The physical background

Hawking's particle-creation calculation concerns quantum fields on a classical collapse background, while his information-loss proposal asks about a complete final description of the initial quantum state Hawking1975,Hawking1976. For an uncharged, nonrotating Schwarzschild black hole, the external semiclassical temperature is

A bosonic mode has a thermal denominator modified by an absorption factor:

These statements do not specify a complete logical-input-to-radiation channel. In particular, one occupation number is not a test of every logical coherence.

Page's random-subsystem analysis and unitary-radiation comparison concern additional assumptions about states and information in radiation PageAverage,PageInformation. Random-subsystem recovery also depends on the input message, initial correlations, and subsystem sizes, rather than on a universal count of “half the emitted quanta” HaydenPreskill. Island and replica-wormhole calculations address entropy in their specified gravitational settings AlmheiriEtAl. They are not replaced here by a finite circuit, and they are not used as a substitute for a missing complete-channel comparison.

The low-energy scalar-reservoir evaporation model of Gaikwad, Kaushal, Mandal, and Wadia has its own dynamics and physical assumptions GaikwadEtAl. Its geometry is not assigned to the finite-band source model below merely because both contain a scalar bath.