cert
plain-language theorem explainer
Packages the three structural properties of the chemistry-domain cost at recognition rung 77 into a single certificate record: diagonal vanishing, non-negativity on positive arguments, and a strictly positive canonical threshold. Anyone citing the structural chemistry prediction at this rung uses this bundle. The body is a pure structure assembly from three already-proved sibling lemmas.
Claim. There is a structural chemistry certificate at rung 77 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
The module states a structural Recognition Science prediction for the Chemistry domain at recognition rung 77, with status structural theorem (zero sorry, zero axiom). The local cost is the chemistry-domain cost, a real bivariate function built from the RS J-cost (the unique cost forced by the Recognition Composition Law, $J(x)=(x+x^{-1})/2-1$).
A structural certificate here is a record of three elementary cost properties: the cost vanishes on the diagonal away from zero, stays non-negative for positive mass/energy-like arguments, and the domain's canonical threshold is positive. Upstream, non-negativity of recognition-event cost is already known from ObserverForcing: "The cost of any recognition event is non-negative," via $J$-cost non-negativity on positive states.
Sibling lemmas domainCost_at_eq, domainCost_nonneg, and canonicalThreshold_pos discharge exactly those three fields for this chemistry instance.
proof idea
One-line structure construction. The definition inhabits StructChemistryM77Cert by assigning the three sibling proofs fieldwise: diagonal vanishing from domainCost_at_eq, non-negativity from domainCost_nonneg, and threshold positivity from canonicalThreshold_pos. No further tactic work.
why it matters
This is the named certificate object for the Chemistry structural prediction at rung 77 in the Plan v7 pass series. It freezes the three cost axioms the rest of the chemistry structural layer can quote without reopening J-cost or threshold lemmas. In the broader RS chain it sits downstream of T5 J-uniqueness and the non-negativity of recognition cost, and it specializes those facts to the chemistry domain cost at the rung-77 slot on the phi-ladder. No downstream consumers are wired in this graph snapshot; the immediate sibling cert_inhabited is the natural next citation point.
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