The Horizon Closure Matrix (HCM): Observable-Native Verification of Strong-Field and Cross-Theory Closure Chains

Resource Type: Publication / Preprint Creator: Darren Dominic Fabri Affiliation: Independent Researcher, Los Angeles, CA ORCID: 0009-0002-0409-2515 Version: v0.43 Date: 2026-09-14 Language: English DOI: 10.5281/zenodo.22740135 Previous Version: 10.5281/zenodo.22731907 The Horizon Closure Matrix (HCM) evaluates whether a declared source and approximation support a specified terminal observable. It separates structural closure from the provenance and strength of the supporting evidence, recording derivations, assumptions, parameter choices, observables, verdicts, failure points, and minimum next requirements. Version v0.43 repairs reproducibility omissions, an ineffective Kerr orbit check, and several claim-domain and attribution issues identified in a post-release technical audit of v0.42. Revision R1 adds targeted clarifications following assessment of a subsequent Red Team critique. The recovered Schwarzschild recurrence is replayed through n = 90, with 720 exact coefficient comparisons and 2,160 finite-field comparisons. Separate downstream checks test Schwarzschild capture and Kerr radial double-root identities. These finite checks remain distinct from the cited all-order derivations. Finite-PM continuation retains partial support at two of four declared velocities. R1 distinguishes the original local numerical-stability criterion from the later held-out errors below 5%. It documents the finite-order operation sequence and explicitly leaves all-order convergence and limit commutativity unestablished. The near-horizon eikonal audit identifies the missing horizon-to-infinity state/observable map and specifies a bounded first matching milestone. Naming this required map does not construct it, and generic eikonal-to-capture closure remains open. A convention-defined HCM calculation within the Kerr critical-matching framework of Uri Kol, arXiv:2411.09814, provides exact algebra, an archived scalar numerical replay, and corrected HCM scalar-current normalization checks. Its support is restricted to the declared scalar domain; global matching and terminal-observable closure remain open. The Yang-Mills section audits the author's own HCM program. R1 distinguishes the valid sourced semiclassical calculation from a proposed source-free quantum extension: the latter lies outside the sourced calculation's scope and remains unconstructed. The surface-fluid section audits the author's separate manuscript, Curvature-Anisotropic Vortex Mapping on Ellipsoidal Thin Shells: A Partial-Slip S² Operator Diagnostic, draft v0.4. This identifier is unrelated to HCM v0.40. The Calabi-Yau discussion distinguishes period geometry contributing to radiation observables from an additional spacetime interpretation. An absent spacetime interpretation does not establish that the geometry fails. The source-backed radiation result is not presented as an independently repeated four-loop calculation. Three reproducible color figures illustrate light-ring coefficients, ellipsoid anisotropy, and scalar matching residuals. A ten-route appendix identifies unresolved transitions and minimum requirements for further research. No generic eikonal-to-capture closure, new black-hole solution, Yang-Mills mass-gap solution, unrestricted three-dimensional Navier-Stokes result, or new-physics discovery is claimed. Files Included: manuscript3_v43_final.pdf manuscript3_v43_final.tex manuscript3_v43_APS_source_package.zip manuscript3_v43_supplemental_toolkit_package.zip manuscript3_v43_reportable_record_example.json manuscript3_v43_AUDIT_REPORT.md manuscript3_v43_final.sha256 manuscript3_v43_AUDIT_REPORT.pdf HCM_v43_Kerr_Critical_Matching_Note.pdf HCM_v43_Kerr_Critical_Matching_Note.tex HCM_v43_Kerr_Critical_Matching_Note_source.zip RELEASE_VERIFICATION.json RELEASE_README.md HCM_v43_RED_TEAM_ADJUDICATION.md HCM_v43_RED_TEAM_ADJUDICATION.pdf HCM_v43_R1_MANUSCRIPT_CHANGES.diff HCM_v43_R1_COMPLETE_RELEASE.zip HCM_v43_R1_COMPLETE_RELEASE.sha256 Additional compilation, reproducibility, input-rejection, and PDF-comparison receipts are included in the RELEASE_CHECKS folder within HCM_v43_R1_COMPLETE_RELEASE.zip. Its HISTORY folder preserves the complete pre-R1 public release. The original AUDIT_REPORT documents the v0.42-to-v0.43 corrections; RED_TEAM_ADJUDICATION documents the subsequent R1 assessment and changes. Earlier verification records retained as historical evidence do not supersede the current R1 record.