Integer Locking on Spherical Horizons: A Double Euler Class from Geometry and Quantum Information

A spherical black hole horizon carrying one qubit per Planck-area patch is forced — by topology alone — into an integer locking relation between geometry and quantum information: χ(H) = 2 c₁(L) The Euler characteristic of the horizon locks to twice the Chern number of a Berry line bundle constructed from the excitation sector. This relation holds uniquely for spherical topology and fails for every other horizon geometry. The Berry bundle is provably independent of the tangent bundle (c₁(L) = 1 ≠ 2 = c₁(TS²)), and its Chern number is fixed by dimensionality alone — no metric input required. The framework generates a sharp, falsifiable prediction: ℓ-independent horizon reflectivity of topological origin. This is cleanly distinguishable from the frequency-dependent Boltzmann reflectivity of quantum horizon models (Oshita–Wang–Afshordi 2020) and from the ℓ-dependent reflectivity of exotic compact objects (Maggio–Pani 2021). Additional predictions include universal QNM phase offsets and oscillatory two-mode Hawking correlations. The paper draws a hard line between theorems, assumptions, and conjectures. The mathematical core is exact under three statedassumptions. The central vulnerability — whether quantum gravity enforces exact qubit-per-patch saturation — is identified, honestly reported, and framed as a testable question rather than a weakness. Five conjectures and three open problems for the community are stated explicitly. Cross-topology predictions: Q = 0 for toroidal horizons, Q < 0 for higher-genus horizons. Valid in the high-frequency regime ω r_s ≫ 1, with predicted thermal corrections at ω ~ T_H.