceed the corresponding maximum leave-one-out distances and retain robust margins above 1.5. The failure occurs because only one of the three frozen spectral bands passes in each signature. Predeclared secondary diagnostics also show that exact global triangle matching does not reproduce the complete local target organization. For example, R_TRI controls still differ from the target in quantities including: - local per-vertex triangle distribution; - average clustering; - four-cycle count; - degree assortativity; - algebraic connectivity; - and other local or higher-order structural observables. Accordingly, the scientifically admissible conclusion is: The previously robust degree-preserving rewire spectral residual is strongly reduced and loses its frozen two-signature multi-band PASS once the exact global triangle count is preserved, supporting triangle/face organization as a major mechanism behind the original R-family effect. Remaining local and higher-order structural differences prevent the conclusion that global triangle count alone fully explains the residual. The locked result ZIP SHA-256 is: 69f927faba83b203d7dffbf028de680e6a6a3e36818002bc0e1ab27d5c01797d This result does not establish: - unique HLV geometry; - physical selection of the golden ratio; - a unique 6D-to-3D microscopic substrate; - spacetime; - extra dimensions; - particle physics; - an absolute energy scale; - gravity; - dark matter; - dark energy; - cosmology; - or experimental validation. The result instead narrows the active research programme toward the structural origin of the surviving local incidence-spectral residual. A natural successor is a separately prospectively frozen mechanism test using stronger controls that preserve local triangle profiles and selected short-cycle or motif structure before evaluating the inherited spectral signatures. The negative full-carrier-specificity results of the earlier HLV programme remain unchanged.