generous_threshold

formal source

  42
  43/-- The generous falsification threshold for ILG chi-squared per dof.
  44    If median chi2/dof > 5.0 across the SPARC sample, ILG is falsified. -/
  45def generous_threshold : ℝ := 5.0
  46
  47/-- The tight threshold matching the RS prediction (median ~ 2.75).
  48    If median chi2/dof > 3.0, the specific RS prediction is refuted
  49    (though ILG as a framework might survive with different parameters). -/
  50def tight_threshold : ℝ := 3.0
  51
  52/-- ILG is falsified if median chi2/dof exceeds the generous threshold. -/
  53def ILG_falsified (median_chi2_dof : ℝ) : Prop :=
  54  generous_threshold < median_chi2_dof
  55
  56/-- The RS-specific prediction is refuted if median > tight threshold. -/
  57def RS_prediction_refuted (median_chi2_dof : ℝ) : Prop :=
  58  tight_threshold < median_chi2_dof
  59
  60/-- If the median is below the generous threshold, ILG PASSES. -/
  61def ILG_passes (median_chi2_dof : ℝ) : Prop :=
  62  median_chi2_dof ≤ generous_threshold
  63
  64/-- The falsification criterion is decidable (for any real number). -/
  65theorem falsification_decidable (x : ℝ) :
  66    ILG_falsified x ∨ ILG_passes x := by
  67  unfold ILG_falsified ILG_passes generous_threshold
  68  exact le_or_gt x 5.0 |>.elim (Or.inr) (Or.inl)
  69
  70/-! ## RS Parameter Lock -/
  71
  72/-- The alpha parameter is locked to alphaLock ≈ 0.191. -/
  73noncomputable def alpha_locked : ℝ := alphaLock
  74
  75/-- The mass-to-light ratio is locked to phi ≈ 1.618. -/