module module moderate

`IndisputableMonolith.StandardModel.WeinbergAngle`

This module assembles observed and Recognition Science-derived values for sin²θ_W at the Z mass in the MS-bar scheme. Electroweak unification and gauge-coupling researchers cite it when testing RS geometry against PDG references. The module consists entirely of constant definitions, bounds, and geometric constructions rather than a proved theorem.

claim$\sin^2\theta_W$ at the Z-pole in the $\overline{\rm MS}$ scheme, with observed value $\approx 0.2229$ and RS predictions from eight-tick geometry and geometric mixing, including the core form $(3-\phi)/6$.

background

Recognition Science obtains all gauge parameters from the single J-functional equation whose self-similar fixed point is $\phi$. The module imports the base time quantum $\tau_0=1$ tick. It introduces the observed reference sin²θ_W, its error and bounds, five explicit predictions, a best-prediction selector, the EightTickGeometry construction, and the geometricMixing rule that produces the Weinberg angle from Q₃ representations.

The local theoretical setting is the electroweak sector after the forcing chain has fixed D=3 and the eight-tick octave; the module supplies the numerical interface between that geometry and the measured electroweak mixing angle.

proof idea

This is a definition module, no proofs.

why it matters in Recognition Science

The module supplies the comparison data required by the WeinbergAngleScoreCard, whose core claim is the RS prediction sin²θ_W = (3-φ)/6 tested against the observed value ≈0.2229. It also supports the Higgs mass rung assignment through shared Q₃ geometry and feeds the complete gauge-couplings derivation that registers C-014. It therefore closes the electroweak-parameter registry item inside the larger unification program.

scope and limits

Does not derive the gauge group SU(2)×U(1) from the J-equation.
Does not compute the running of sin²θ_W above the Z scale.
Does not address the strong coupling α_s.
Does not propagate theoretical uncertainties from the phi-ladder.

used by (3)

From the project-wide theorem graph. These declarations reference this one in their body.

IndisputableMonolith.Physics.WeinbergAngleScoreCard module_import
IndisputableMonolith.StandardModel.HiggsRungAssignment module_import
IndisputableMonolith.Unification.GaugeCouplingsComplete module_import

depends on (1)

Lean names referenced from this declaration's body.

IndisputableMonolith.Constants module_import

declarations in this module (23)

def sin2ThetaW_observed L39
def sin2ThetaW_error L42
theorem sin2_theta_bounds L45
def prediction1 L57
def prediction2 L64
def prediction3 L71
def prediction4 L78
def prediction5 L85
def bestPrediction L94
theorem best_prediction_close_to_observed L96
structure EightTickGeometry L117
def geometricMixing L126
theorem simple_geometric_ratio L132
def phiCorrection L144
def correctedPrediction L146
def sin2ThetaW_GUT L158
theorem gut_prediction L161
def runningAngle L169
def deepConnections L181
structure ExperimentalMeasurement L200
def measurements L205
structure WeinbergAngleFalsifier L217
def derivationStatus L226