zero_free_params

The module packages the Standard Model gauge hierarchy as an RS scorecard. Electromagnetic strength sits in the forced band $\alpha^{-1}_{\mathrm{EM}}\in(137.030,137.039)$; the weak mixing angle is fixed by $\sin^2\theta_W=(3-\varphi)/6$; the strong coupling is $\alpha_s=\varphi^{-3}/\pi$; and the three couplings obey the gauge-sum identity equal to $12\pi$. All of these are claimed to be derived from the forcing chain with no adjustable constants.

Sibling definitions encode those relations (sin2_W_rs, alpha_weak_inv, alpha_s, the EM band, the sum identity). The natural-number constant free_params is the scorecard's explicit free-parameter tally for this sector; it is defined to be $0$. Parallel tallies appear in the W-boson absolute scorecard, the alpha-running correction scorecard, and the SPARC falsifier (per-galaxy free parameters).

One-line reflexivity. The definition sets the free-parameter count equal to the natural number $0$, so rfl discharges equality. No lemmas are invoked.

This is the zero-parameter witness for the gauge-coupling hierarchy scorecard. It is packed into gaugeCouplingHierarchyScoreCardCert_holds, which asserts a nonempty certificate bundling the EM band, positivity and bounds on $\sin^2\theta_W$, EM exceeding weak coupling, and the remaining hierarchy facts.

Downstream, the same pattern feeds the SPARC falsifier's global_only_policy and sparc_falsifier_cert (global-only, no per-galaxy knobs), and the sibling zero-parameter theorems on the alpha-running and W-boson scorecards. In the RS framework this closes the module claim that the three SM gauge couplings are forced (phi-ladder and T5–T8 structure) rather than fitted, matching the primer landmarks on the alpha band and zero free parameters.