IndisputableMonolith.StandardModel.RS_STD_Structural_004
Structural certificate module for RS Standard Model item 004. It packages a nonnegative domain cost, a positive canonical threshold, and an inhabited certificate record tying those facts together. Cite it when auditing SM structural claims that compare a domain cost against a fixed threshold. The module is mostly definitions plus elementary nonnegativity and positivity lemmas over the RS cost layer.
claimDefine a domain cost $C_{\mathrm{dom}}$, prove $C_{\mathrm{dom}}\ge 0$, fix a canonical threshold $\theta>0$, and assemble an inhabited certificate $\mathrm{Cert}_{004}$ asserting the structural comparison of domain cost against $\theta$ in RS-native units.
background
Recognition Science measures mismatch with a nonnegative cost built from the unique $J$-functional forced by the Recognition Composition Law. The Cost import supplies that layer; Constants supplies the RS tick and related native units.
This module sits in the StandardModel structural track. Item 004 is a certificate-shaped packaging: a domain-level cost, its evaluation identity, nonnegativity, a positive canonical threshold, and a record that those pieces inhabit a single certificate type. No particle spectrum or coupling fit is claimed here; the objects are structural gates used by later SM audits.
Upstream, only Constants and Cost are imported. The local vocabulary is therefore cost nonnegativity and a fixed positive threshold, not the full forcing chain T0–T8.
proof idea
Definition-heavy module. Domain cost and the canonical threshold are introduced as defs; nonnegativity and positivity are short lemmas over the Cost/Constants layer. The certificate type and an inhabitation witness bundle those facts. No deep tactic proof: algebraic identities and sign facts, then a structure value.
why it matters in Recognition Science
Gives a named, checkable structural gate (RS_STD_Structural_004) inside the StandardModel domain: domain cost versus a positive canonical threshold, with an inhabited certificate. Downstream use is not wired in this graph snapshot (used_by empty), so the module is presently a leaf certificate package rather than a proved input to a named parent theorem. It supports the broader RS program of turning SM structural claims into Lean certificates over the same cost language as the forcing chain, without yet touching mass ladders, $\alpha$, or eight-tick dynamics.
scope and limits
- Does not derive the Standard Model gauge group or particle content.
- Does not prove numerical mass or coupling predictions.
- Does not connect domain cost to the phi-ladder mass formula.
- Does not cite or close T5–T8 forcing steps.
- Does not supply downstream consumers in the current dependency graph.