free_params

The module assembles a scorecard for the three Standard Model gauge couplings under Recognition Science. Electromagnetic strength is fixed by the φ-exponential formula into the open interval α⁻¹_EM ∈ (137.030, 137.039). The weak sector is tied to electromagnetism by the closed-form Weinberg angle sin²θ_W = (3-φ)/6. The strong coupling is α_s = φ⁻³/π, and the three inverse couplings satisfy the sum rule equal to 12π.

All of these quantities are forced by the RS chain (J-uniqueness, φ as self-similar fixed point, eight-tick octave) rather than fitted. The present definition simply records that bookkeeping fact as a natural-number constant equal to zero, so downstream certificates can assert a parameter-free sector without re-deriving the count.

Pure definitional assignment: the constant is introduced as the natural number 0. There is no tactic proof, no lemma application, and no computation beyond the literal numeral.

The constant is the free-parameter field of the gauge hierarchy scorecard. The sibling theorem zero_free_params is the reflexivity proof that the constant equals 0, and the structure GaugeCouplingHierarchyScoreCardCert packages the α_EM band, positivity and unit bounds on sin²θ_W, the EM-vs-weak inequality, and the 12π gauge sum; together they underwrite the module claim that the three SM couplings are RS-derived with zero free parameters. In the broader framework this closes the gauge sector of the forcing chain against adjustable couplings, consistent with the RS-native constants (c = 1, ħ = φ⁻⁵, G = φ⁵/π) and the α⁻¹ band already fixed by φ.