IndisputableMonolith.StandardModel.RS_STD_Structural_001
Structural certificate module for Recognition Science Standard Model claim 001: a nonnegative domain cost, a positive canonical threshold, and an inhabited certificate packaging both. Particle-physics auditors cite it when checking that RS cost structure is in place before mass or coupling derivations. The file is mostly definitions plus elementary nonnegativity and positivity lemmas over the imported J-cost.
claimThe module introduces a domain cost $C_{\mathrm{dom}}$ (built from the RS $J$-cost), proves $C_{\mathrm{dom}}\ge 0$ and an evaluation identity, fixes a canonical threshold $\theta_*>0$, and packages these into an inhabited structural certificate $\mathrm{Cert}_{001}$ for Standard Model claim RS-STD-Structural-001.
background
Recognition Science derives physics from a unique cost functional $J$ fixed by the Recognition Composition Law and the forcing chain (T5: $J(x)=(x+x^{-1})/2-1$). The Cost import supplies that $J$-cost; Constants supplies RS-native units (including the tick $\tau_0$).
This StandardModel submodule does not yet derive masses or couplings. It sets the structural layer: a domain-level cost assembled from $J$, a positive threshold against which that cost is compared, and a certificate record that later SM lemmas can assume as a single hypothesis.
Sibling names indicate the local API: domainCost with equality-at-point and nonnegativity, canonicalThreshold with positivity, and RSSTDStructural001Cert / cert / cert_inhabited as the bundled witness.
proof idea
Definition-heavy module, not a deep proof development. Domain cost is defined from the imported Cost layer; nonnegativity is inherited from nonnegativity of $J$ (or a direct rewrite). The evaluation identity is a one-line unfolding. The canonical threshold is a positive constant definition; positivity is immediate arithmetic. The certificate is a structure (or sigma-type) bundling those facts, with an inhabited instance built by supplying the definitions and the two positivity/nonnegativity lemmas.
why it matters in Recognition Science
In the RS stack, Standard Model numerics (phi-ladder masses, $\alpha^{-1}$ band, rung gaps) sit on structural hypotheses: costs are well-defined and nonnegative, and comparison thresholds are positive. This module is the named home for claim RS-STD-Structural-001 and the certificate object downstream SM files can require in one hypothesis.
No used_by edges are recorded yet, so it is currently a leaf certificate provider rather than an intermediate lemma in a proved chain. It sits under the StandardModel domain and imports only Constants and Cost, keeping the structural layer thin before phenomenology modules attach.
Framework landmarks touched only indirectly: $J$-uniqueness (T5) via Cost, and the RS unit system via Constants. Mass-formula and eight-tick material are out of scope here.
scope and limits
- Does not derive particle masses, mixings, or coupling constants.
- Does not prove uniqueness of the domain cost beyond the imported J-cost.
- Does not connect the threshold to measured SM observables.
- Does not discharge later SM claims; only packages structural hypotheses.
- Does not reference the eight-tick octave, D=3, or alpha band numerics.