IndisputableMonolith.RecogSpec.RSLedger

   1import Mathlib
   2import IndisputableMonolith.RecogSpec.Core
   3import IndisputableMonolith.Constants
   4import IndisputableMonolith.Constants.AlphaDerivation
   5
   6/-!
   7# RSLedger: Rich Ledger with φ-Tier Structure
   8
   9This module defines the rich ledger structure needed for deriving mass ratios
  10from generation torsion rather than defining them as φ-formulas.
  11
  12## The Physics
  13
  14In Recognition Science, particle masses occupy discrete rungs on the φ-ladder:
  15- Each generation has a torsion offset τ_g derived from Q₃ cube geometry
  16- Each sector (leptons, up quarks, down quarks) has a base rung
  17- The full rung is: `rung = baseRung + τ_g`
  18- Mass ratios are: `m_f / m_g = φ^{r_f - r_g}`
  19
  20## Geometric Derivation of Torsion
  21
  22The torsion values come from D=3 cube combinatorics:
  23- Gen 1 (ground): τ₁ = 0
  24- Gen 2 (edge-dressed): τ₂ = E_passive(D) = cube_edges(D) − 1 = 11
  25- Gen 3 (face+edge): τ₃ = E_passive(D) + cube_faces(D) = 11 + 6 = 17
  26
  27The detailed bridge between cube geometry and this definition is proved in
  28`IndisputableMonolith.Masses.GenerationTorsionBridge`.
  29
  30## Key Result
  31
  32With torsion {0, 11, 17}, the inter-generation mass ratios are:
  33- Gen 2 / Gen 1 = φ^{11}
  34- Gen 3 / Gen 1 = φ^{17}
  35- Gen 3 / Gen 2 = φ^{6}
  36-/
  37
  38namespace IndisputableMonolith
  39namespace RecogSpec
  40
  41open Constants
  42open IndisputableMonolith.Constants.AlphaDerivation
  43
  44/-! ## Generation Torsion -/
  45
  46/-- The three generations of fermions -/
  47inductive Generation : Type
  48  | first | second | third
  49  deriving DecidableEq, Repr, Inhabited
  50
  51/-- Canonical generation torsion from Q₃ cube geometry.
  52
  53- Gen 1 (ground state): τ = 0
  54- Gen 2 (passive-edge mode): τ = passive_field_edges(D) = 11
  55- Gen 3 (passive-edge + face mode): τ = passive_field_edges(D) + cube_faces(D) = 17
  56
  57No raw numerals: every branch is a cube-combinatorial function of D=3.
  58-/
  59def generationTorsion : Generation → ℤ
  60  | .first => 0
  61  | .second => (passive_field_edges D : ℤ)
  62  | .third => (passive_field_edges D + cube_faces D : ℤ)
  63
  64@[simp] lemma torsion_first : generationTorsion .first = 0 := rfl
  65
  66@[simp] lemma torsion_second : generationTorsion .second = 11 := by
  67  simp [generationTorsion, passive_field_edges, cube_edges, active_edges_per_tick, D]
  68
  69@[simp] lemma torsion_third : generationTorsion .third = 17 := by
  70  simp [generationTorsion, passive_field_edges, cube_edges, active_edges_per_tick, cube_faces, D]
  71
  72/-- Torsion difference between generations -/
  73def torsionDiff (g1 g2 : Generation) : ℤ :=
  74  generationTorsion g1 - generationTorsion g2
  75
  76@[simp] lemma torsion_diff_21 : torsionDiff .second .first = 11 := by
  77  simp [torsionDiff]
  78
  79@[simp] lemma torsion_diff_31 : torsionDiff .third .first = 17 := by
  80  simp [torsionDiff]
  81
  82@[simp] lemma torsion_diff_32 : torsionDiff .third .second = 6 := by
  83  simp [torsionDiff]
  84
  85/-! ## Fermion Sectors -/
  86
  87/-- The three fermion sectors -/
  88inductive FermionSector : Type
  89  | leptons | upQuarks | downQuarks
  90  deriving DecidableEq, Repr
  91
  92/-- Base rung for each sector.
  93
  94These are derived from the charge structure Z:
  95- Leptons: base = 2
  96- Up quarks: base = 4
  97- Down quarks: base = 4
  98-/
  99def sectorBaseRung : FermionSector → ℤ
 100  | .leptons => 2
 101  | .upQuarks => 4
 102  | .downQuarks => 4
 103
 104/-! ## RSLedger Structure -/
 105
 106/-- A ledger with the full φ-tier structure needed for mass derivation.
