IndisputableMonolith.Chemistry.RS_Chem_Module_005
Chemistry module 005 packages a domain-level cost functional, its nonnegativity, a positive canonical threshold, and an inhabited certificate record for RS chemistry. Formal chemists working the phi-ladder mass and recognition-cost side would cite it when wiring domain costs into larger certificates. The content is mostly definitions plus elementary positivity and inhabitation lemmas over the shared Cost and Constants imports.
claimOn the RS chemistry domain, define a domain cost $C$, prove $C \ge 0$ and $C$ agrees with its pointwise evaluation, fix a canonical threshold $\theta > 0$, and exhibit an inhabited certificate bundling these facts for module 005.
background
Recognition Science measures mismatch with a nonnegative cost built from the unique $J$-functional $J(x)=(x+x^{-1})/2-1$ (equivalently $\cosh(\log x)-1$). The Cost import supplies that infrastructure; Constants supplies RS-native units (including the tick $\tau_0$).
This module specializes that cost language to a chemistry domain: a domain cost map, equality with its evaluation-at-a-point form, and a canonical positive threshold used as a cutoff or acceptance scale. The certificate record packages those facts so downstream chemistry developments can assume a single inhabited witness rather than re-proving the local lemmas.
proof idea
Definition-and-lemma module, not a deep derivation. Domain cost is introduced as a def; agreement-at-evaluation and nonnegativity are short lemmas reducing to the imported Cost nonnegativity and definitional unfolding. The canonical threshold is a positive constant (positivity is elementary). The certificate type bundles the above; inhabitation is a constructor application assembling those lemmas.
why it matters in Recognition Science
Places a named chemistry-domain cost and threshold into the RS monolith so later chemistry results can cite one certificate rather than ad-hoc cost facts. It sits on Constants and Cost only; no downstream users are wired yet in the graph. In the broader framework it is scaffolding for chemical recognition costs on the phi-ladder side (mass yardsticks, rung gaps), not a step of the T0–T8 forcing chain. Its value is organizational: a stable interface for module 005 chemistry claims.
scope and limits
- Does not derive molecular masses, spectra, or reaction rates.
- Does not prove uniqueness of the domain cost beyond the imported Cost facts.
- Does not connect the threshold to alpha, G, or the eight-tick octave.
- Does not discharge any global chemistry theorem; used_by is empty.
- Does not specify units conversion outside RS-native Constants.