Three different statements called a Page curve

We distinguish:

1. a designed entropy turnover, such as $h_2(q)$;

2. the random-state Page law, with entropy approximately the logarithm of the smaller subsystem dimension;

3. a gravitational radiation-entropy history obtained from a specified physical theory and radiation interface.

The first does not establish the second, and the second does not identify the third.

Page proposed the exact random-subsystem average; Sen proved it PageAverage,Sen. Page's radiation discussion supplies a separate physical interpretation PageRadiation. Existing gravitational entropy analyses have additional dynamical and geometric content Penington,AlmheiriEtAl. They are not instantiated by naming finite registers “radiation” and “black hole.”