IndisputableMonolith.Chemistry.RS_Chem_Module_011
Chemistry module 011 packages a domain cost functional, a positive canonical threshold, and an inhabited certificate tying them together. A chemist or RS auditor would cite it when checking that a chemical recognition cost stays nonnegative and meets the module's threshold. The file is mostly definitions plus short positivity and equality lemmas over the shared Cost layer.
claimModule 011 introduces a chemistry domain cost $C_{011}$, proves $C_{011}\ge 0$ and an evaluation identity, fixes a canonical threshold $\theta_{011}>0$, and supplies an inhabited certificate $\mathrm{RSChem011Cert}$ bundling these facts.
background
Recognition Science measures mismatch with a nonnegative cost built from the unique $J$-functional forced by the Recognition Composition Law. The shared Cost import supplies that infrastructure; Constants supplies the RS-native tick $\tau_0=1$ used as the time unit.
This chemistry file specializes that cost to domain 011. Sibling declarations name a domain cost, its pointwise evaluation identity, nonnegativity, a canonical threshold with a positivity proof, and a certificate type together with an inhabitation witness. The setting is therefore a thin chemistry-facing wrapper: fix the cost and threshold for this domain, then package them so downstream chemistry checks can assume a single cert rather than re-proving the local inequalities.
proof idea
Definition-heavy module, not a single deep theorem. domainCost and canonicalThreshold are introduced as defs; domainCost_nonneg and canonicalThreshold_pos are short nonnegativity/positivity arguments over the Cost layer; domainCost_at_eq is an evaluation identity. RSChem011Cert bundles the local facts, and cert_inhabited supplies a concrete witness so the certificate type is nonempty.
why it matters in Recognition Science
In the RS chemistry stack, each numbered module pins a domain cost and threshold so later mass, bonding, or recognition checks can cite one certificate instead of rebuilding inequalities. No downstream edges are recorded yet, so this file currently stands as a leaf packaging layer: it closes the local cost/threshold interface for domain 011 and is ready for chemistry theorems that need $C_{011}\ge 0$ and $\theta_{011}>0$. It sits downstream of Constants and Cost only, consistent with a thin specialization rather than a new forcing step (T0–T8 remain upstream foundation).
scope and limits
- Does not derive domain 011 cost from the forcing chain T0–T8.
- Does not compute numerical chemical constants or spectra.
- Does not prove uniqueness of the canonical threshold beyond positivity.
- Does not yet feed recorded downstream chemistry theorems.
- Does not replace the global J-cost theory in the Cost module.