Common validity interval

Let $I_{\mathrm{geom}}$ be an interval with a proved gravitational correspondence, $I_{\mathrm{access}}$ an interval with a proved radiation receiver comparison, and $I_{\mathrm{cert}}$ an interval on which an actual microscopic certificate is small. The required success set is

A recovery-during-evaporation result must exhibit parameters and a nonempty interval in this intersection. The existence of finite approximations in Theorem thm:regulator proves neither smallness of the residual nor nonemptiness of that intersection.

The gravitational approximation budget remains distinct from the channel budget. A metric, dilaton, or stress-tensor error is not added to a diamond-norm error without a proved conversion.