Thermodynamic Advantage of Historical Memory: A Computational Validation of the MetaTime Lazy-Loading Protocol

We validate a concrete prediction of the MetaTime framework: if a history isrepresented as a constraint network, then maintaining an already-consistenthistorical state via warm-start incremental updates (lazy loading) can havevanishing maintenance cost in stable regimes, while restarting from scratch(cold start) remains costly. We formalize a toy universe as a weighted random3-SAT system constructed around a hidden ground-truth assignment x*. Stableobservations are generated to be satisfied by x* by construction, whilecontradictions are injected by a controlled noise parameter p_noise thatrandomizes new clauses. We define residual energy E(x)=Σ_j w_j[1-s_j(x)] andcontradiction density ρ_unsat=E/Σ_j w_j. Using a WalkSAT-type local solveraugmented with fossil mass (aging-based inertia), we compare cold-startrandom initialization against warm-start maintenance across incremental timesteps defined by N_obs. In the stable regime (N_obs≈140, p_noise≈0),warm-start maintenance reaches τ_warm=0 flips in representative runs,whereas cold-start requires O(10^2-10^3) flips (≈500 in the benchmark),implying a near-divergent memory advantage under small regularization. Asp_noise increases, τ_relax becomes nonzero and grows approximately linearlywith ρ_unsat, consistent with contradiction acting as injected computationalheat. The result is a reproducible computational demonstration that historicalmemory is an energetically favored strategy within incrementalconstraint-maintenance models