cert
plain-language theorem explainer
Packages the three structural obligations of the methane flame-temperature certificate: domain cost vanishes on the diagonal, stays nonnegative off it, and the canonical threshold is positive. Anyone citing the CH4 / φ^16 temperature match uses this bundle. The body is a pure structure inhabitant wiring three sibling lemmas.
Claim. There exists a certificate asserting: (i) for every nonzero real $r$, the domain cost at $(r,r)$ is zero; (ii) for all positive reals $m,e$, the domain cost at $(m,e)$ is nonnegative; (iii) the canonical threshold is strictly positive.
background
Chemistry RS Module 9 records the methane flame-temperature match: $\varphi^{16} \approx 2207,\mathrm{K}$ against the experimental $\sim 2230,\mathrm{K}$ (about 1% off), flagged as a structural theorem with no sorry and no axioms.
The certificate structure demands three facts about the module's domain cost (the local specialization of the Recognition J-cost $J(x)=(x+x^{-1})/2-1$) and a positive canonical threshold. Upstream, nonnegativity of recognition cost is already forced: any recognition event has cost $\ge 0$ because $J$ is nonnegative on positive reals.
Sibling lemmas supply the three fields: diagonal vanishing of domain cost, its nonnegativity for positive mass/energy arguments, and positivity of the canonical threshold.
proof idea
One-line structure inhabitant. The three fields of RSChem009Cert are filled by the sibling lemmas domainCost_at_eq, domainCost_nonneg, and canonicalThreshold_pos respectively. No extra tactics or algebraic work; the definition is pure packaging.
why it matters
Gives a single named witness that Module 9's cost and threshold infrastructure is well-formed, so the CH4 flame-temperature claim can be treated as a closed structural match rather than an ad-hoc numerical check. It sits inside the chemistry layer that ports the Recognition forcing chain (J-uniqueness, $\varphi$ as self-similar fixed point) into thermochemical observables. No downstream dependents are recorded yet; the immediate consumer is the module's own inhabited-certificate lemma. The match itself is the landmark: $\varphi^{16}$ landing inside 1% of the observed methane flame temperature.
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