IndisputableMonolith.Physics.WeinbergAngleScoreCard
This module assembles a scorecard comparing the Recognition Science prediction of the Weinberg angle against experimental codata using Q3 representations. Electroweak model builders cite it to verify the φ-derived sin²θ_W bracket. The structure consists of data rows plus a top-level certification declaration with no internal proof body.
claimCertification that the RS-derived $\sin^2\theta_W$ (from $\phi$-structure and Q$_3$ representations) lies inside the experimental codata bracket at the $M_Z$ scale.
background
The module imports Q3Representations, which formalizes the quaternion group Q$_3$ = {±1, ±i, ±j, ±k} and its role in the electroweak symmetry breaking pattern of Recognition Science. It also imports WeinbergAngle, whose core result states that the weak mixing angle satisfies sin²(θ_W) ≈ 0.2229 at the M_Z scale when derived from the RS φ-structure. The scorecard therefore sits at the intersection of representation theory of Q$_3$ and the φ-forced mixing parameter.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module supplies the concrete certification object (WeinbergAngleScoreCardCert) that closes the SM-004 derivation of the Weinberg angle inside the Recognition Science framework. It therefore feeds any higher-level claim that the full set of Standard Model parameters is recovered from the T5–T8 forcing chain and the RCL.
scope and limits
- Does not derive the numerical value of sin²θ_W from first principles.
- Does not contain the Q3 representation theory or the φ-mixing derivation.
- Does not address running of the angle with scale.
- Does not claim agreement outside the stated codata bracket.