IndisputableMonolith.Chemistry.Structural_Chemistry_mod87
Module packaging the structural-chemistry certificate for residue class 87: a nonnegative domain cost built from the RS J-cost, a positive canonical threshold, and an inhabited certificate record asserting the cost sits below that threshold. Chemists and RS auditors cite it when checking that a discrete chemistry domain is admissible under the cost calculus. The argument is definitional plus elementary positivity and inequality facts from Constants and Cost.
claimDefine a structural-chemistry domain cost $C_{87}$ from the RS cost $J$, a canonical threshold $\theta_{87}>0$, and a certificate asserting $C_{87}\le\theta_{87}$ (with nonnegativity of $C_{87}$). The module supplies the cost, the threshold, their elementary properties, and an inhabited certificate record for residue 87.
background
Recognition Science measures mismatch by the J-cost $J(x)=(x+x^{-1})/2-1$ (equivalently $\cosh(\log x)-1$), forced unique by the Recognition Composition Law. The Cost import exposes that functional and its basic calculus; Constants supplies the RS-native units and fixed scales against which chemistry domains are scored.
Structural chemistry here is treated as a discrete domain whose admissibility is a cost-versus-threshold comparison. The module introduces a domain cost specialized to the residue-87 structural class, proves it is nonnegative, and fixes a positive canonical threshold against which the cost is compared.
The local setting is certificate-style: rather than deriving a full spectral or bonding model, the file packages the numerical gate (cost below threshold) as a small Lean record that downstream chemistry layers can require as a hypothesis.
proof idea
Definition module with thin supporting lemmas. The domain cost is defined from the imported J-cost; equality-at-evaluation and nonnegativity are recorded as short lemmas. The canonical threshold is a positive constant (positivity lemma immediate from the Constants/Cost layer). The certificate is a structure bundling the inequality; inhabitation is a one-line constructor application once cost, threshold, and the comparison are in hand. No deep tactic proof; the work is naming the gate and discharging positivity.
why it matters in Recognition Science
Gives the Chemistry domain a concrete, checkable gate for structural class 87 inside the RS cost calculus, so later bonding or periodic-structure results can assume an inhabited certificate rather than re-proving the inequality. Feeds any parent development that requires StructChemistryM87Cert or cert_inhabited as a hypothesis interface for admissible chemistry domains. Sits downstream of the Cost layer (J-uniqueness / T5 in the forcing chain) and the Constants scales; it does not itself advance T6–T8, but keeps chemistry aligned with the same cost that forces $\varphi$ and the eight-tick octave elsewhere. No used_by edges are recorded yet, so its present role is as a leaf certificate ready for import.
scope and limits
- Does not derive molecular spectra, bond angles, or reaction rates.
- Does not prove uniqueness of the residue-87 class among all chemistry domains.
- Does not connect the threshold to measured lab constants beyond RS-native cost units.
- Does not discharge global chemistry soundness; only packages one local cost-threshold certificate.
- Does not depend on or extend the T6–T8 forcing steps (phi, eight-tick, D=3).