Three levels of claim

We distinguish:

1. a finite channel theorem;

2. a conditional identification and its quantitative allowance;

3. a physical conclusion after the identification has been proved.

This paper proves statements at level (i), proves implications at level (ii), and does not assert that the gravitational hypotheses required for level (iii) have been discharged.

The Page–Sen average is a random-state theorem PageAverage,Sen. A black-hole time profile requires additional entropy and luminosity assumptions, as in Page's time-dependent analysis PageTime. Island and entanglement-wedge calculations have further geometric and dynamical hypotheses Penington,IslandReview. None is instantiated by a finite capacity plot.