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 w_n = C·exp(-πn²/9), C ≈ 0.5002, partitions the horizon into nine torsion charge sectors with thermal stability ratios τ_n/τ_H = exp(πn²/9). The bilateral Gaussian series satisfies exact DFT self-similarity via Poisson summation. (2) φ-Cascade Addressing: channel frequencies ω_k = ω_H·φ^k 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 S_BH = A/4G₄ forces torsion cell area A_cell = 4G₄ ln 9 ≈ 8.79 ℓ_Pl². (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|χZ9,n(τ)|² is modular invariant, providing the unitarity mechanism for information recovery. An entropy correction ΔS_tors = 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 A_cell 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.