IndisputableMonolith.Physics.HiggsMassScoreCard

   1import Mathlib
   2import IndisputableMonolith.StandardModel.HiggsRungAssignment
   3
   4/-!
   5# Phase 2 — P2-HIGGS: Higgs mass `m_H` scorecard (EW + Q₃ correction chain)
   6
   7**Predicted (RS):** `mH_rs_level3 = v * sqrt(sin²θ_W * 17/16)` with
   8`v = 246` GeV (canonical EWSB display) and `sin²θ_W = (3-φ)/6`.
   9
  10**Observed:** PDG `m_H ≈ 125.2` GeV.
  11
  12**Falsifier (one sentence):** If a future `m_H` world average moves outside
  13`(120, 130)` GeV while the RS `sin²θ_W` and `v` inputs remain in their proved bands,
  14the interval prediction is false.
  15
  16**Status:** `PARTIAL_THEOREM` — the `(120,130)` window and 5% proximity to 125.2 GeV are proved;
  17`v = 246` GeV remains a display anchor (same residual family as the Fermi-constant row).
  18
  19**Lean: 0 sorry, 0 new axiom**
  20-/
  21
  22namespace IndisputableMonolith.Physics.HiggsMassScoreCard
  23
  24open IndisputableMonolith
  25open IndisputableMonolith.StandardModel
  26open IndisputableMonolith.StandardModel.HiggsRungAssignment
  27
  28noncomputable section
  29
  30noncomputable def row_mH_codata : ℝ := mH_obs
  31
  32theorem row_mH_codata_pos : 0 < row_mH_codata := by
  33  unfold row_mH_codata mH_obs
  34  norm_num
  35
  36theorem row_mH_pred_interval :
  37    120 < mH_rs_level3 ∧ mH_rs_level3 < 130 := mH_prediction_in_interval
  38
  39theorem row_mH_within_five_percent :
  40    |mH_rs_level3 - row_mH_codata| / row_mH_codata < 0.05 := by
  41  simpa [row_mH_codata] using mH_within_5_percent_of_observed
  42
  43structure HiggsMassScoreCardCert where
  44  mass_interval : 120 < mH_rs_level3 ∧ mH_rs_level3 < 130
  45  five_percent : |mH_rs_level3 - mH_obs| / mH_obs < 0.05
  46
  47theorem higgsMassScoreCardCert_holds : Nonempty HiggsMassScoreCardCert :=
  48  ⟨{ mass_interval := row_mH_pred_interval
  49     five_percent := mH_within_5_percent_of_observed }⟩
  50
  51end
  52
  53end IndisputableMonolith.Physics.HiggsMassScoreCard
  54