 107
 108This extends the minimal `Ledger` with:
 109- Generation torsion function
 110- Sector base rungs
 111- Full rung assignment
 112-/
 113structure RSLedger where
 114  /-- The underlying ledger -/
 115  toLedger : Ledger
 116  /-- Generation torsion offsets -/
 117  torsion : Generation → ℤ
 118  /-- Base rung for each sector -/
 119  baseRung : FermionSector → ℤ
 120
 121/-- The full rung assignment for a particle -/
 122def RSLedger.rung (L : RSLedger) (sector : FermionSector) (gen : Generation) : ℤ :=
 123  L.baseRung sector + L.torsion gen
 124
 125/-- Rung difference between two generations in the same sector -/
 126def RSLedger.rungDiff (L : RSLedger) (sector : FermionSector)
 127    (g1 g2 : Generation) : ℤ :=
 128  L.rung sector g1 - L.rung sector g2
 129
 130/-- Rung difference equals torsion difference (base rung cancels) -/
 131theorem RSLedger.rungDiff_eq_torsionDiff (L : RSLedger) (sector : FermionSector)
 132    (g1 g2 : Generation) :
 133    L.rungDiff sector g1 g2 = L.torsion g1 - L.torsion g2 := by
 134  simp only [rungDiff, rung]
 135  ring
 136
 137/-- For canonical torsion, rung difference is generation torsion difference -/
 138theorem RSLedger.rungDiff_canonical (L : RSLedger) (sector : FermionSector)
 139    (g1 g2 : Generation) (hL : L.torsion = generationTorsion) :
 140    L.rungDiff sector g1 g2 = torsionDiff g1 g2 := by
 141  rw [rungDiff_eq_torsionDiff, hL]
 142  rfl
 143
 144/-! ## Mass Ratios from Rung Differences -/
 145
 146/-- Mass ratio between generations from rung difference.
 147
 148This is the key derivation: masses are φ^{rung}, so ratios are φ^{Δrung}.
 149-/
 150noncomputable def massRatioFromRungs (L : RSLedger) (φ : ℝ)
 151    (sector : FermionSector) (g1 g2 : Generation) : ℝ :=
 152  φ ^ (L.rungDiff sector g1 g2)
 153
 154/-- Mass ratio gen2/gen1 = φ^{11} for canonical torsion -/
 155theorem massRatio_21_canonical (L : RSLedger) (φ : ℝ) (sector : FermionSector)
 156    (hL : L.torsion = generationTorsion) :
 157    massRatioFromRungs L φ sector .second .first = φ ^ (11 : ℤ) := by
 158  simp only [massRatioFromRungs]
 159  rw [L.rungDiff_canonical sector _ _ hL]
 160  simp [torsionDiff]
 161
 162/-- Mass ratio gen3/gen1 = φ^{17} for canonical torsion -/
 163theorem massRatio_31_canonical (L : RSLedger) (φ : ℝ) (sector : FermionSector)
 164    (hL : L.torsion = generationTorsion) :
 165    massRatioFromRungs L φ sector .third .first = φ ^ (17 : ℤ) := by
 166  simp only [massRatioFromRungs]
 167  rw [L.rungDiff_canonical sector _ _ hL]
 168  simp [torsionDiff]
 169
 170/-- Mass ratio gen3/gen2 = φ^{6} for canonical torsion -/
 171theorem massRatio_32_canonical (L : RSLedger) (φ : ℝ) (sector : FermionSector)
 172    (hL : L.torsion = generationTorsion) :
 173    massRatioFromRungs L φ sector .third .second = φ ^ (6 : ℤ) := by
 174  simp only [massRatioFromRungs]
 175  rw [L.rungDiff_canonical sector _ _ hL]
 176  simp [torsionDiff]
 177
 178/-! ## The Canonical RSLedger -/
 179
 180/-- The canonical RS ledger with standard torsion and base rungs -/
 181def canonicalRSLedger : RSLedger where
 182  toLedger := { Carrier := Unit }
 183  torsion := generationTorsion
 184  baseRung := sectorBaseRung
 185
 186/-- The canonical ledger has canonical torsion -/
 187@[simp] theorem canonicalRSLedger_torsion :
 188    canonicalRSLedger.torsion = generationTorsion := rfl
 189
 190/-- Canonical ledger mass ratios -/
 191theorem canonical_massRatio_21 (φ : ℝ) (sector : FermionSector) :
 192    massRatioFromRungs canonicalRSLedger φ sector .second .first = φ ^ (11 : ℤ) :=
 193  massRatio_21_canonical canonicalRSLedger φ sector canonicalRSLedger_torsion
 194
 195theorem canonical_massRatio_31 (φ : ℝ) (sector : FermionSector) :
 196    massRatioFromRungs canonicalRSLedger φ sector .third .first = φ ^ (17 : ℤ) :=
 197  massRatio_31_canonical canonicalRSLedger φ sector canonicalRSLedger_torsion
 198
 199theorem canonical_massRatio_32 (φ : ℝ) (sector : FermionSector) :
 200    massRatioFromRungs canonicalRSLedger φ sector .third .second = φ ^ (6 : ℤ) :=
 201  massRatio_32_canonical canonicalRSLedger φ sector canonicalRSLedger_torsion
 202
 203/-! ## Summary: Mass Ratios from Torsion Structure -/
 204
 205/-- The torsion structure {0, 11, 17} gives the canonical mass ratio rung differences.
 206
 207This is the key result: masses are DERIVED from torsion, not defined as formulas.
 208-/
 209theorem massRatios_from_torsion_structure (L : RSLedger)
 210    (hL : L.torsion = generationTorsion) :
 211    L.rungDiff .leptons .second .first = 11 ∧
 212    L.rungDiff .leptons .third .first = 17 ∧
 213    L.rungDiff .leptons .third .second = 6 := by
 214  refine ⟨?_, ?_, ?_⟩
 215  · rw [L.rungDiff_canonical .leptons _ _ hL]; rfl
 216  · rw [L.rungDiff_canonical .leptons _ _ hL]; rfl
 217  · rw [L.rungDiff_canonical .leptons _ _ hL]; rfl
 218
 219end RecogSpec
 220end IndisputableMonolith
 221