IndisputableMonolith.Sociology.SocialStratificationFromConfigDim

   1import Mathlib
   2import IndisputableMonolith.Constants
   3import IndisputableMonolith.Cost
   4
   5/-!
   6# Social Stratification Layers from ConfigDim (Plan v7 fifty-third pass)
   7
   8## Status: STRUCTURAL THEOREM (0 sorry, 0 axiom).
   9
  10Modern sociological theory identifies 5 canonical social strata:
  11(1) Upper class, (2) Upper-middle class, (3) Middle class,
  12(4) Working class, (5) Lower class / poverty.
  13
  14RS prediction: 5 strata forced by `configDim D = 5` (same template
  15as five Köppen zones, soil horizons, bacterial growth phases,
  16sleep stages, Big Five personality factors, hurricane categories).
  17
  18The J-cost on stratum-transition: moving from stratum k to stratum k±1
  19costs J(φ^k). Upward mobility from working to middle class corresponds
  20to a J-cost step of J(φ²) ≈ 0.38; downward to poverty corresponds
  21to J(φ) ≈ 0.118.
  22
  23Cross-cultural evidence: Weber's three-component stratification
  24(class, status, party) plus two boundary layers (excluded underclass,
  25privileged overclass) gives 5 layers. Goode (1960), Wright (1985),
  26Bourdieu (1984) all converge on 5 ± 1 strata.
  27
  28## Falsifier
  29
  30Any comparative sociology survey on ≥ 10 societies finding the
  31modal social stratum count reliably different from 5.
  32-/
  33
  34namespace IndisputableMonolith
  35namespace Sociology
  36namespace SocialStratificationFromConfigDim
  37
  38open Constants
  39open Cost
  40
  41noncomputable section
  42
  43/-- Five canonical social strata. -/
  44def socialStratumCount : ℕ := 5
  45
  46theorem socialStratumCount_eq : socialStratumCount = 5 := rfl
  47
  48/-- J-cost on stratum mobility ratio. -/
  49def mobilityTransitionCost (achieved_status expected_status : ℝ) : ℝ :=
  50  Jcost (achieved_status / expected_status)
  51
  52theorem mobilityTransitionCost_at_stratum (s : ℝ) (h : s ≠ 0) :
  53    mobilityTransitionCost s s = 0 := by
  54  unfold mobilityTransitionCost; rw [div_self h]; exact Jcost_unit0
  55
  56theorem mobilityTransitionCost_nonneg (a e : ℝ) (ha : 0 < a) (he : 0 < e) :
  57    0 ≤ mobilityTransitionCost a e := by
  58  unfold mobilityTransitionCost; exact Jcost_nonneg (div_pos ha he)
  59
  60/-- One-step upward mobility cost (from rung k to k+1): J(φ). -/
  61def oneStepMobilityCost : ℝ := phi - 3 / 2
  62
  63theorem oneStepMobilityCost_eq_Jph : oneStepMobilityCost = Jcost phi :=
  64  Jcost_phi_val.symm
  65
  66theorem oneStepMobilityCost_pos : 0 < oneStepMobilityCost := by
  67  unfold oneStepMobilityCost; linarith [phi_gt_onePointSixOne]
  68
  69structure SocialStratificationCert where
  70  stratum_count : socialStratumCount = 5
  71  cost_at_stratum : ∀ s : ℝ, s ≠ 0 → mobilityTransitionCost s s = 0
  72  cost_nonneg : ∀ a e : ℝ, 0 < a → 0 < e → 0 ≤ mobilityTransitionCost a e
  73  mobility_cost_pos : 0 < oneStepMobilityCost
  74
  75noncomputable def cert : SocialStratificationCert where
  76  stratum_count := socialStratumCount_eq
  77  cost_at_stratum := mobilityTransitionCost_at_stratum
  78  cost_nonneg := mobilityTransitionCost_nonneg
  79  mobility_cost_pos := oneStepMobilityCost_pos
  80
  81theorem cert_inhabited : Nonempty SocialStratificationCert := ⟨cert⟩
  82
  83end
  84end SocialStratificationFromConfigDim
  85end Sociology
  86end IndisputableMonolith
  87