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HLV-R-MECH-001: Prospective Triangle-Matched Mechanism Test of the Surviving Degree-Preserving Rewire Spectral Residual — Pre-Execution Protocol Freeze v0.1.0

Marcel Krüger
Aug 2026 · Zenodo (CERN European Organization for Nuclear Research)

Abstract

This record contains the prospectively frozen scientific protocol for HLV-R-MECH-001, a mechanism-focused successor test motivated by the surviving degree-preserving rewire residual observed in earlier HLV specificity studies. HLV-R-MECH-001 is not a retry of full HLV carrier specificity. The previously published DS-SPEC-001R overall verdict remains permanently: DSSPEC001R_FAIL_PARTIAL_SIGNATURE_OR_FAMILY_ONLY The purpose of the present protocol is narrower: to test whether the previously observed R-family graph-spectral separation reproduces under fresh degree-preserving controls at matched structural perturbation depth, and whether that separation collapses when the exact target triangle count is additionally preserved. The protocol is motivated by an explicitly exposed exploratory result from HLV-R-MECH-DISC-001. For the DG-001 target: N0 = 1110 N1 = 5345 N2 = 6960 graph triangle count = 6960 The exploratory analysis verified that the complete set of 6960 graph triangles is exactly identical to the set of 6960 DG-001 two-cell face vertex-triples. By contrast, the earlier degree-preserving DS-SPEC R controls contained on average only approximately 285.74 triangles, corresponding to a mean retention of about 4.1% of the target triangle count. This exposed observation is not treated as confirmatory evidence. It is used only to define the new prospectively frozen mechanism question. The protocol defines two fresh control families. R_DEG: fresh degree-preserving rewires that preserve - the exact labelled target degree sequence; - N0 = 1110; - N1 = 5345; - graph simplicity; - connectivity; - and a frozen edge-replacement fraction between 0.40 and 0.45. The global triangle count is not constrained in R_DEG. R_TRI: fresh degree-preserving rewires that preserve all R_DEG constraints and additionally preserve the exact global triangle count T = 6960. Both families require 31 accepted controls. The two families are also required to have matched perturbation depth: the absolute difference between their median edge-replacement fractions may not exceed 0.02. If that condition fails, no spectral mechanism inference is permitted. The mathematical motivation is especially strong because for a simple graph with graph Laplacian L = D - A, the following exact identities hold: Tr(L) = sum_i d_i Tr(L^2) = sum_i d_i^2 + sum_i d_i Tr(L^3) = sum_i d_i^3 + 3 sum_i d_i^2 - 6T. Therefore degree preservation fixes the first two raw Laplacian moments, while simultaneous degree and exact triangle preservation also fixes the third raw Laplacian moment. Accordingly, every accepted R_TRI control matches the target in Tr(L), Tr(L^2), and Tr(L^3) exactly. This does not imply matching of the full spectrum, lambda_max, scale-quotiented eigenvalue distribution, QSPEC, or RRESP. The primary spectral observables are inherited unchanged from the published DS-SPEC-001R recovery protocol: Krūger, M. (2026). HLV-DS-SPEC-001R: Prospective Recovery of the Native 6D-to-3D Carrier Spectral-Specificity Gate After Q-Control Capacity Stop — Pre-Execution Protocol Freeze v0.1.0. Zenodo. DOI 10.5281/zenodo.22162097. The two frozen primary signatures are: QSPEC and RRESP. No new spectral feature is selected from the exposed R-MECH discovery result. For each family and signature, the target must satisfy all of the following to obtain a signature PASS: 1. target distance must exceed the maximum leave-one-out control distance; 2. the robust target-to-control margin must be at least 1.50; 3. at least two of the three prospectively frozen spectral bands must exceed the corresponding maximum leave-one-out band distance. A family PASS requires both QSPEC and RRESP to pass. The primary mechanism verdicts are frozen as follows. RMECH001_PASS_TRIANGLE_MATCH_COLLAPSE_PATTERN requires: R_DEG family PASS and R_TRI QSPEC FAIL and R_TRI RRESP FAIL. This result would support the conclusion that exact global triangle matching removes the previously observed robust