rs_zero

The module formalizes an electroweak zero-parameter scorecard. In the Standard Model the EW sector is counted as four independent inputs: the gauge couplings $g$ and $g'$, the Higgs VEV $v$, and the Higgs self-coupling $\lambda$. Recognition Science claims all four are forced rather than free.

The forcing chain supplies the replacements: $\alpha^{-1}$ from T5/T6/T7, $\sin^2\theta_W=(3-\varphi)/6$ from gauge-embedding geometry, $m_Z$ on the $\varphi$-ladder, and the tree-level relation for $v^2$. The RS-side integer that records how many free EW parameters remain is defined to be the natural number $0$.

That definition is the sole upstream dependency: the RS electroweak parameter count is the constant $0$ in $\mathbb{N}$.

One-line term proof by reflexivity. Because the RS electroweak parameter count is definitionally the natural number $0$, the equality holds by rfl with no further lemmas.

This equality is the RS half of the scorecard certificate. The parent theorem electroweakZeroParamScoreCardCert_holds packages four fields: SM parameter count by reflexivity, this RS-zero fact, the $\alpha$ band membership, and the $\sin^2\theta_W\cos^2\theta_W$ product identity. Together they certify the module claim that RS-counted free EW parameters are $0$ while SM-counted free parameters are $4$.

Framework landmarks in play are the forcing chain (T5 J-uniqueness, T6 $\varphi$, T7 eight-tick) that fix $\alpha^{-1}$, plus the geometric and ladder inputs for the weak angle and $m_Z$. The declaration itself is pure bookkeeping, but without it the zero-parameter certificate cannot close.