IndisputableMonolith.Physics.FineStructureConstantFromRS

   1import Mathlib
   2import IndisputableMonolith.Constants
   3
   4/-!
   5# The 44π factor (HONEST STATUS: identification, not a derivation of α)
   6
   7This module records trivial facts about the number 44π used as the seed in
   8the α⁻¹ CONSTRUCTION. HONEST STATUS (2026-07-06): the seed 4π·11 is an
   9IDENTIFICATION, not a derived coupling (the gauge-invariant photon count on
  10Q₃ is the cycle rank b₁ = 5, not 11), the construction's first-order value
  11is excluded by measurement at >30,000σ
  12(`Constants.AlphaGenesis.MeasurementVerdict`), and within RS the exact
  13value of α⁻¹(0) is a free boundary datum
  14(`Constants.AlphaGenesis.KappaGammaIrreducibility`). Nothing here derives
  15the fine-structure constant.
  16
  17Lean status: 0 sorry, 0 axiom.
  18-/
  19
  20namespace IndisputableMonolith.Physics.FineStructureConstantFromRS
  21
  22def alphaRung : ℕ := 44
  23theorem alphaRung_eq : alphaRung = 44 := rfl
  24
  25noncomputable def rsAlphaFactor : ℝ := 44 * Real.pi
  26
  27theorem rsAlphaFactor_pos : 0 < rsAlphaFactor := by
  28  unfold rsAlphaFactor; positivity
  29
  30theorem rsAlphaFactor_gt_100 : rsAlphaFactor > 100 := by
  31  unfold rsAlphaFactor
  32  linarith [Real.pi_gt_three]
  33
  34/-- 44π is the gauge loop area denominator in the RS α⁻¹ formula. -/
  35theorem alpha_rung_factor : (alphaRung : ℝ) * Real.pi = rsAlphaFactor := by
  36  unfold rsAlphaFactor; norm_cast
  37
  38structure FineStructureCert where
  39  alpha_rung : alphaRung = 44
  40  factor_pos : 0 < rsAlphaFactor
  41  factor_gt_100 : rsAlphaFactor > 100
  42
  43noncomputable def fineStructureCert : FineStructureCert where
  44  alpha_rung := alphaRung_eq
  45  factor_pos := rsAlphaFactor_pos
  46  factor_gt_100 := rsAlphaFactor_gt_100
  47
  48end IndisputableMonolith.Physics.FineStructureConstantFromRS
  49