IndisputableMonolith.StandardModel.RS_STD_Structural_003
Certificate module for RS Standard Model structural claim 003: a nonnegative domain cost, its evaluation identity, a positive canonical threshold, and an inhabited certificate packing those facts. Model builders cite it when wiring structural gates that compare domain cost against a fixed cutoff. The file is mostly definitions plus short positivity and equality lemmas over the imported cost layer.
claimDefine a domain cost $C_{\mathrm{dom}}$, prove $C_{\mathrm{dom}}\ge 0$ and an evaluation identity at equality cases, fix a canonical threshold $\theta>0$, and package these into an inhabited structural certificate for RS-STD claim 003.
background
Recognition Science measures mismatch with the J-cost from the Cost layer (the unique cost forced by the Recognition Composition Law, $J(x)=(x+x^{-1})/2-1$). Constants supplies the RS-native tick and related units. This module sits in the StandardModel domain and treats structural claim 003 as a cost-versus-threshold gate rather than a particle-spectrum derivation.
The local objects are a domain cost functional, its nonnegativity, a pointwise evaluation identity, and a strictly positive canonical threshold. Those pieces are then wrapped as a single certificate record so downstream SM structural checks can assume one inhabited bundle instead of re-proving the arithmetic each time.
proof idea
Definition-heavy module: introduce the domain cost and canonical threshold, then discharge short lemmas (nonnegativity, positivity of the threshold, evaluation-at-equality). The certificate type and an inhabitation witness assemble those facts; no deep tactic proof is required beyond the imported cost and constant infrastructure.
why it matters in Recognition Science
Gives a reusable structural certificate (claim 003) for Standard Model wiring in the RS monolith: cost nonnegativity and a positive cutoff in one place. No downstream consumers are linked yet in the graph, so it currently anchors the SM structural stack rather than feeding a named parent theorem. It aligns with the broader program of forcing SM structure from J-cost and RS units, without touching the T5–T8 forcing chain or the mass ladder directly.
scope and limits
- Does not derive SM gauge groups, generations, or coupling constants.
- Does not prove uniqueness of the domain cost beyond the imported Cost layer.
- Does not connect to mass-ladder rungs, alpha band, or eight-tick dynamics.
- Does not supply numerical phenomenology or experimental bounds.
- Does not list downstream theorems; the use graph is currently empty.