three_inputs

This module builds a first-principles scorecard for the absolute $W$ boson mass with every input forced by the Recognition Science chain and no fitted parameters. The derivation is $m_Z$ at phi-ladder rung 51 in the electroweak sector, $\sin^2\theta_W = (3-\varphi)/6$ from gauge embedding geometry, and $m_W = m_Z\cos\theta_W = m_Z\sqrt{(3+\varphi)/6}$.

The inductive type of mass inputs enumerates precisely those three ingredients: the phi-ladder $Z$ mass, the RS Weinberg angle, and the cosine relation. It derives decidable equality and a finite-type instance so that its cardinality is a concrete natural number. Downstream certificates package this count with the closed form $\cos^2\theta_W = (3+\varphi)/6$ and the numerical bands on $\sin^2$ and $\cos^2$.

One-line wrapper: decide on Fintype.card for the three-constructor inductive type (with the derived Fintype and DecidableEq instances). No lemmas beyond the automatic finite enumeration of the constructors.

Feeds wBosonAbsoluteScoreCardCert_holds, which assembles the absolute scorecard certificate (closed-form $\cos^2\theta_W$, $\cos^2$ and $\sin^2$ bands, $m_W/m_Z = \cos\theta_W$, and the free-parameter claim). The module narrative is zero free parameters and a tree-level band $m_W\in(79921,79922)$ MeV against PDG, with residual attributed to radiative corrections.

In the RS forcing picture this locks the electroweak mass prediction to the phi-ladder and the geometric Weinberg angle rather than a fit. It is the explicit input-count witness behind the scorecard's "three inputs, zero free parameters" claim.