The Horizon Closure Matrix (HCM): Observable-Native Verification of Microscopic-to-Black-Hole Capture and Radiation Chains

Abstract

Title:The Horizon Closure Matrix (HCM): Observable-Native Verification of Microscopic-to-Black-Hole Capture and Radiation Chains Creator:Darren Dominic Fabri Affiliation:Independent Researcher, Los Angeles, CA ORCID:0009-0002-0409-2515 Version:v0.40 Publication Date:2026-08-17 Resource Type:Publication / Preprint Language:English Description: This v0.40 preprint presents the Horizon Closure Matrix (HCM), a reality-strict verification framework for evaluating claims that microscopic scattering or field-theory data determine macroscopic black-hole observables. Version v0.40 makes the closure criterion explicitly observable-native. The intermediate representation required by HCM is determined by the terminal observable rather than imposed universally. For photon spheres, shadows, critical impact parameters, and capture cross sections, a spacetime metric, optical metric, or equivalent invariant null Hamiltonian remains mandatory. For directly defined scattering or radiation observables, a source-native field-theory chain may close without reconstructing a local metric, provided the action, reduction, approximation domain, boundary data, observable map, and validation evidence are supplied. The manuscript retains the first passing source-native HCM capture control through the four-dimensional Schwarzschild direct-current route: Einstein gravity plus a massive spinless point source-> eight-component off-shell current recursion-> gothic inverse metric-> exact Schwarzschild metric-> null Hamiltonian-> photon sphere-> critical impact parameter-> capture cross section. The official endpoint-regularized eight-component recursion was independently certified through n = 90, corresponding to 89 loops, with 720/720 exact four-dimensional coefficient matches and 2160/2160 exact finite-field recurrence matches across three independent prime-field evaluations. Current conservation was verified at every supplied order. The reconstructed geometry yields R_ph = 3 G_N M,b_crit = 3 sqrt(3) G_N M,sigma_cap = 27 pi G_N^2 M^2. The proof boundary remains explicit: the action-to-recursion derivation is source-backed rather than independently regenerated from Feynman rules, and an arbitrary-n symbolic recurrence proof remains open. Version v0.40 also adds a second, structurally distinct observable control from the published 5PM-1SF worldline-QFT black-hole scattering calculation. Its source-native chain is Einstein-Hilbert gravity plus point-particle worldlines-> WQFT-> 426 diagrams-> integration-by-parts reduction-> 236 even-parity + 232 odd-parity master integrals-> differential equations-> Calabi-Yau-threefold period block in the odd-parity sector-> impulse-> radiated energy and recoil. The Calabi-Yau periods are treated strictly as master-integral/function-space geometry. They are not interpreted as black-hole spacetime geometry, an extra physical dimension, or evidence for a string compactification. The published calculation supplies public computational notebooks and source data, but HCM v0.40 does not claim an independent clean-room rerun of the complete four-loop computation. The generic positive-geometry/residue/eikonal-to-capture target remains NOT CLOSED: R_alpha-> A_grav-> chi-> metric / optical metric / equivalent null Hamiltonian-> capture observable. No generic source-native eikonal-to-geometry reconstruction with a demonstrated capture-domain overlap has yet been supplied. The central v0.40 methodological result is therefore a separation between structural closure and evidence grade. A source may derive a structurally complete observable chain even when the present audit has not independently reproduced every internal calculation; conversely, a reproducible intermediate result cannot close a missing handoff to the terminal observable. Files Included: 1. manuscript3_v40_final.pdf — APS/PRD reprint-mode compiled manuscript PDF suitable for Zenodo distribution. 2. manuscript3_v40_final.tex — APS/PRD REVTeX 4.2 manuscript source used to generate the PDF. 3. manuscript3_v40_APS_source_package.zip — Clean APS-style source package containing the manuscript TeX source, compiled reference PDF, source README, and checksums. 4. manuscript3_v40_supplemental_toolkit_package.zip — Reproducibility package containing the HCM v0.40 toolkit, machine-readable outputs, closure matrix, Schwarzschild certification ledger and source hashes, reconstructed D=4 coefficient table, 5PM-1SF radiative-control source ledger, audit report, compile report, static checks, reportable record, and visual contact sheet. 5. manuscript3_v40_reportable_record_example.json — Machine-readable observable-native HCM records for the Schwarzschild capture control, 5PM-1SF radiative control, and generic open residue/eikonal capture route. 6. manuscript3_v40_AUDIT_REPORT.md — Reality-strict audit report documenting assumptions, derivation status, approximation domains, observable status, reproducibility boundaries, technical gaps, allowed claims, and final verdicts. 7. manuscript3_v40_final.sha256 — SHA-256 checksums for the principal manuscript and supporting release files.