IndisputableMonolith.StandardModel.RS_STD_Structural_008
Certificate module for Standard Model structural item 008: a non-negative domain cost compared against a positive canonical threshold. It packages the inequality and an inhabited certificate type so downstream SM audits can cite a single named witness. The argument is definitional plus elementary positivity and evaluation lemmas over the RS cost layer.
claimDefine a domain cost $C_{\mathrm{dom}}$ (non-negative), a canonical threshold $\theta>0$, and a structural certificate asserting the 008 comparison between $C_{\mathrm{dom}}$ and $\theta$ in RS-native units built from the $J$-cost and constants layer.
background
Recognition Science measures mismatch with the unique cost $J(x)=(x+x^{-1})/2-1$ forced by the Recognition Composition Law. The Cost import supplies that functional; Constants supplies the RS time quantum $\tau_0=1$ tick and related native units.
This module sits in the Standard Model structural track. It introduces a domain-level cost functional, records that the cost is non-negative, and fixes a positive canonical threshold against which the structural 008 claim is checked. Sibling equalities pin evaluation at distinguished points so the certificate is not free-floating.
The local setting is certificate packaging rather than a new dynamical law: one named cert type bundles the comparison for later SM audits.
proof idea
Definition module with short supporting lemmas. Domain cost is introduced as a Cost-layer functional; non-negativity and pointwise evaluation are recorded directly. The canonical threshold is a positive constant in RS units. The certificate type and an inhabited instance wrap those facts so callers obtain a single witness without replaying the inequalities.
why it matters in Recognition Science
Closes structural slot 008 in the RS Standard Model ledger: domain cost versus a fixed positive threshold, ready for audit. No downstream edges are recorded yet; the module is a leaf certificate meant to be imported by higher SM structural aggregates. It ties the Cost/$J$ layer and Constants into a named SM claim rather than leaving the comparison ad hoc. Landmarks touched only indirectly: $J$-uniqueness (T5) via Cost, and RS-native units from Constants.
scope and limits
- Does not derive the Standard Model gauge group or particle content.
- Does not prove numerical mass or coupling values beyond the threshold comparison.
- Does not establish uniqueness of the domain cost functional itself.
- Does not discharge other RS_STD structural indices outside 008.
- Does not connect to forcing-chain steps T6–T8 beyond shared Cost/Constants imports.