IndisputableMonolith.Chemistry.RS_Chem_Module_007
Chemistry module 007 packages a domain cost functional on the Recognition cost landscape together with a positive canonical threshold and an inhabited certificate type. Chemists and RS auditors cite it when they need a nonnegativity-checked cost gate for chemical-scale recognition events. The module is mostly definitional: cost identities, positivity lemmas, and a trivial certificate inhabitant.
claimDefine a chemistry-domain cost $C_{\mathrm{chem}}$ built from the Recognition $J$-cost, prove $C_{\mathrm{chem}}\ge 0$ and an evaluation identity at equality cases, fix a canonical threshold $\theta>0$, and supply an inhabited certificate record $\mathrm{RSChem007Cert}$ bundling these facts.
background
Recognition Science measures mismatch with the $J$-cost $J(x)=(x+x^{-1})/2-1$ (equivalently $\cosh(\log x)-1$), forced unique by the Recognition Composition Law. The Cost import exposes that functional and its elementary inequalities; Constants supplies the RS-native tick $\tau_0=1$.
Chemistry modules specialize the same cost to molecular or reaction-scale recognition events. This file introduces a domain cost $C_{\mathrm{chem}}$, records that it is nonnegative, and fixes a strictly positive canonical threshold used as a gate for admissible chemical configurations. The certificate type packages those lemmas so downstream chemistry developments can assume a single inhabited witness rather than re-proving the local cost facts.
proof idea
Definitional module with short supporting lemmas. domainCost is introduced as a Cost-derived functional; domainCost_at_eq and domainCost_nonneg discharge the evaluation identity and nonnegativity by reduction to Cost facts. canonicalThreshold is a positive constant; canonicalThreshold_pos is the positivity proof. RSChem007Cert is a structure bundling the above; cert and cert_inhabited supply a canonical inhabitant, typically by constructor application with the proved fields.
why it matters in Recognition Science
Sits in the Chemistry domain of the RS monolith as a self-contained cost-and-threshold certificate for module 007. No downstream edges are recorded yet, so it presently serves as a local interface: later reaction, bonding, or spectroscopy developments can import the inhabited cert rather than reopen Cost. It does not touch the T0–T8 forcing chain, the mass ladder, or the alpha band; its role is the chemical-scale specialization of $J$-cost nonnegativity and a fixed positive gate.
scope and limits
- Does not derive chemical binding energies or reaction rates from first principles.
- Does not connect domain cost to the phi-ladder mass formula or rung gaps.
- Does not prove uniqueness of the canonical threshold, only positivity.
- Does not feed recorded downstream theorems; used_by is empty.
- Does not address eight-tick timing or spatial dimension forcing (T7–T8).