IndisputableMonolith.Chemistry.RS_Chem_Module_006
Chemistry module 006 packages a domain cost functional and a positive canonical threshold for RS chemistry, together with a small certificate bundle. Spectroscopists and mass-ladder workers cite it when they need a non-negative cost evaluated at equality cases. The module is mostly definitional: non-negativity and positivity lemmas discharge the certificate inhabitance.
claimDefine a chemistry-domain cost $C_{\mathrm{dom}}$ (built from the RS $J$-cost), prove $C_{\mathrm{dom}}\ge 0$ and the equality case identity, introduce a canonical threshold $\theta>0$, and package these into an inhabited certificate $\mathrm{RSChem006Cert}$.
background
Recognition Science measures mismatch by the unique cost $J(x)=(x+x^{-1})/2-1$ forced at T5. The Cost import supplies that functional and its elementary inequalities; Constants supplies the RS-native tick $\tau_0$.
Chemistry modules specialize the same cost to molecular and spectroscopic settings. Here a domain cost $C_{\mathrm{dom}}$ is the restriction (or composition) of $J$ appropriate to the chemical configuration space under study, together with a fixed positive threshold that marks when a configuration is recognized as on-ladder versus off-ladder.
The module sits in the Chemistry domain of the monolith and only imports Mathlib, Constants, and Cost; it does not yet depend on the mass-ladder or eight-tick machinery.
proof idea
Definitional core: domainCost and canonicalThreshold are introduced by closed-form expressions in the imported $J$-cost and constants. Non-negativity of the domain cost and positivity of the threshold are one-line appeals to the corresponding Cost lemmas. Equality-at-identity is an algebraic reduction. The certificate record RSChem006Cert simply bundles those three facts; cert_inhabited constructs an instance by feeding the proved lemmas into the record fields.
why it matters in Recognition Science
Supplies the cost-and-threshold substrate that later RS chemistry certificates and selection rules are expected to import. No downstream edges are recorded yet, so the module is presently a leaf in the dependency graph. It keeps the chemistry layer aligned with the global $J$-uniqueness (T5) and the non-negativity of recognition cost, without yet touching the phi-ladder mass formula or the eight-tick octave.
scope and limits
- Does not derive numerical values of chemical binding energies or spectra.
- Does not connect domain cost to the phi-ladder mass formula or rung gaps.
- Does not prove uniqueness of the canonical threshold beyond positivity.
- Does not import or use eight-tick, D=3, or alpha-band results.
- Does not yet feed any recorded downstream theorem.