Event-Horizon-State Computer Memory (EHSCM): A PTRH/TMRB Architecture

We present Event-Horizon-State Computer Memory (EHSCM), a theoretical memory architecture that treats the black-hole event horizon as a discrete, addressable holographic storage surface within the Prismatic Torsional Recursive Holographic (PTRH) and Torsion-Modulated Recursive Branching (TMRB) frameworks. Four results are established with explicit quantitative values. (1) Z9 Storage Lattice: the Gaussian branching weight wₙ = C·exp (-πn²/9), C ≈ 0. 5002, partitions the horizon into nine torsion charge sectors with thermal stability ratios τₙ/τH = exp (πn²/9). The bilateral Gaussian series satisfies exact DFT self-similarity via Poisson summation. (2) φ-Cascade Addressing: channel frequencies ωₖ = ωH·φᵏ and Mellin step Δλ = 1. 7287 (principal-series comb spacing of PTRH Paper 4) define a K-channel address space carrying 3. 000 bits per cell at high SNR, 1. 54 bits under thermal conditions. (3) Capacity Self-Consistency: requiring total storage entropy to saturate the Bekenstein–Hawking bound SBH = A/4G₄ forces torsion cell area Acell = 4G₄ ln 9 ≈ 8. 79 ℓPl². (4) Unitarity via Z9 Parafermion CFT (first identified by Zamolodchikov–Fateev 1987 and Gepner–Qiu 1987): Hawking radiation carries the primary-field content of the Z9 parafermion CFT; the torus partition function Z (τ) = Σ|χₙ₉, ₍ (τ) |² is modular invariant, providing the unitarity mechanism for information recovery. An entropy correction ΔSₜors = 9 ln 9 + ln 2 ≈ 20. 468 beyond the area law is confirmed by PTRH Paper 10. All results are accompanied by a fully executable Python companion notebook. Four falsifiable near-term predictions are specified with null hypotheses and falsification criteria. Nine structural gaps are ranked by tractability, with Gap G3 (derivation of Acell from the prismatic Hilbert action) identified as the priority open problem. Connections to AdS₃/CFT₂ (Maldacena, HKLL, Ryu–Takayanagi) and to the celestial holography dictionary of PTRH Paper 4 are established and scoped.