cert_inhabited

FinalModule_1400 is a structural milestone module in the Recognition Science physics layer (Plan v7, 109th pass). It packages a domain-coverage certificate with zero sorry and zero axioms.

A milestone certificate is a structure with two fields: the diagonal identity that the domain cost of $(r,r)$ is zero for every nonzero real $r$, and the positivity assertion $0 < $ the canonical threshold. The domain cost is the local cost functional used to score coverage of the recognition domain; the canonical threshold is the positive cutoff against which that cost is compared.

The module already defines a concrete value cert assembling those two properties from the sibling lemmas that establish diagonal vanishing and threshold positivity. The present declaration only records that the certificate type is therefore inhabited.

One-line term proof. The anonymous constructor ⟨cert⟩ supplies the existing concrete certificate as a witness for Nonempty MilestoneCert. No tactics, no further lemmas: inhabitance is immediate from the prior definition of that witness.

This is the inhabitance seal on the FinalModule_1400 structural certificate for domain coverage. Downstream consumers that only need existence of a milestone certificate (rather than its internal fields) can cite this fact without unpacking the cost identity or the threshold bound.

In the broader Recognition Science stack it sits in the physics layer as a bookkeeping theorem: the forcing chain (T0–T8), the J-cost, and the phi-ladder are not re-proved here; the module only certifies that the local domain-cost and threshold package is consistent and nonempty. With no external used-by edges recorded, its role is local closure of the milestone rather than a bridge into a named parent theorem.