Exact coherent, number-record, and referenced-recovery optima

The limit in (eq:thermalweightlimit) is an analytic comparison, not an admissible $L=\infty$ emission from finite mass $M$. In particular, the actual greybody-calibrated occupation in (eq:calibratedq), not temperature alone, determines whether even the ideal conditional completion crosses the trusted classical bound. A nonzero advantage over $1/2$ and a violation of $3/4$ are different claims.

The recovery error in (eq:optimaldiamond) is also a different quantity from the delayed-query score. This distinction parallels the separate recovery and executable-access optima in En02-C/D and the key/transfer separation in Em03-E CheungEn02C,CheungEn02D,CheungEm03E. Those finite models are not imported as Hawking dynamics.