Reasoning. The first-law analogy dM = (kappa/8pi) dA + Omega dJ vs dU = T dS + work terms suggests T ∝ kappa, S ∝ A; kappa’s constancy over the horizon parallels the zeroth law. Bekenstein proposed the identification was literal and formulated the Generalized Second Law (S_matter + const x A never decreases), but without emission the GSL fails: a hole in a colder radiation bath would absorb entropy-carrying radiation while… conversely a hole immersed in radiation at lower temperature than kappa/2pi must emit more than it absorbs or the combined entropy budget is violated. With emission at exactly kappa/2pi, the GSL holds and S = A/4 (in Planck units) is fixed, with gravitational collapse understood as converting baryons and leptons into entropy. This is a consistency (coherence) argument: it carries no empirical information, but shows the emission rate is not an artifact of one derivation — it is the unique rate compatible with thermodynamics.
Step 6 — validity verdict
approved / checked. Reconstruction — premises: the classical laws of black-hole mechanics (first law with kappa/8pi, area theorem, kappa constant on the horizon); Bekenstein’s literal thermodynamic identification and the Generalized Second Law. Load-bearing step: an absorb-only hole immersed in radiation colder than kappa/2pi generates GSL violations, and emission at exactly T = kappa/2pi is the unique rate restoring consistency (simultaneously fixing S = A/4). Conditional on the GSL premise this uniqueness argument is valid, and the conclusion is properly hedged as coherence support — the body itself says “it carries no empirical information”. Candidate defeater — “the mechanics/thermodynamics parallel is merely formal” — denies the literal-identification premise rather than breaking the inference, so it is priced in step 7. Inference traced; author-blind (the argument stands on the GSL logic, not on Hawking having made it).