Paper XC: The Black Hole as a Brane Puncture: Holography as Topology, the G2 Microstate Partition Function, and a Microscopic Derivation of the BekensteinHawking Entropy Coecient from Framework-Native Parameters

We propose that a black hole in the brane-bulk octonionic framework is not a region of 3+1-dimensional spacetime but a topological puncture in the brane fabric through which the 5D AdS bulk is exposed. The event horizon is the boundary of this puncture the edge where 4D brane geometry ends. This identication makes holog- raphy automatic rather than conjectural: the interior volume has no brane denition, and the only observable associated with a black hole from the brane is the area of the puncture boundary. The BekensteinHawking entropy S = A/4ℓ2 P is rst derived ther- modynamically as a consequence of the T ∗ 2 dephasing temperature (Paper LXXXIX), then conrmed microscopically. The microstate partition function is: ZG2 = Z G2 dµ(g) e−βHV (g; θG2, εrr) where dµ(g) is the Haar measure on G2, θG2 = 4.00◦is the Fano genesis tilt (Papers I, LXXXIII), and εrr = 1/2 is the horizon radial shear. The base formula √ 2 ln 7/(2π √ 3) = 0.25287 lies within 1.1% of the target 1/4. Dynamical corrections the Fano tilt pin- ning e7, radial shear randomly distributed across the three H+ modes with sub-Planck superimposition between adjacent faces, the running tilt angle during infall, and higher- order local T ∗ 2 eects bring the estimate systematically toward 1/4. The full G2 Haar measure integral, with all inputs xed by the framework and no free parameters, is pro- posed as the exact calculation that closes to S = A/4ℓ2 P precisely. Four new predictions are made (P33P36). 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.