four_source_theorems

The electroweak zero-parameter scorecard contrasts the Standard Model's four independent EW parameters ($g$, $g'$, $v$, $\lambda$) with the RS claim that all four are forced. Module context: $\alpha^{-1}$ from the T5/T6/T7 chain, $\sin^2\theta_W=(3-\varphi)/6$ from gauge embedding geometry, $m_Z$ on the $\varphi$-ladder, and $v$ from the tree-level relation; RS free-parameter count is zero.

EWSourceTheorem is the inductive tag type whose constructors name the four proved origins: T5 J-cost uniqueness $J(x)=(x+x^{-1})/2-1$, T6 $\varphi$ as self-similar fixed point, T7 eight-tick octave (period $2^3$), and cube gauge embedding. The type derives Fintype and DecidableEq, so its cardinality is a closed computational fact rather than an analytic estimate.

One-line tactic proof: by decide. Lean uses the derived Fintype instance on the four-constructor inductive to evaluate Fintype.card EWSourceTheorem and discharge equality to 4 by computation. No lemmas are invoked beyond the automatic instances.

This cardinality pins the "four source theorems" half of the scorecard bookkeeping. Downstream, electroweakZeroParamScoreCardCert_holds packages the certificate that SM param count is 4, RS param count is 0, $\alpha$ lies in the band $(137.030,137.039)$, and the $\sin^2\cos^2$ product identity holds; the four-source count is the structural witness that each forcing input traces to a named proved origin rather than a free fit.

Framework landmarks: T5 J-uniqueness, T6 $\varphi$-forcing, and T7 eight-tick octave from the forcing chain, plus the cube gauge embedding that supplies $\sin^2\theta_W$. The declaration does not itself prove those theorems; it only certifies that the scorecard enumerates exactly those four.