Correlated Ensemble Solver Simulation of a 16×16 Topological Molecular Memory Lattice: Phase Diagram, Finite-Size Crossing, Geometric Readout, and Cascade Stability

A 16×16 lattice of coupled C12F2 topological switching cells — each a four-state unit derived from the quarter-Möbius molecule predicted in a companion paper — is simulated using the Correlated Ensemble Solver (CES), a classical exact solver for the global structural functional over large correlated variable sets. The memory architecture is prepared and kinetically retained: cells are written into metastable half-Möbius states by STM voltage pulses and held by the switching barrier ΔE2 = 7.533 kcal/mol, which exceeds thermal energy by a factor of ~950 at 4 K. Eight results are reported. (1) A complete phase diagram over temperature and retention threshold τ identifies T < 77 K as the protected operating window, with the CES memory stability functional P rising from 0.003 at 300 K to 0.999 at 4 K for τ = 0.90. (2) Scale invariance: P(τ = 0.90) increases monotonically with lattice size at 4 K, from 0.795 at 4×4 to 0.999 at 16×16, the same qualitative scaling signature as the quantum error-correction threshold theorem, emerging without parameter calibration. (3) A finite-size crossing with clear size-ordered separation is identified between 120 K and 150 K, confirming a collective threshold-like crossover rather than a single-size artefact. (4) Seeded domain reversals of all sizes from one cell to half the lattice produce no reduction in P within the operating temperature window; local domain perturbations leave the global structural functional unchanged or slightly raised. (5) P increases with encoded bit density, a direct consequence of the Rate Function non-factorisation property of the CES. (6) Ordered domain trajectories yield P = 1.000 versus P = 0.0012 for thermal noise via trajectory-correlation, a contrast ratio of 842×. (7) Cascade erasure stability is confirmed by Ouroboros iteration: no tipping point is found at design coupling. (8) A self-reinforcing attractor with P* ranging from 0.821 to 0.977 across feedback strengths converges in 9–11 iterations. Two additional probes return negative results consistent with the perturbative coupling regime. All lattice energetics are derived from a fixed-point string theory framework with zero fitted parameters.