cert_inhabited
plain-language theorem explainer
The milestone certificate type is inhabited: there is a packed witness that domain cost vanishes on the diagonal for every nonzero real and that the canonical threshold is strictly positive. Anyone citing the FinalModule_1397 domain-coverage structural milestone uses this existence fact. The proof is a one-line term that feeds the concrete certificate value into Nonempty.
Claim. The type of milestone certificates is nonempty. Equivalently, there exists a certificate packing (i) $\mathrm{domainCost}(r,r)=0$ for every real $r\neq 0$, and (ii) the canonical threshold is strictly positive.
background
FinalModule_1397 is a Recognition Science structural milestone module (Plan v7, 109th pass). Its status line is explicit: structural theorem, zero sorry, zero axiom. The local object is a domain-coverage certificate, not a dynamical derivation of masses or couplings.
A milestone certificate is a structure with two fields. The first asserts that the module's domain cost vanishes on the diagonal: for every nonzero real $r$, the cost of the pair $(r,r)$ is zero. The second asserts that the module's canonical threshold is strictly positive. Both fields are pure real-analytic side conditions on the cost and threshold definitions imported from Constants and Cost.
The concrete certificate value already assembles those two facts. The present declaration only records that the certificate type is inhabited, so downstream code can demand a Nonempty witness without naming the concrete value.
proof idea
One-line term proof. Nonempty is introduced by the anonymous constructor applied to the already-built certificate value, so the witness is exactly that certificate. No tactics, no lemmas, no rewriting.
why it matters
This is the existence seal on the FinalModule_1397 structural certificate. The module doc frames the file as a Recognition Science domain-coverage milestone with zero sorry and zero axiom; inhabitation is the clean top-level claim that the certificate type is not vacuous.
It does not itself touch the forcing chain (T0–T8), the Recognition Composition Law, or the phi-ladder mass formula. It only certifies that the local cost-and-threshold package is realized. With empty used-by edges in the supplied graph, its role is archival and compositional: later milestone aggregators can require Nonempty of this certificate type without re-proving the diagonal cost identity or threshold positivity.
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