ElectroweakZeroParamScoreCardCert
plain-language theorem explainer
Certificate structure packaging the electroweak zero-parameter claim: SM counts four free EW parameters (g, g', v, λ) while RS counts zero, with α⁻¹ inside (137.030, 137.039), the Weinberg product identity sin²θ_W cos²θ_W = (8-φ)/36, and four forcing inputs each tied to a source theorem. Auditors of the RS electroweak reduction cite this bundle. The structure is pure data; inhabitance is proved by assembling sibling lemmas.
Claim. A certificate asserting that the Standard Model electroweak sector has exactly four free parameters, the Recognition Science count is zero, the inverse fine-structure constant satisfies $137.030 < \alpha^{-1} < 137.039$, $\sin^2\theta_W^{\mathrm{RS}}\cos^2\theta_W^{\mathrm{RS}}=(8-\varphi)/36$ with the product strictly positive, there are exactly four forcing inputs and four source theorems, and the parameter reduction equals four.
background
In the Standard Model the electroweak sector is parameterized by four independent quantities: the SU(2) and U(1) gauge couplings $g$ and $g'$, the Higgs vacuum expectation value $v$, and the Higgs self-coupling $\lambda$. Recognition Science claims all four are forced from the T5–T7 chain and gauge-embedding geometry, leaving zero free parameters.
The module enumerates four forcing inputs (electromagnetic $\alpha$, Weinberg angle, $Z$-mass rung, tree-level VEV) and four source theorems (J-cost uniqueness T5, $\varphi$-forcing T6, eight-tick T7, cube gauge embedding). The RS Weinberg angle is fixed by geometry as $\sin^2\theta_W=(3-\varphi)/6$, so $\cos^2\theta_W=1-\sin^2\theta_W$. The inverse fine-structure constant is the closed form $\alpha^{-1}=44\pi\exp(-w_8\ln\varphi/(44\pi))$ (equivalently the seed-exponential assembly), required to lie in the band $(137.030,137.039)$.
proof idea
This is a structure definition, not a proved theorem. Each field is a proposition that a later constructor must discharge. The inhabitance theorem builds an instance by reflexivity on the SM count of four, the lemma that the RS count is zero, the numerical certificate that $\alpha^{-1}$ lies in band, the algebraic product identity for $\sin^2\theta_W\cos^2\theta_W$, positivity of that product, Fintype cardinality of the two four-constructor inductives, and the arithmetic reduction $4-0=4$.
why it matters
This scorecard is the formal packaging of the module claim that RS electroweak physics is zero-parameter. Downstream, the inhabitance theorem proves the certificate is nonempty (module status: 0 sorry, 0 axiom). It ties directly to forcing-chain landmarks T5 (J-uniqueness), T6 ($\varphi$ as self-similar fixed point), T7 (eight-tick octave), and the cube gauge embedding that fixes the Weinberg angle. The $\alpha$ window matches the RS-native band $(137.030,137.039)$. The exact infrared boundary $\alpha^{-1}(0)=137.035999$ remains OPEN upstream and is not closed here.
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