IndisputableMonolith.Chemistry.Structural_Chemistry_mod77
Module packaging a structural-chemistry certificate for residue class 77 in the Recognition Science cost calculus. It defines a domain cost on the relevant configuration space, a canonical positive threshold, and an inhabited certificate record tying those facts together. Chemists or RS auditors checking discrete structural selection rules would cite it. The content is definitional plus short positivity/nonnegativity lemmas over the imported J-cost.
claimOn the structural-chemistry domain associated with residue $77$, a domain cost $C$ is defined from the Recognition $J$-cost, satisfying $C \ge 0$ and agreeing with its pointwise evaluation. A canonical threshold $\theta > 0$ is fixed, and an inhabited certificate record packages these facts for downstream discharge.
background
Recognition Science measures mismatch with the unique cost $J(x) = (x + x^{-1})/2 - 1$ (equivalently $\cosh(\log x) - 1$), forced by the T5 step of the unified forcing chain and the Recognition Composition Law. The Cost import supplies that $J$-calculus; Constants supplies the RS-native tick $\tau_0 = 1$.
Structural chemistry in this codebase treats discrete configuration classes (here tagged mod 77) as domains on which a derived cost and a selection threshold decide which geometries are admissible. The module sits in the Chemistry domain and exposes sibling objects: a domain cost with equality-at-a-point and nonnegativity lemmas, a strictly positive canonical threshold, and a certificate type with an inhabited instance.
proof idea
Definition module with thin supporting lemmas, not a deep derivation. Domain cost is introduced from the imported Cost layer; domainCost_at_eq is an evaluation identity and domainCost_nonneg lifts $J$-nonnegativity to the domain. The canonical threshold is a positive constant (canonicalThreshold_pos). StructChemistryM77Cert is a structure bundling those facts; cert and cert_inhabited supply a concrete inhabited witness so downstream tactics can discharge the chemistry-side hypothesis interface by instance or constructor.
why it matters in Recognition Science
Gives the Chemistry lane a named, checkable certificate for the mod-77 structural class so later selection or mass-ladder arguments can assume a nonnegative domain cost and a positive threshold without re-proving them. No downstream consumers are wired in the current graph (used_by is empty), so the module is presently a leaf certificate pack rather than a step inside T0–T8. It still anchors the RS pattern that discrete chemical structure is gated by $J$-cost against a canonical cutoff, parallel to Berry-threshold and rung-gap bookkeeping elsewhere in the monolith.
scope and limits
- Does not derive mod-77 residue meaning from the forcing chain T0–T8.
- Does not compute numerical spectra, bond lengths, or experimental chemistry data.
- Does not prove uniqueness of the canonical threshold beyond positivity.
- Does not connect domain cost to the mass ladder or alpha band.
- Does not supply downstream consumers; the use graph is currently empty.