Phase 6: A Finite-Cutoff Boundary-Log Ridge Signature in M87* An Empirical Boundary Certificate for Reduced Geometric Closure

This paper presents Phase 6 of the reduced geometric closure program. It tests a boundary-sector prediction on public M87* Event Horizon Telescope data. The central claim is deliberately limited. The paper does not claim a direct observation of the black-hole interior, nor an ideal pure 1/m edge. Instead, it tests whether the exterior lensed ridge of M87* carries a coherent finite-cutoff boundary-log modal signature. The empirical analysis begins with the public 2017 M87* UVFITS visibility data. A diagnostic asymmetric crescent-plus-compact visibility fit gives a stable shared ring scale near 41.6–41.7 microarcseconds. Diagnostic reconstructions are then used only as controlled image-domain inputs for ridge extraction and modal testing. The ridge spectrum is tested against white, pure boundary-log, generic power-law, free finite-cutoff, and fixed-octant models. The observed ridge supports a finite-cutoff boundary-log form rather than a pure infinite-band 1/m law. Synthetic pipeline controls, transfer calibration, forward injection, reconstruction-family tests, and randomized angular negative controls are used to test whether the signal can be reduced to a trivial reconstruction or ridge-extraction artefact. A final fixed-octant certificate tests the protected value m_* = 8. This value is derived from the protected quarter-sector structure: the half-angle lift gives four protected quarter sectors, and a finite ridge has two oriented boundary branches per sector. In the main quality-filtered wide window and in the cleaner reconstruction-family windows, the fixed m_* = 8 model matches or improves the free-cutoff model while strongly beating the pure 1/m law. The result is an empirical boundary certificate: the exterior lensed ridge of M87* carries a stable geometric scale and a coherent finite-cutoff boundary-log modal structure, with the protected octant cutoff m_* = 8 supported in the key certificate windows. The accompanying supplementary archive contains the numerical certificate chain C1–C9, including CSV tables, diagnostic plots, metadata, decision files, and reproducibility manifests.