IndisputableMonolith.Chemistry.RS_Chem_Module_010
Chemistry module 010 packages a domain-level cost functional, its nonnegativity and evaluation identities, and a positive canonical threshold into a single inhabited certificate. Chemists and RS auditors cite it when they need a named, checkable bundle that the chemistry sector sits on the same J-cost infrastructure as the rest of the monolith. The module is mostly definitional: cost wrappers plus a Prop-level certificate record with an inhabitation proof.
claimThe module introduces a chemistry domain cost $C_{\mathrm{chem}}$, proves $C_{\mathrm{chem}}\ge 0$ and an evaluation identity at equality cases, fixes a canonical threshold $\theta>0$, and packages these into an inhabited certificate $\mathrm{RSChem010Cert}$.
background
Recognition Science routes every sector through the same cost calculus. The imported Cost layer supplies the J-cost $J(x)=(x+x^{-1})/2-1$ (equivalently $\cosh(\log x)-1$), forced unique by the T5 step of the unified forcing chain. Constants supplies the RS-native tick $\tau_0=1$ and the golden-ratio ladder used for rung placements.
This chemistry module does not re-derive $J$. It specializes the cost interface to a chemistry domain cost, records nonnegativity, and names a positive canonical threshold against which chemical recognition events can be compared. Sibling declarations (domainCost, canonicalThreshold, RSChem010Cert) are the concrete carriers of that specialization.
The local setting is therefore a thin sector adapter: import the global cost and constants, expose a domain cost and threshold, and wrap them in a certificate Prop so downstream chemistry lemmas can depend on one named object rather than a scatter of hypotheses.
proof idea
Definition-heavy module, not a deep proof development. domainCost is introduced as the chemistry specialization of the Cost interface; domainCost_nonneg and domainCost_at_eq discharge the standard cost axioms (nonnegativity and the equality case) by reduction to the upstream Cost lemmas. canonicalThreshold is a positive scalar; canonicalThreshold_pos is the positivity witness. RSChem010Cert is a structure (or Prop bundle) collecting those facts; cert and cert_inhabited supply a concrete inhabitant so the certificate is not vacuous.
why it matters in Recognition Science
Sector certificates keep the chemistry layer aligned with the forcing chain without duplicating T5 J-uniqueness or the Recognition Composition Law. Downstream chemistry results can assume one inhabited RSChem010Cert instead of re-proving cost nonnegativity and threshold positivity in every file. Used-by is currently empty in the graph, so this module is a leaf adapter: it closes a local packaging obligation and stands ready for mass-ladder or bonding lemmas that need a named chemistry cost and threshold. It does not itself force $\phi$, the eight-tick octave, or $D=3$; those remain upstream in the unified forcing chain.
scope and limits
- Does not derive J-uniqueness or the Recognition Composition Law; those stay in Cost and the forcing chain.
- Does not compute numerical binding energies, spectra, or reaction rates.
- Does not fix the fine-structure band or the mass yardstick; only a domain cost and threshold.
- Does not assert experimental chemistry claims beyond the formal certificate bundle.
- Does not yet show up as a dependency of named parent theorems in the graph.