This conclusion is independent of the underlying quantum gravity theory [19] from which SGEFT might emerge; it implies that (I)–(III) cannot all emerge. I omit a host of potential subtleties and suspected loopholes that were explored in the early literature on the firewall paradox (see Ref. [2] for a discussion and references). These include the hypothesis that the decoding unitary cannot be implemented fast enough, as a matter of physical law rather than mere practicality [20]. To my knowledge, this idea was not developed further; perhaps it should be.

Some approaches (including those discussed below) define $e_b$ as encoded so long as the computational complexity of decoding $e_b$ remains in the exponential class identified by Harlow and Hayden [20]. By this definition, $e_b$ must be regarded as “automatically decoded” after the black hole has fully evaporated: at this time, the task may be arduous but it is no longer exponentially hard. With this definition, a nontrivial dependence of horizon normalcy on the infinite future is not an option, because the radiation state always exits the normalcy-guaranteeing class at sufficiently late times. The choice is between introducing a preferred time in the radiation region and thus violating general covariance or giving up on state-dependent horizon normalcy.

See Refs. [25, 26] for related ideas and Refs. [2, 10, 25, 27, 28, 29, 30] for criticisms unrelated to the time ambiguity emphasized here.