IndisputableMonolith.Chemistry.RS_CHM_Structural_005
Chemistry module packaging structural certificate 005: a domain cost built from the RS J-cost, its nonnegativity, a positive canonical threshold, and an inhabited cert record. RS chemistry auditors cite it when wiring structural stability bounds to the cost layer. Content is definitions plus elementary positivity and equality lemmas over Constants and Cost.
claimDefine a domain cost $C$ on the RS cost layer, prove $C \ge 0$ and an evaluation identity, fix a canonical threshold $\theta > 0$, and package an inhabited structural certificate that $C$ and $\theta$ satisfy the CHM-005 criteria.
background
Recognition Science measures mismatch with the J-cost $J(x) = (x + x^{-1})/2 - 1$ (equivalently $\cosh(\log x) - 1$), forced unique by the T5 step of the unified forcing chain and obeying the Recognition Composition Law. The Cost import supplies that functional; Constants supplies the RS-native tick $\tau_0 = 1$ and related units.
This module sits in the Chemistry domain. It introduces a domain-level cost (a specialization or pullback of J-cost to a chemical structural domain), records that the cost is nonnegative, and names a positive canonical threshold against which structural claims are checked.
The certificate record bundles those facts into a single inhabited witness used by downstream chemistry structural arguments, without yet stating a full physical theorem about molecules.
proof idea
Definition-and-certificate module, not a deep theorem. domainCost is introduced as a def over the Cost layer; domainCost_at_eq and domainCost_nonneg are short algebraic or rewriting lemmas. canonicalThreshold is a positive constant (canonicalThreshold_pos). RSCHMStructural005Cert is a structure; cert and cert_inhabited assemble and inhabit it. No multi-step forcing or analytic argument appears at module scope.
why it matters in Recognition Science
Gives Chemistry a named structural-005 certificate tied to the J-cost and a positive threshold, so later CHM claims can depend on one inhabited record rather than ad hoc inequalities. Upstream edges are only Constants and Cost; the forcing landmarks (T5 J-uniqueness, RCL) enter indirectly through Cost. used_by is empty in the graph snapshot, so this module is a leaf provider: it standardizes the 005 interface for future structural or stability theorems rather than closing a parent proof today.
scope and limits
- Does not derive molecular spectra, bond energies, or mass-ladder rungs.
- Does not prove uniqueness of the domain cost beyond the imported J-cost facts.
- Does not fix numerical chemistry constants outside the named threshold.
- Does not discharge broader CHM claims; only packages the 005 cert interface.
- Does not connect to eight-tick, D=3, or alpha-band results.