Post-Theoretical Relativistic Holography: Horizon Thermodynamics and Information Structure from the Z₉ Chern–Simons Reduction

We derive the horizon thermodynamics of the Post-Theoretical Relativistic Holography (PTRH) framework after the Z9 reduction of the torsion-prismatic sector to an abelian Chern-Simons theory at level k=9. The resulting modular tensor category supplies both the Wald-Noether contribution δS₉ = log 9 and the universal topological entanglement entropy log 3, combining to give a net topological shift 3 log D = log 27 in the generalised entropy. The differential first law remains macroscopically standard, while the modified island formula acquires an additive 3 log D term. The same Z9 structure yields a quantitative late-time information release rate estimated via a gap-activated Arrhenius form Γ_info ≈ Δ_min exp(−2πΔ_min) with Δ_min = 2 sin(π/9). A complete bulk-to-horizon dictionary maps prismatic curvature, multi-temporal foliation, and soft-hair charges onto anyonic holonomies and sectors. Three structural gaps in the PTRH programme are thereby closed.