Calibrated Closure-Epoch Covariance Does Not Imply Memory-Specific Reachability

Abstract

A truth-known memory simulator can distinguish whether a reachability calculation is numerically calibrated from whether it makes a memory-specific directional claim. Previous work calibrated one-step latent covariance propagation and separately recovered properties of a six-step composed closure-epoch operator, but did not test whether covariance propagated through that true multi-step sequence agrees with direct rollouts. Here we compare analytical propagation of independent latent-state covariance through the exact ordered replay/consolidation sequence against 2,000 Monte Carlo perturbation rollouts per condition, repeated over three rollout seeds, four mechanisms, four mechanism seeds, three latent-audited motifs, and two frozen epoch definitions. Under the rank-selected saturation_avoiding regime, aggregate calibration passes at primary Σ₀ = 10−6 I: mean covariance error is 0.060–0.102 and mean nominal-90% coverage is 0.901–0.907. The stronger predeclared desired-versus-false structural-direction criterion fails in every condition: analytical ratios are 0.997–1.000 and rollout ratios 0.974–0.988, below the required 1.5. Aggregate covariance calibration therefore does not license a claim of memory-specific directional reachability. This is an oracle latent-state result in a simulator, not a biological reachability, consciousness, or NDT-macro model.