Completion of the Black Hole Entropy Calculation: a2 = +1 from Fano Dispersion, Framework-Wide Prediction Table (P1P46), and the Exact Bekenstein-Hawking Co- ecient at All Orders

This paper closes the black hole entropy calculation begun in Paper LXXXIX. The a2 coecient in the area expansion Aeff j = jℓ2 P (1 + a2x2 + · · · ) is derived from the Fano lattice TT shear wave dispersion: a2 = +1. The correction x2 = (ℓP /rT ∗ 2 )2 is smaller than 10−60 for all physical black holes, conrming that a2 has no measur- able eect. The exact coecient 1/4 is given to all orders in x by the master relation H7(a∗) = π p 3/8 (Paper XCIII) a pure result of Fano representation theory with no x-dependent corrections. The complete framework-wide prediction table, updated through Paper XCV, is presented. Status: Papers IXCV, Predictions P1P46, 26 con- rmed, 0 falsied. Part of the One-Octonion Brane-Bulk Framework series. Anchor DOI: 10.5281/zenodo.19120873. Community: one-octonion-brane-bulk. Author: Bharathi Dasan Jagadeesan, M.D., University of Minnesota. ORCID: 0000-0002-1143-941X.