IndisputableMonolith.Constants.AlphaNumericsScaffold

   1import Mathlib
   2import IndisputableMonolith.Constants.Alpha
   3import IndisputableMonolith.Constants.GapWeightNumericsScaffold
   4
   5/-!
   6# Alpha Numeric Checks (Scaffold)
   7
   8This module contains **numeric evaluation / match-to-CODATA** checks for the symbolic
   9alpha derivation in `IndisputableMonolith.Constants.Alpha`.
  10-/
  11
  12namespace IndisputableMonolith
  13namespace Constants
  14
  15noncomputable section
  16
  17/-- Check: derived α⁻¹ is approximately 137.036. -/
  18def alphaInv_predicted_range_check : Prop :=
  19  137.030 < alphaInv ∧ alphaInv < 137.039
  20
  21/-- Check: the 8-tick gap weight is approximately 2.49057. -/
  22theorem gap_weight_approx :
  23    2.490 < w8_from_eight_tick ∧ w8_from_eight_tick < 2.491 := by
  24  constructor
  25  · calc (2.490 : ℝ) < (2.490564399 : ℝ) := by norm_num
  26      _ < w8_from_eight_tick := Numerics.W8Bounds.w8_computed_gt
  27  · calc w8_from_eight_tick < (2.490572090 : ℝ) := Numerics.W8Bounds.w8_computed_lt
  28      _ < 2.491 := by norm_num
  29
  30end
  31end Constants
  32end IndisputableMonolith
  33