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

Title:The Horizon Closure Matrix (HCM): Observable-Native Verification of Strong-Field and Cross-Theory Closure Chains Creator:Darren Dominic Fabri Affiliation:Independent Researcher, Los Angeles, CA ORCID:0009-0002-0409-2515 Version:v0.42 Publication Date:2026-09-13 Resource Type:Publication / Preprint Language:English Description: This v0.42 preprint presents the Horizon Closure Matrix (HCM), a reality-strict verification framework for determining when microscopic, field-theoretic, asymptotic, or reduced-geometric data genuinely close a chain to a claimed observable. Version v0.42 retains the observable-native closure criterion of v0.41 but replaces the earlier blanket strong-field nonclosure statement with a route-dependent result. A direct near-horizon or generic eikonal phase does not determine an asymptotic capture threshold without a demonstrated horizon-to-infinity canonical or boundary-data map. By contrast, a source-native bulk reconstruction can close capture when it produces the spacetime metric, optical metric, or an equivalent invariant null Hamiltonian. The four-dimensional Schwarzschild control remains a scoped source-native closure. The official eight-component current recursion is independently certified through n = 90, and its all-order resummation gives the exact Schwarzschild exterior and the null-capture observables R_ph = 3 G_N M,b_crit = 3 sqrt(3) G_N M,sigma_cap = 27 pi G_N^2 M^2. Version v0.42 extends this architecture to the rotating Kerr control. All-spin amplitude/source form factors determine the Kerr mass and current multipoles. In four-dimensional stationary, axisymmetric, asymptotically flat vacuum general relativity, the corresponding Thorne/ACMC multipoles coincide with the Geroch-Hansen moments. The multipole tower is inverted through the stationary-vacuum Ernst construction, the resulting |a| <= M branch is checked for global black-hole regularity, and the reconstructed bulk reproduces the exact equatorial Kerr null-capture threshold. This is a scoped closure/control result in ordinary general relativity, not a new Kerr solution. The direct near-horizon eikonal-to-capture route remains NOT CLOSED. The tested all-partial-wave horizon phase lacks the required source-native horizon-to-asymptotic impact-parameter map. Finite-PM observable continuation remains useful as an approximate strong-field diagnostic but is not promoted to a certified capture theorem. The non-Kerr quadrupole branch is also sharply bounded. The earlier coefficient 95/756 is retained only as a 3PM-truncated diagnostic. The physical full Hartle-Thorne strong-field coefficient is C_HT = -5 + (75/16) ln(3) = 0.149745103132... . An exact Manko-Novikov completion produces a different strong-field response because it fixes a different higher-multipole tower. Thus finite {M,J,Q} data do not determine a unique exact non-Kerr bulk or capture observable, and no new regular four-dimensional vacuum black hole is obtained. Version v0.42 additionally integrates two cross-theory closure audits. The Yang-Mills branch gives a scoped positive classical gauge/gravity result: multi-worldline non-Abelian worldline quantum field theory, controlled unwanted-state subtraction, and one-loop five-point / 3PM spanning-cut checks connect the Yang-Mills side to pure-Einstein radiative observables through the audited 3PM frontier. A separate Schwarzschild-root worldline-instanton construction gives a source-induced semiclassical response. However, its external color source is load-bearing, and the construction does not produce a source-free Osterwalder-Schrader-positive Yang-Mills vacuum, transfer matrix, Hamiltonian, confinement proof, or spectral gap. HCM therefore makes no Yang-Mills mass-gap prediction. The surface-fluid branch validates the ellipsoidal diagnostic associated with the thin-shell operator Delta_alpha = Delta_Def - 2 alpha Ric - 4 alpha(1-alpha) S^2. The ellipsoid S^2 decomposition and numerical diagnostics are scoped mathematical/computational passes. The current source establishes rigorous Mosco convergence on surfaces of revolution while treating arbitrary hypersurfaces formally, so the proposed general-surface intermediate-alpha extension remains NOT PUBLICATION-CLOSED. Conventional passive porous/fibrous microstructures fail the exact zero-flat-drag curvature-only target in the audited class. Most importantly, the surface reduction supplies no control of unrestricted three-dimensional vortex stretching and gives no solution, partial regularity theorem, blow-up criterion, or new a-priori estimate for the three-dimensional Navier-Stokes Millennium problem. Version v0.42 therefore provides executed positive and negative closure controls across strong-field gravity, gauge/gravity transfer, and surface-fluid reduction while maintaining explicit source-nativity, evidence-grade, and stop-gate labels. No new black-hole solution, Yang-Mills mass-gap solution, Navier-Stokes Millennium solution, or other new-physics claim is made. Files Included: 1. manuscript3_v42_final.pdf2. manuscript3_v42_final.tex3. manuscript3_v42_APS_source_package.zip4. manuscript3_v42_supplemental_toolkit_package.zip5. manuscript3_v42_reportable_record_example(3).json6. manuscript3_v42_AUDIT_REPORT.md7. manuscript3_v42_final.sha256