IndisputableMonolith.StandardModel.RS_STD_Structural_006
Structural certificate module for Standard Model claim 006 in the Recognition Science ledger. It packages a nonnegative domain cost functional, a strictly positive canonical threshold, and an inhabited certificate record tying the two together. A model builder cites it when checking that a sector or coupling sits above the RS cost floor. The content is definitional plus elementary positivity lemmas, not a deep existence proof.
claimDefine a domain cost $C_{\mathrm{dom}}$ on the relevant Standard Model sector, prove $C_{\mathrm{dom}}\ge 0$ and $C_{\mathrm{dom}}(x)=C_{\mathrm{dom}}(x)$ at evaluation points, fix a canonical threshold $\theta>0$, and assemble an inhabited certificate record asserting the structural 006 claim relative to $(C_{\mathrm{dom}},\theta)$.
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 Recognition Composition Law. The Cost import supplies that functional and its elementary inequalities; Constants supplies the RS-native tick $\tau_0=1$ and related units.
This module sits in the Standard Model structural layer. Domain cost is the sector-level specialization of J (or a monotone transform of it) used to score how far a coupling, mass ratio, or charge assignment sits from the self-similar fixed point $\varphi$. The canonical threshold is the positive cutoff against which that score is compared when issuing a pass/fail structural certificate.
Sibling names indicate the usual RS certificate pattern: a cost, its nonnegativity, a positive threshold, and a bundled Cert type with an inhabited instance so downstream checkers can demand a witness rather than a bare Prop.
proof idea
Definition module with thin positivity lemmas. domainCost is introduced as a real-valued functional; domainCost_at_eq is a trivial evaluation identity; domainCost_nonneg reduces to nonnegativity of the underlying J-cost (or a sum of such terms) from the Cost import. canonicalThreshold is a positive constant (likely a fixed power of $\varphi$ or a plain rational in RS units); canonicalThreshold_pos is immediate arithmetic. The certificate record RSSTDStructural006Cert packages cost and threshold; cert and cert_inhabited supply a concrete witness so the structural claim is data, not an open hypothesis.
why it matters in Recognition Science
Closes the ledger entry for Standard Model structural item 006: a machine-checkable cost-versus-threshold certificate rather than a prose claim. No downstream edges are recorded yet, so the module is a leaf certificate in the present graph; parent consumers are expected to be SM aggregation theorems that fold many RSSTDStructural00kCert witnesses into a global Standard Model structural theorem.
In the broader forcing chain this is application-layer bookkeeping, not T5–T8 uniqueness. It still matters: RS claims about the Standard Model are only as strong as the certificates that pin each sector to the J-cost floor and the $\varphi$-ladder. Without inhabited certs, those claims remain hypothesis interfaces.
scope and limits
- Does not derive the numerical value of any SM coupling or mass from first principles.
- Does not prove uniqueness of the domain cost; only nonnegativity and certificate packaging.
- Does not connect to electroweak breaking, CKM/PMNS data, or running couplings.
- Does not discharge T5–T8 forcing; those live in UnifiedForcingChain.
- Does not assert experimental agreement beyond the structural cost threshold.