IndisputableMonolith.StandardModel.RS_STD_Structural_010
Structural certificate module for a Standard Model domain-cost gate in Recognition Science. It packages a nonnegative domain cost, a positive canonical threshold, and an inhabited certificate record that asserts the cost sits at the threshold. Model builders cite it when wiring SM sector checks to the J-cost infrastructure. The content is mostly definitions plus elementary positivity and equality lemmas.
claimDefine a domain cost $C$ (nonnegative), a canonical threshold $\theta>0$, and a structural certificate asserting the equality $C=\theta$ (or the matching evaluation identity) for the RS Standard Model structural check labeled 010.
background
Recognition Science measures mismatch with the J-cost $J(x)=(x+x^{-1})/2-1$ from the Cost layer, with RS-native constants (including the tick $\tau_0=1$) from Constants. Standard Model structural modules turn those primitives into sector-level gates: a domain cost that scores how far a configuration sits from the forced RS pattern, and a canonical threshold that marks the acceptance cut.
This module sits in the StandardModel domain. It does not re-derive $J$ or the forcing chain; it only introduces the local cost/threshold pair and the certificate record that packages the structural claim for check 010. Upstream imports are Mathlib plus Constants and Cost.
proof idea
Definition-heavy module. domainCost and canonicalThreshold are introduced as defs; domainCost_nonneg and canonicalThreshold_pos discharge the obvious sign obligations; domainCost_at_eq records the evaluation identity used by the gate. RSSTDStructural010Cert is a Prop/structure bundling those facts, with cert and cert_inhabited supplying a concrete inhabited instance. No deep tactic proof: elementary nonnegativity and equality scaffolding over Cost/Constants.
why it matters in Recognition Science
Gives the Standard Model stack a named structural certificate (010) so later SM assembly can treat domain-cost gating as a single inhabited record rather than ad-hoc inequalities. It ties the sector check to the shared J-cost and constant layer without reopening T5–T8. No downstream used_by edges are recorded yet; the module is a leaf certificate package meant for SM structural audits and cert aggregation.
scope and limits
- Does not derive the Standard Model particle content or gauge group.
- Does not prove uniqueness of the domain cost or threshold from the forcing chain.
- Does not compute numerical masses, couplings, or alpha.
- Does not discharge global SM consistency; only the local 010 certificate bundle.
- Does not add new physics beyond Cost/Constants wrappers.