cert_inhabited
plain-language theorem explainer
The milestone certificate type for FinalModule_1396 is inhabited: there exists a record asserting that the domain cost vanishes on the diagonal for every nonzero real and that the canonical threshold is strictly positive. Anyone citing the structural domain-coverage milestone would use this existence fact. The proof is a one-line term that packages the concrete witness certificate.
Claim. The type of milestone certificates is nonempty: there exists a certificate whose fields assert that $\mathrm{domainCost}(r,r)=0$ for every real $r\neq 0$, and that the canonical threshold is strictly positive.
background
FinalModule_1396 is a Recognition Science structural milestone module (Plan v7, 109th pass). It packages a domain-coverage certificate with zero sorry and zero axioms.
The certificate structure has two fields. The first requires that the domain cost functional evaluates to zero on the diagonal: for every nonzero real $r$, the cost of the pair $(r,r)$ is zero. The second requires that the module's canonical threshold is strictly positive. Both conditions are the local structural checks that mark this domain milestone as closed.
The module sits in the Physics layer and imports the shared Constants and Cost infrastructure. No external lemmas are required beyond the in-module witness that already assembles those two field proofs.
proof idea
One-line term proof. The theorem is Nonempty MilestoneCert, proved by the anonymous constructor ⟨cert⟩, which supplies the concrete in-module certificate value as the witness. No tactics, no external lemmas: inhabitation is immediate from the already-built certificate record.
why it matters
This declaration closes the structural certificate for FinalModule_1396: the milestone is not merely defined, it is inhabited. In the Recognition Science ledger that tracks domain-coverage passes, an inhabited certificate is the audit token that the diagonal cost identity and the positive-threshold check both hold.
It does not itself advance the forcing chain (T0–T8), the Recognition Composition Law, or the mass ladder. Its role is bookkeeping: a zero-sorry, zero-axiom existence fact that downstream milestone aggregators can cite when counting completed domain modules. With no recorded used-by edges yet, it stands as a leaf certificate ready for a higher-level coverage theorem to collect.
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