IndisputableMonolith.Chemistry.IR5
Chemistry-layer module that packages a domain cost, its nonnegativity, and a positive canonical threshold into an IR5 certificate type that is inhabited. Auditors of RS chemistry gates cite it when they need a cost-threshold witness rather than a dynamical derivation. The content is definitions plus elementary positivity and equality lemmas over the imported Cost and Constants layers.
claimThe module defines a domain cost $C$, records $C\ge 0$ and the identity of $C$ at a reference point, fixes a canonical threshold $\theta>0$, and assembles these into an inhabited IR5 certificate bundle.
background
Recognition Science chemistry sits on the same cost calculus used elsewhere in the monolith. The Cost import supplies the J-style recognition cost (and related defect measures); Constants supplies the RS-native tick $\tau_0=1$ and the golden-ratio ladder used to fix numerical gates.
IR5 is the local certificate interface for a chemistry domain gate: one needs a nonnegative domain cost functional, a strictly positive threshold against which that cost is compared, and a single inhabited record that packages both so downstream chemistry lemmas can assume the gate without re-proving positivity.
Sibling names in the module (domainCost, canonicalThreshold, IR5Cert, cert_inhabited) match that pattern: cost definition, threshold definition, certificate structure, and a witness that the structure is nonempty.
proof idea
Definition-and-certificate module, not a deep derivation. Domain cost is introduced as a Cost-layer object; nonnegativity and a pointwise equality lemma are recorded as short lemmas. The canonical threshold is a positive real constant (positivity lemma separate). IR5Cert bundles cost and threshold data; cert / cert_inhabited supply an explicit inhabitant so the interface is not vacuous.
why it matters in Recognition Science
Gives the chemistry domain a named, inhabited cost-threshold certificate (IR5) aligned with the monolith Cost and Constants layers. Downstream chemistry results that need a gate of the form "domain cost below canonical threshold" can depend on this bundle rather than ad-hoc inequalities. No used_by edges are recorded yet, so the module is presently a leaf interface: it closes a local scaffolding slot for chemistry audits without feeding a named parent theorem in the current graph. It does not itself force $\phi$, the eight-tick octave, or $D=3$; those live in the T0--T8 forcing chain.
scope and limits
- Does not derive domain cost from the Recognition Composition Law or J-uniqueness.
- Does not prove any mass, binding-energy, or spectral formula.
- Does not fix numerical values of $\alpha$, $G$, or particle rungs.
- Does not assert dynamical stability or reaction kinetics.
- Does not discharge upstream Cost axioms; it only packages them.