IndisputableMonolith.Physics.WeinbergAngleScoreCard

   1import Mathlib
   2import IndisputableMonolith.StandardModel.WeinbergAngle
   3import IndisputableMonolith.StandardModel.Q3Representations
   4
   5/-!
   6# Phase 2 — P2-θW: electroweak `sin²θ_W` (Weinberg angle) scorecard
   7
   8**Predicted (RS) core:** `sin²θ_W = (3-φ)/6` (alias `sin2ThetaW_RS` in
   9`Q3Representations`).
  10
  11**Observed (PDG-style reference):** `sin²θ_W ≈ 0.2229` in `WeinbergAngle.sin2ThetaW_observed`.
  12
  13**Falsifier (one sentence):** If a future on-shell or MS `sin²θ_W` reference moves by more
  14than 0.01 from `(3-φ)/6` *without* a change in the certified φ/α input bounds, the
  15identity-level match is false.
  16
  17**Status:** The tight match `|bestPrediction - 0.2229| < 0.01` is a proved **PARTIAL** bridge
  18(leading formula vs one reference number); rung-normalization and scheme dependence is the
  19residual, named below.
  20
  21**Lean: 0 sorry, 0 new axiom**
  22-/
  23
  24namespace IndisputableMonolith.Physics.WeinbergAngleScoreCard
  25
  26open IndisputableMonolith
  27open IndisputableMonolith.StandardModel
  28open IndisputableMonolith.StandardModel.Q3Representations
  29
  30noncomputable section
  31
  32def row_sin2_thetaW_codata : ℝ := WeinbergAngle.sin2ThetaW_observed
  33
  34theorem row_sin2_thetaW_codata_bracket :
  35    (0.22 : ℝ) < row_sin2_thetaW_codata ∧ row_sin2_thetaW_codata < (0.23 : ℝ) := by
  36  simpa [row_sin2_thetaW_codata] using WeinbergAngle.sin2_theta_bounds
  37
  38theorem row_sin2_thetaW_RS_bracket :
  39    0.228 < sin2ThetaW_RS ∧ sin2ThetaW_RS < 0.232 := sin2ThetaW_RS_approx
  40
  41theorem row_best_prediction_match :
  42    |WeinbergAngle.bestPrediction - row_sin2_thetaW_codata| < 0.01 :=
  43  WeinbergAngle.best_prediction_close_to_observed
  44
  45structure WeinbergAngleScoreCardCert where
  46  codata_in_ref_band :
  47    (0.22 : ℝ) < row_sin2_thetaW_codata ∧ row_sin2_thetaW_codata < (0.23 : ℝ)
  48  rs_bracket : 0.228 < sin2ThetaW_RS ∧ sin2ThetaW_RS < 0.232
  49  one_cent_match : |WeinbergAngle.bestPrediction - row_sin2_thetaW_codata| < 0.01
  50
  51theorem weinbergAngleScoreCardCert_holds : Nonempty WeinbergAngleScoreCardCert :=
  52  ⟨{ codata_in_ref_band := row_sin2_thetaW_codata_bracket
  53     rs_bracket := row_sin2_thetaW_RS_bracket
  54     one_cent_match := row_best_prediction_match }⟩
  55
  56end
  57
  58end IndisputableMonolith.Physics.WeinbergAngleScoreCard
  59