IndisputableMonolith.Chemistry.RS_Chem_Module_012
Chemistry scaffolding module that packages a domain cost, its nonnegativity, a positive canonical threshold, and an inhabited certificate `RSChem012Cert`. Chemists and RS auditors cite it when wiring cost-gated chemical selection into the phi-ladder mass and recognition stack. The module is mostly definitions plus elementary positivity and equality lemmas over the imported J-cost.
claimThe module introduces a chemistry domain cost $C_{\mathrm{dom}}$, proves $C_{\mathrm{dom}}\ge 0$ and an evaluation identity, fixes a canonical threshold $\theta>0$, and packages these into an inhabited certificate for RS chemistry module 012.
background
Recognition Science routes selection and stability through a nonnegative cost built from the unique J-functional $J(x)=(x+x^{-1})/2-1$ (T5). The Cost import supplies that infrastructure; Constants supplies the RS-native tick $\tau_0=1$.
This chemistry module specializes that cost to a domain-level functional $C_{\mathrm{dom}}$ and a fixed positive threshold $\theta$ used as a gate for chemical recognition events. Sibling names indicate elementary structural facts only: evaluation at a point, nonnegativity, and positivity of the threshold.
No forcing-chain step (T0–T8) is closed here. The module sits downstream of Cost/Constants and upstream of any certificate consumers in the chemistry layer.
proof idea
Definition-heavy module. domainCost and canonicalThreshold are introduced as defs; domainCost_nonneg and canonicalThreshold_pos are short nonnegativity/positivity lemmas over the imported cost. domainCost_at_eq is an evaluation identity. RSChem012Cert / cert bundle those facts; cert_inhabited is a one-line inhabitation witness. No deep tactic proof or forcing argument.
why it matters in Recognition Science
Gives the chemistry layer a named, certifiable cost-and-threshold package so later RS chemistry results can assume a single inhabited certificate rather than re-proving cost nonnegativity. Used_by is empty in the graph snapshot, so this is a leaf scaffolding unit: it standardizes Module 012’s interface without yet feeding a named parent theorem. Lands in the broader program that ties chemical selection to J-cost, the phi-ladder mass formula, and recognition thresholds (Berry scale $\varphi^{-1}$, etc.), but does not itself derive masses, $\alpha$, or D=3.
scope and limits
- Does not derive atomic or molecular masses on the phi-ladder.
- Does not prove uniqueness of J or any T5–T8 forcing step.
- Does not fix numerical values of c, hbar, G, or alpha.
- Does not establish reaction kinetics, bonding geometry, or spectroscopic selection rules.
- Does not discharge downstream chemistry theorems; used_by is empty here.