What is taken from Hawking's paper

For a nonrotating uncharged black hole, Hawking's late-time packet calculation gives, in the natural-unit convention,

for bosons, with the corresponding plus sign in the denominator for fermions. Here ${\Gamma }_{\omega \ell m}$ is the absorption probability, not an additional information-recovery certificate. The temperature is

when $\kappa$ denotes the horizon redshift rate in inverse-time units. If surface gravity is instead expressed as an acceleration ${\kappa }_{\mathrm{acc}}$, then $\kappa ={\kappa }_{\mathrm{acc}}/c$. These are external semiclassical statements, not conclusions of the finite theorems below Hawking1975 (Section 2, especially Eq. (2.29)).

Hawking's backreaction discussion associates net positive outgoing energy flux with decreasing black-hole mass and an ingoing negative-energy flux in the semiclassical description. Net mass loss requires the outgoing flux to exceed incoming energy. The same paper explicitly states that the quasi-stationary classical-metric approximation breaks down at the Planck-scale endpoint Hawking1975 (Sections 1 and 4). Consequently, its final-disappearance discussion is not used here as a construction of a complete microscopic endpoint isometry.

The historical estimate that sufficiently light primordial black holes would have evaporated “by now” belongs to the cosmological age assumptions used in the 1975 paper. It is not a present-day numerical estimate in this manuscript.

The entropy expression relevant to the historical comparison is

The abbreviated expression $S+A/4$ assumes the corresponding natural units. Black-hole mechanics and the generalized second law are separate gravitational and thermodynamic subjects BardeenCarterHawking,Bekenstein1974,Hawking1975. Neither an area theorem nor a generalized-second-law proof is derived from a code dimension in this paper.