IndisputableMonolith.Physics.WeinbergAngleScoreCard
This module assembles a scorecard that tabulates experimental codata for sin²θ_W against Recognition Science brackets derived from the φ fixed point and Q3 representations. It defines comparison rows and a certification object for the electroweak mixing angle. Physicists checking precision electroweak predictions would cite the scorecard to confirm the RS value lies inside the codata interval. The module consists of data-row definitions followed by a single certification declaration.
claimA scorecard comparing the Recognition Science prediction for the weak mixing angle, with rows for codata sin²θ_W, RS bracket from φ-structure, and a certification that the best-match prediction holds.
background
The module imports the quaternion-group representation theory of Q3 (Q8) that encodes spin-0 versus spin-1 Casimir eigenvalues for electroweak symmetry breaking, together with the derivation of the Weinberg angle from the RS φ fixed point. Q3 supplies the discrete structure underlying the mixing, while the WeinbergAngle module supplies the target value sin²θ_W ≈ 0.2229 at the M_Z scale. The scorecard therefore sits at the interface between the representation-theoretic input and the numerical prediction for the mixing parameter.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The scorecard certifies the numerical agreement between the φ-derived Weinberg angle and experimental codata, thereby supporting the core claim of SM-004 that the weak mixing angle follows from RS φ-structure. It supplies the concrete comparison object that downstream Standard Model validation steps can reference.
scope and limits
- Does not derive sin²θ_W from the forcing chain.
- Does not compute radiative corrections beyond the tree-level RS bracket.
- Does not address running of the angle above the M_Z scale.