Recovery time and prefix consistency

For a fixed null and access prescription, define

A robust crossing requires a certified lower bound for the accessible score to exceed a certified upper bound for the null.

If an earlier accessible radiation prefix can be obtained by a CPTP restriction of a later prefix, and earlier quantum storage has not degraded, data processing proves that the ideal score is nondecreasing. A changing, decohering observer need not have that monotonicity.

No equality between (eq:recoverytime) and a Page time is claimed. Fine-grained entropy calculations, including replica-wormhole calculations in their specified gravitational settings, do not by themselves construct the present operational decoder AlmheiriEtAl2020.