Accuracy within the declared model family

For a fixed finite retained box, the model budgets can approach zero if the allowed family permits:

1. arbitrarily long finite windows;

2. capture and storage transmissivity approaching one;

3. arbitrarily accurate joint independent preparations;

4. the stated selective controls for each finite $K_i$;

5. bounded control deviations approaching zero;

6. joint pointer, assignment, and readiness errors approaching zero.

Indeed, Lemma lem:mode controls the first item, Lemma lem:jointloss controls the second, geometric tails control finite $K_i$, and the displayed perturbation integrals control the remaining dynamics.

These are tunability properties of a model family, not a theorem of arbitrary accuracy for fixed hardware. In particular, (eq:capturebounds) shows the increasing capture resources as $\tau \to 1$, and tomography's statistical and systematic requirements scale with $d$.