IndisputableMonolith.StandardModel.RS_STD_Structural_002
Structural certificate module for Recognition Science Standard Model item 002: a non-negative domain cost functional and a strictly positive canonical threshold. It packages equality-at-evaluation, non-negativity, and positivity into an inhabited certificate record. Model builders cite it when gating domain-level acceptance against the RS cost. The content is definitional plus elementary positivity lemmas over the imported cost layer.
claimDefine a domain cost $C_{\mathrm{dom}}$ (non-negative), a canonical threshold $\theta>0$, and a certificate record asserting $C_{\mathrm{dom}}\ge 0$, evaluation identities for $C_{\mathrm{dom}}$, and $\theta>0$. The certificate type is inhabited.
background
Recognition Science measures mismatch with a unique cost $J$ forced by the Recognition Composition Law; the Cost import supplies that layer, and Constants supplies the RS-native tick $\tau_0=1$. This module sits in the Standard Model structural track: it does not derive particle spectra, but records a domain-level cost and a fixed positive threshold used as an acceptance gate.
Sibling definitions introduce the domain cost, its pointwise evaluation identity, non-negativity, the canonical threshold and its positivity, then wrap those facts in a certificate structure with an inhabitation witness. Upstream material is only the Constants and Cost modules; no forcing-chain theorem is invoked here.
proof idea
Definition-and-certificate module rather than a deep proof development. Domain cost and canonical threshold are introduced as defs; non-negativity and positivity are short lemmas over the Cost import; evaluation equality is a definitional or one-line identity. The certificate record bundles those props, and inhabitation is a constructor application assembling the proved fields.
why it matters in Recognition Science
Gives a reusable structural gate (cost plus positive threshold) for Standard Model domain checks inside the RS monolith. No downstream used_by edges are recorded yet, so the module is a leaf certificate rather than a step in T0–T8. It keeps domain acceptance aligned with the non-negative $J$-cost discipline without claiming mass formulae, $\alpha$ bounds, or eight-tick dynamics. Parent consumers would be higher Standard Model assembly theorems that require an inhabited structural certificate of this shape.
scope and limits
- Does not derive particle masses, charges, or coupling constants.
- Does not prove uniqueness of the domain cost beyond the local defs.
- Does not connect the threshold to phi-ladder rungs or Berry thresholds.
- Does not invoke T5–T8 forcing (J-uniqueness, phi, eight-tick, D=3).
- Does not supply numerical comparison to experimental SM data.