Cutoffs and stopping criteria

A physical cutoff certificate must specify a channel on all admitted inputs, including references. A tail probability for one preparation is not such a certificate.

If truncation, preparation, and implementation comparisons are proved on the same complete interface, their half-diamond allowances can be combined by Lemma lem:telescoping. They cannot be added merely because they share the word “error.”

A stopping mass $M_{\mathrm{cut}}$ limits the claimed physical domain. A recovery bound valid at or above $M_{\mathrm{cut}}$ does not determine the subsequent evaporation endpoint.