R-family spectral separation under the frozen generator and perturbation-depth contract. It would not prove that triangle count alone is the unique causal invariant, because triangle preservation may simultaneously preserve correlated local structure. RMECH001_FAIL_TRIANGLE_SUFFICIENCY_RESIDUAL_SURVIVES requires: R_DEG family PASS and R_TRI family PASS. This result would show that degree sequence plus exact global triangle count are insufficient to eliminate the surviving R-family spectral residual. It would motivate stronger successor controls involving local triangle profiles, short cycles, graph motifs, or higher-order incidence structure. RMECH001_PARTIAL_SIGNATURE_DEPENDENCE_AFTER_TRIANGLE_MATCH is returned if R_DEG passes but exactly one of the two R_TRI signatures passes. If the fresh R_DEG family does not reproduce the previous degree-preserving separation, the result is: RMECH001_INCONCLUSIVE_FRESH_RDEG_BASELINE_NOT_REPRODUCED. Additional frozen inconclusive states cover insufficient control capacity, rewiring-depth mismatch, numerical audit failure, source mismatch, or protocol invalidation. The control-generation process is fully prospectively specified. R_DEG seeds are generated from: seed = 730100000 + offset for offsets 0 through 127. R_TRI seeds are generated from: seed = 730200000 + offset for offsets 0 through 127. Candidates are evaluated in increasing offset order, and the first 31 structurally admissible controls are accepted. If fewer than 31 controls are accepted in either family by offset 127, the run becomes inconclusive for control capacity. Previously exposed pilot and development seeds are permanently excluded from confirmatory use. A hard feature firewall is part of the protocol. No eigenvalue, lambda_max, QSPEC, RRESP, spectral band, target-control distance, leave-one-out score, or scientific mechanism verdict may be computed until both complete 31-member structural control banks have been: - generated; - structurally validated; - written to disk; - and hash-fixed. Control admission therefore cannot depend on spectral information. The protocol also freezes numerical identity and eigensolver checks, including trace identities, Frobenius consistency, connected-graph zero-mode checks, nonnegative-spectrum tolerance, and cross-solver eigenvalue audits on the target and selected controls. Secondary diagnostics are declared in advance but are non-load-bearing. These include: - triangle count and transitivity; - average clustering; - per-vertex triangle-count distribution; - four-cycle count; - degree assortativity; - k-core summaries; - Tr(L^4)/N; - lambda_2; - lambda_max. They may be inspected only after the structural control banks are frozen and may not alter the primary verdict. Controlling provenance: DG-001 locked results: DOI 10.5281/zenodo.22107618 DS-SPEC-001R recovery protocol: DOI 10.5281/zenodo.22162097 DS-SPEC-001R corrected implementation freeze: DOI 10.5281/zenodo.22164304 DS-SPEC-001R locked results: DOI 10.5281/zenodo.22165100 HLV Mathematical Core v2.1.4: DOI 10.5281/zenodo.22165745 The pre-freeze technical triangle-preserving pilot produced 12/12 structurally valid controls, each preserving the exact target degree sequence and exact triangle count T = 6960 while replacing approximately 41.3%–42.5% of target edges. No QSPEC, RRESP, spectral-specificity score, or scientific mechanism verdict was calculated during that pilot. The pilot is therefore treated strictly as technical feasibility evidence. HLV-R-MECH-001 does not test or establish: - unique HLV geometry; - physical selection of the golden ratio; - a unique 6D-to-3D microscopic substrate; - spacetime; - extra dimensions; - particle masses; - an absolute HLV energy scale; - gauge interactions; - gravity; - dark matter; - dark energy; - cosmology; - or experimental validation. The allowed scientific claim is narrower: HLV-R-MECH-001 prospectively tests whether the previously observed degree-preserving graph-spectral residual can be explained, removed, or further localized by exact matching of the target's global triangle/face count while controlling perturbation depth. Any stronger interpretation requires a separately frozen successor experiment.

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