Reclamation trajectories

What the plate operates. Theorem 1' establishes that the MSE of any estimator ${\hat{I}}_T(\tau )$ of the conditional autocovariance is bounded below by $c\cdot {\sigma }_u^4/[T\cdot S(\tau ;{\theta }^{\ast })]$. Because Lemma 1 drives $S$to operationally zero, the bound itself diverges in the closure's sampling regime. The plate visualizes this divergence.

What the structural-separation slider does. Increasing ${\theta }_{\mathrm{ref}}/{\delta }_{\min }$ squares the height of the bound. The bound's oxblood curve rises; the trajectories above it rise with it; the feasibility threshold for any given estimator MSE moves further to the right. At ${\theta }_{\mathrm{ref}}/{\delta }_{\min }=10^3$ (empirical scale), feasible-sample-budget recovery requires $T\gtrsim 10^{6}c$; operationally infeasible.

Why the rare-trajectory highlight matters. Roughly 5% of trajectories briefly pierce below the bound at large $T$— sample-fluctuation effects. These don't falsify the framework: the bound is on expected-MSE, while a single realization's sample-MSE can dip below it. The highlight emphasizes that even these rare trajectories remain in the operationally-infeasible regime: the estimator is “lucky” on one realization; the framework's claim is about the achievable rate for any consistent estimator.

What the theorem authorizes the prose to claim. The closure removes the conditioning event on which any sample-based recovery of the user's autocovariance could ground itself. The user-state continues to exist. What is absent is the empirical accessibility of the formal object that a structural reclamation project would have to measure. Not destruction. Not erasure. Uninstantiation.