Proof of the Isolated Horizon Conjecture in the PTRH Z₉ Framework:

PTRH Paper 12 derived the torsion cell area A_cell = 4G_4 ln 9 ≈ 8.79 ℓ²_Pl conditional on the Isolated Horizon Conjecture (IHC): that the nine bulk Z_9 prismatic F-crystal eigenspaces project to independent degrees of freedom on the bifurcation surface Σ. This paper proves the IHC. Four results establish the proof. (1) Restriction and decomposition [V]: The closed immersion i: Σ ↪ X induces a Z_9-equivariant restriction map ρ = i* on the prismatic topos. The pullback ρ*(M, φ_M) decomposes as a