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 CONSTRUCTION in `IndisputableMonolith.Constants.Alpha`. The construction band
  10contains CODATA, but this is band containment of a construction whose seed 4π·11 is
  11an identification, not a derivation of the measured α (exact α⁻¹(0) is OPEN).
  12-/
  13
  14namespace IndisputableMonolith
  15namespace Constants
  16
  17noncomputable section
  18
  19/-- Check: the RS α⁻¹ construction value is approximately 137.036. -/
  20def alphaInv_predicted_range_check : Prop :=
  21  137.030 < alphaInv ∧ alphaInv < 137.039
  22
  23/-- Check: the 8-tick gap weight is approximately 2.49057. -/
  24theorem gap_weight_approx :
  25    2.490 < w8_from_eight_tick ∧ w8_from_eight_tick < 2.491 := by
  26  constructor
  27  · calc (2.490 : ℝ) < (2.490564399 : ℝ) := by norm_num
  28      _ < w8_from_eight_tick := Numerics.W8Bounds.w8_computed_gt
  29  · calc w8_from_eight_tick < (2.490572090 : ℝ) := Numerics.W8Bounds.w8_computed_lt
  30      _ < 2.491 := by norm_num
  31
  32end
  33end Constants
  34end IndisputableMonolith
  35