cert
plain-language theorem explainer
Packages three elementary properties of the chemistry-domain cost at recognition rung 97 into a single structural certificate: diagonal vanishing, non-negativity on positive arguments, and a positive canonical threshold. Anyone citing the chemistry structural certificate at mod 97 uses this inhabitant. The construction is a pure field assembly of three sibling lemmas; no new algebra is proved here.
Claim. There is a structural chemistry certificate at recognition rung 97 consisting of: (i) $\mathrm{domainCost}(r,r)=0$ for all $r\neq 0$; (ii) $\mathrm{domainCost}(m,e)\ge 0$ whenever $m>0$ and $e>0$; (iii) the canonical threshold is strictly positive.
background
This module states the Recognition Science structural certificate for the Chemistry domain at recognition rung 97 (Plan v7, 120th pass). Status is structural theorem: zero sorry, zero axiom. The certificate is a three-field structure whose fields are the minimal cost axioms needed to treat chemistry as an RS domain.
Domain cost is the local cost functional on pairs of positive reals used for this domain; the certificate demands it vanish on the diagonal (equal measure and expectation) and stay non-negative off it. The canonical threshold is the positive cutoff against which domain cost is compared in structural predictions.
Upstream, non-negativity of recognition cost is already forced in ObserverForcing: "The cost of any recognition event is non-negative," via the J-cost minimum. The chemistry certificate reuses that pattern at the domain level rather than re-deriving J-uniqueness.
proof idea
One-line structure inhabitant. The three fields of StructChemistryM97Cert are filled by the sibling lemmas domainCost_at_eq, domainCost_nonneg, and canonicalThreshold_pos respectively. No tactics, no rewriting, no new proof obligations: pure record assembly of already-proved facts in the same module.
why it matters
Gives the inhabited structural certificate that the Chemistry domain at rung 97 meets the RS cost axioms (diagonal zero, non-negativity, positive threshold). Module status marks this as a structural theorem with no sorry and no axiom, so downstream chemistry predictions can cite a single packed witness rather than three separate lemmas.
No used_by edges are recorded yet; the natural consumers are any chemistry-domain forcing or mass/threshold comparisons that need a StructChemistryM97Cert hypothesis. In the broader framework this sits under the cost layer (J-cost non-negativity, T5 uniqueness of J) specialized to a chemistry rung, not under the T0–T8 forcing chain itself. It closes the local scaffolding for mod-97 chemistry structure without claiming spectroscopic or bonding numerics.
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