cert
plain-language theorem explainer
A packaged certificate that reaction-pathway cost vanishes on the diagonal, stays nonnegative for positive major/minor arguments, and that the canonical selectivity threshold is positive. Anyone citing the structural regioselectivity result (major/minor = φ^n) needs this bundle as the cost-side hypotheses. The definition is a pure structure assembly of three already-proved sibling lemmas.
Claim. There is a certificate recording three facts about the reaction-pathway cost $C$: $C(r,r)=0$ for every $r\neq 0$; $C(m,e)\ge 0$ whenever $m>0$ and $e>0$; and the canonical selectivity threshold $T$ satisfies $T>0$.
background
The module treats regioselectivity as a J-cost comparison on competing reaction pathways. In Recognition Science the unique cost is $J(x)=(x+x^{-1})/2-1$ (T5), forced by the Recognition Composition Law; here that cost is specialized to a two-argument domain cost $C(m,e)$ on major and minor pathway coordinates.
The certificate structure packages the three elementary cost properties needed before any selectivity ratio can be stated: vanishing on the equal-ratio diagonal, nonnegativity off the diagonal for positive arguments, and positivity of a fixed threshold against which rung advantages are measured. Upstream, nonnegativity of recognition cost is already known from ObserverForcing (cost_nonneg: every recognition event has nonnegative cost, via Jcost_nonneg).
Local setting (module doc): structural theorem, zero sorry/axiom; predicted major/minor ratio is $\varphi^n$ for an $n$-rung recognition advantage, so $n=1$ gives the moderate $\varphi:1\approx 1.618:1$ (~62%) selectivity band.
proof idea
One-line structure construction. The three fields are filled by direct assignment of the sibling lemmas domainCost_at_eq (diagonal vanishing), domainCost_nonneg (nonnegativity for positive major/minor), and canonicalThreshold_pos (strict positivity of the threshold). No new algebra is performed; the definition only bundles those three facts into the certificate type.
why it matters
This certificate is the cost-side interface for the module's structural regioselectivity claim: major/minor product ratio equals $\varphi^n$ when the recognition-rung advantage is $n$. Without diagonal vanishing, nonnegativity, and a positive threshold, the comparison that produces the $\varphi$-ladder ratio is not well-posed.
It sits inside the chemistry layer that imports Constants and Cost, so it inherits the forced $J$ from T5 and the self-similar scale $\varphi$ from T6. The module itself reports status STRUCTURAL THEOREM (0 sorry, 0 axiom) and targets moderate regioselectivity consistent with $n=1$. No downstream consumers are wired yet in the graph; the immediate sibling cert_inhabited is the natural next use site.
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