cert_inhabited
plain-language theorem explainer
The RS 2026 state certificate type is inhabited: there is at least one package of the three structural cost and threshold facts. Anyone citing the 2026 structural status report uses this existence claim. The proof is a one-line term that packages the concrete witness `cert` into `Nonempty`.
Claim. The type of RS 2026 state certificates is nonempty: there exists a package asserting (i) the domain cost vanishes on the diagonal, $\mathrm{domainCost}(r,r)=0$ for all $r\neq 0$; (ii) the domain cost is nonnegative for positive mass and energy arguments; and (iii) the canonical threshold is strictly positive.
background
This module packages a compact "2026 state of the art" certificate for Recognition Science: a structural theorem layer with zero sorry and zero extra axioms, sitting above the completed forcing chain T0–T8 and the derived constants.
The certificate is the structure RS2026State3Cert. Its three fields are pure Prop obligations on the local cost and threshold data: diagonal vanishing of domainCost, nonnegativity of domainCost on the positive orthant, and positivity of canonicalThreshold. Sibling lemmas in the same file discharge those three facts and assemble them into a concrete value cert.
Nonempty α is the standard Mathlib existence type for a type α. Here it records that the certificate structure is not vacuous.
proof idea
One-line term proof. The concrete inhabitant cert : RS2026State3Cert (built from the three sibling proofs of diagonal vanishing, nonnegativity, and threshold positivity) is wrapped as ⟨cert⟩, which is the canonical constructor of Nonempty RS2026State3Cert. No tactics, no further lemmas.
why it matters
This is the existence seal on the 2026 structural certificate. The module doc frames the file as a status snapshot: forcing chain T0–T8 complete, constants derived, zero code sorries. Inhabiting the certificate type turns the three local cost/threshold facts into a single citable nonempty package rather than three loose lemmas.
No downstream dependents are recorded in the graph yet; the declaration is an end-of-module existence marker for auditors and for any later theorem that wants a single Nonempty hypothesis instead of the three field proofs. It does not itself re-derive J-uniqueness, φ, the eight-tick octave, or D = 3; those live upstream in the forcing chain.
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