cert
plain-language theorem explainer
Packages three structural facts about the chemistry-domain cost at recognition rung 47 into one certificate record: diagonal vanishing, non-negativity off the identity, and a strictly positive canonical threshold. Cited by anyone invoking the structural chemistry prediction at that rung. The definition is a direct structure instance wiring three already-proved sibling lemmas.
Claim. There is a structural chemistry certificate at recognition rung 47 asserting: (i) the domain cost vanishes on the diagonal, $C(r,r)=0$ for all $r\neq 0$; (ii) $C(m,e)\ge 0$ whenever $m>0$ and $e>0$; (iii) the canonical threshold $T$ satisfies $T>0$.
background
This module records a structural Recognition Science prediction for the Chemistry domain at recognition rung 47 (Plan v7, 120th pass). Status is a structural theorem: zero sorry, zero axioms.
The certificate structure demands three properties of the local domain cost $C$. First, identity: $C(r,r)=0$ for nonzero $r$, so matched measure and expectation carry zero cost. Second, non-negativity for positive arguments, aligning with the global fact that every recognition-event cost is non-negative (via the J-cost minimum at $x=1$). Third, the canonical threshold used to gate the domain is strictly positive.
Upstream, ObserverForcing supplies the general non-negativity of recognition costs through J-cost positivity. The local lemmas domainCost_at_eq, domainCost_nonneg, and canonicalThreshold_pos specialize that picture to the chemistry rung-47 cost.
proof idea
One-line structure instance. The three fields of the certificate are filled by the sibling lemmas that already prove diagonal vanishing of the domain cost, non-negativity of the domain cost on positive arguments, and positivity of the canonical threshold. No further tactic work.
why it matters
Gives a single named inhabitant of the structural chemistry certificate at rung 47, so downstream chemistry arguments can assume the three cost axioms by projecting fields rather than re-proving them. Fits the RS pattern of domain certificates that package J-cost identity, non-negativity, and a positive threshold before any mass-ladder or spectroscopic claim. Module status is structural theorem (0 sorry, 0 axiom). No downstream consumers are wired yet; the immediate sibling is the inhabitedness witness for the same certificate type. Does not itself touch the forcing chain T0–T8, RCL, or the alpha band; it only locks the cost interface for this chemistry rung.
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