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 Rₐlpha -> Agrav (s, t) -> chiBH (b, s) -> hAB or gₒpt^AB -> Vₑff' (x_*) = 0 -> bcrit. 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 rhoI -> delta Agrav -> delta chi -> cₐlpha, 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. manuscript3ᵥ32final. pdf — APS/PRD reprint-mode compiled manuscript PDF, suitable for Zenodo upload. 2. manuscript3ᵥ32final. tex — APS/PRD REVTeX 4. 2 manuscript source. 3. manuscript3ᵥ32APSₛourceₚackage. zip — Clean APS-style source package containing the manuscript TeX source, compiled PDF, required figure assets, and checksums. 4. manuscript3ᵥ32ₛupplementalₜoolkitₚackage. 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. manuscript3ᵥ32ᵣeportableᵣecordₑxample. json — Example standardized theoretical reportable record for candidate amplitude-to-capture closure claims. 6. manuscript3ᵥ32AUDITREPORT. md — Audit report describing the v0. 32 critique evaluation, metric-necessity clarification, Nil/Sol launchpad, convergence criteria, and verification checks. 7. manuscript3ᵥ32final. sha256 — SHA256 checksums for the main manuscript and supporting files.