The Horizon Closure Matrix (HCM): A Residual-Gated Verification Framework for Eikonal Bridges, Metric Residuals, and Capture Observables

This v0.32 preprint presents the Horizon Closure Matrix (HCM), a reality-strict theoretical verification framework for evaluating claims that microscopic scattering-boundary data determine macroscopic black-hole capture observables. The central target chain is R_alpha -> A_grav(s,t) -> chi_BH(b,s) -> h_AB or g_optAB -> V_eff'(x_*) = 0 -> b_crit. The manuscript does not claim that this chain is closed. Instead, it defines the reportables, residual gates, overlap-domain conditions, energy-condition checks, diagnostic feedback paths, source-native validation constraints, hard black-hole shadow controls, quantitative convergence criteria, milestone levels, and observable extraction steps that any future closure claim must satisfy. Version v0.32 clarifies why a metric, optical metric, equivalent null Hamiltonian, or invariant capture map is mandatory when the claimed observable is a black-hole photon sphere, shadow, critical impact parameter, or capture cross section. This requirement is not a rejection of S-matrix, bootstrap, holographic, or positive-geometry methods. It is a domain requirement: amplitude-side boundary data may be valid amplitude physics, but local strong-gravity capture observables require sufficient geometric or optical data to compute null capture. The version also adds a concrete Nil/Sol launchpad for F2 residual-gate calibration using exact five-dimensional Einstein controls, an amplitude-side launchpad rho_I -> delta A_grav -> delta chi -> c_alpha, and explicit convergence monitors for the F1-to-F2 handoff. The manuscript distinguishes valuable amplitude-side, premetric, supplied-metric, candidate-bridge, and full-closure milestones while preserving the central NOT CLOSED verdict. Files Included:1. manuscript3_v32_final.pdf — APS/PRD reprint-mode compiled manuscript PDF, suitable for Zenodo upload.2. manuscript3_v32_final.tex — APS/PRD REVTeX 4.2 manuscript source.3. manuscript3_v32_APS_source_package.zip — Clean APS-style source package containing the manuscript TeX source, compiled PDF, required figure assets, and checksums.4. manuscript3_v32_supplemental_toolkit_package.zip — Supplemental package containing the reproducibility toolkit, toolkit outputs, audit report, compile report, static check report, structured reportable record example, and visual contact sheet.5. manuscript3_v32_reportable_record_example.json — Example standardized theoretical reportable record for candidate amplitude-to-capture closure claims.6. manuscript3_v32_AUDIT_REPORT.md — Audit report describing the v0.32 critique evaluation, metric-necessity clarification, Nil/Sol launchpad, convergence criteria, and verification checks.7. manuscript3_v32_final.sha256 — SHA256 checksums for the main manuscript and supporting files.