hawking_clause_is_cert

This module answers a formal-methods referee objection to the unconditional quantum-gravity master theorem: witness slots of shape $\Sigma(P:\mathrm{Prop}), P$ carry no content unless the plugged-in propositions are genuine, independently named physics. For each atom of the master conjunction the audit supplies an rfl-level disclosure of what the field actually is, plus a standalone proof that it holds without assuming any master clause.

The Hawking field is one such atom. Upstream, the SI Hawking temperature is fixed by the master-plan identity $T_{\mathrm{hawking,SI}}(M)=\hbar_{\mathrm{SI}} c_{\mathrm{SI}}^3/(8\pi G_{\mathrm{SI}} k_{B,\mathrm{SI}} M)$ for $M>0$. The certificate structure packages that identity together with positivity, strict anti-monotonicity, the bridge lift of the RS-native $T_{\mathrm{hawking}}$, a Schwarzschild-radius reformulation, and the SI Page-time $M^3$ scaling. The master field is defined as the carried thermodynamic content (M4) conjoined with nonemptiness of that certificate.

One-line term proof by reflexivity. The master definition of the Hawking-temperature clause is already the conjunction of the carried thermodynamic proposition with Nonempty of the SI certificate, so equating the clause to that conjunction is definitional equality; no lemmas are applied.

In the classification key of the non-circularity audit this clause is an inhabitedCert: not a trivialPlaceholder equal to True, and not a self-referential copy of the master conclusion. The disclosure lets a referee inspect, by pure definitional equality, that the thermodynamic content is the named M4 carried proposition plus a concrete SI certificate whose fields are the standard Hawking formula and its corollaries.

Sibling audit lemmas discharge the other master atoms (T0–T8 forcing chain, cost uniqueness, BMV positivity, Lorentzian structure, $c_{\mathrm{RS}}$) the same way; the assembly lemmas then collect that every carried clause holds and every closed certificate is inhabited. That is the peer-review path from "unconditional master theorem" to "assembled from independently proved, non-self-referential propositions." No downstream consumer is wired yet; the declaration exists for audit transparency rather than as a computational stepping stone.