IndisputableMonolith.Chemistry.Structural_Chemistry_mod47
Defines the structural-chemistry domain cost and a canonical positivity threshold for the mod-47 certificate layer. Supplies nonnegativity of the cost, equality at the evaluation point, and an inhabited certificate record. Chemists and RS auditors cite it when wiring structural constraints into the cost calculus. The module is mostly definitions plus short positivity lemmas over the imported J-cost.
claimOn the structural-chemistry domain one has a cost $C_{\mathrm{sc}}$ built from the RS $J$-cost, a canonical threshold $\theta>0$, and a certificate record asserting $C_{\mathrm{sc}}\ge 0$ together with the threshold positivity data (mod-47 packaging).
background
Recognition Science measures mismatch by the unique cost $J(x)=(x+x^{-1})/2-1$ forced at T5 of the unified forcing chain. The Cost import exposes that functional; Constants supplies the RS-native tick $\tau_0=1$. Structural chemistry here means the discrete packing and bonding constraints that sit on the $\phi$-ladder mass formula, not continuum quantum chemistry.
This module packages those constraints as a domain cost $C_{\mathrm{sc}}$ and a single positive threshold used by certificate checks. Sibling names indicate pointwise evaluation equality, nonnegativity, threshold positivity, and an inhabited certificate type StructChemistryM47Cert. No external physics axioms beyond Cost and Constants are imported.
proof idea
Definition-first module. The domain cost is introduced as a def over the imported $J$-cost; nonnegativity and evaluation-at-equality are short lemmas. The canonical threshold is a positive constant with a one-line positivity proof. The certificate record bundles those facts and is shown inhabited by constructing a default witness. No deep tactic scripts or multi-step forcing arguments appear.
why it matters in Recognition Science
Places structural chemistry inside the same cost calculus used for the forcing chain and the $\phi$-ladder mass formula. Downstream consumers (none linked yet in the graph) would discharge structural side-conditions by inhabiting the mod-47 certificate rather than re-proving $J\ge 0$ locally. Ties chemistry scaffolding to T5 $J$-uniqueness and the RS-native constants without claiming new particle or bond spectra. Closes a named certificate interface so later chemistry theorems can depend on a single inhabited record.
scope and limits
- Does not derive molecular geometries or bond angles from first principles.
- Does not prove the full mass formula or rung assignments for nuclides.
- Does not fix $\alpha$ or other continuum constants beyond Cost/Constants imports.
- Does not assert experimental structural-chemistry predictions.
- Does not discharge downstream theorems; used_by is empty in the graph.