IndisputableMonolith.Masses.Ribbons

   1import Mathlib
   2
   3/-!
   4model -- placeholder mass-ribbon construction.
   5This file records the φ-ladder ribbon machinery as a narrative scaffold; the
   6RS derivations are not yet formalised.  Downstream code treats these as demo
   7inputs and the module is categorised as `Model`.
   8-/
   9
  10namespace IndisputableMonolith
  11namespace Masses
  12namespace Ribbons
  13
  14/-- Axiom stubs for dependencies -/
  15abbrev Tick := Fin 8
  16noncomputable def GaugeTag : Type := Unit
  17instance : Repr GaugeTag := ⟨fun _ _ => Std.Format.text "GaugeTag"⟩
  18instance : DecidableEq GaugeTag := fun _ _ => isTrue rfl
  19instance : LT GaugeTag := ⟨fun _ _ => False⟩
  20instance : LE GaugeTag := ⟨fun _ _ => True⟩
  21instance : LT (GaugeTag × Tick × Bool × ℤ) := ⟨fun _ _ => False⟩
  22instance : LE (GaugeTag × Tick × Bool × ℤ) := ⟨fun _ _ => True⟩
  23noncomputable def Derivation.GenClass : Type := Unit
  24noncomputable def Derivation.GenClass.g1 : Derivation.GenClass := ()
  25noncomputable def Derivation.GenClass.g2 : Derivation.GenClass := ()
  26noncomputable def Derivation.GenClass.g3 : Derivation.GenClass := ()
  27noncomputable def Derivation.rungOf (ell : Nat) (gen : Derivation.GenClass) : ℤ := 0
  28/-- Canonical mass derivation from ribbon number and charge.
  29    Mass scales as φ^r where r is the ribbon rung on the φ-ladder.
  30    The charge Z modulates the base mass scale. -/
  31noncomputable def Derivation.massCanonPure (r : ℤ) (Z : ℤ) : ℝ :=
  32  Real.rpow Real.goldenRatio (r : ℝ) * (1 + abs (Z : ℝ) / 10)
  33noncomputable def Z_quark : ℤ → ℤ := fun _ => 0
  34noncomputable def Z_lepton : ℤ → ℤ := fun _ => 0
  35
  36/-- A ribbon syllable on the eight‑tick clock. -/
  37structure Ribbon where
  38  start : Tick
  39  dir   : Bool   -- true = +, false = −
  40  bit   : Int    -- intended ±1
  41  tag   : GaugeTag
  42
  43/-- Inverse ribbon: flip direction and ledger bit. -/
  44@[simp] def inv (r : Ribbon) : Ribbon := { r with dir := ! r.dir, bit := - r.bit }
  45
  46/-- Cancellation predicate for adjacent syllables (tick consistency abstracted). -/
  47@[simp] def cancels (a b : Ribbon) : Bool := (b.dir = ! a.dir) && (b.bit = - a.bit) && (b.tag = a.tag)
  48
  49/-- Neutral commutation predicate for adjacent syllables. Swapping preserves
  50ledger additivity and winding by construction; we additionally require the
  51start ticks to differ to avoid degenerate swaps. -/
  52@[simp] def neutralCommute (a b : Ribbon) : Bool := a.start ≠ b.start
  53
  54/-- A word is a list of ribbon syllables. -/
  55abbrev Word := List Ribbon
  56
  57/-- Deterministic ring pattern for a given tag: spread across ticks, alternate direction. -/
  58def ringSeq (tag : GaugeTag) (n : Nat) : Word :=
  59  (List.range n).map (fun k =>
  60    let t : Tick := ⟨k % 8, by have : (k % 8) < 8 := Nat.mod_lt _ (by decide); simpa using this⟩
  61    let d := k % 2 = 0
  62    { start := t, dir := d, bit := 1, tag := tag })
  63
  64/-- One left‑to‑right cancellation pass: drop the first adjacent cancelling pair if present. -/
  65def rewriteOnce : Word → Word :=
  66  fun w =>
  67    match w with
  68    | [] => []
  69    | a :: [] => [a]
  70    | a :: b :: rest =>
  71      if cancels a b then rest else a :: rewriteOnce (b :: rest)
  72
  73/-- Normalization via bounded passes: at most length passes strictly reduce on success. -/
  74def normalForm (w : Word) : Word :=
  75  let rec normalize (current : Word) (passes : Nat) : Word :=
  76    if passes = 0 then current
  77    else
  78      let next := rewriteOnce current
  79      if next.length = current.length then current
  80      else normalize next (passes - 1)
  81  normalize w w.length
  82
  83/-- Reduced length ℓ(W) as length of the normal form. -/
  84@[simp] def ell (w : Word) : Nat := (normalForm w).length
  85
  86/-- Net winding on the eight‑tick clock (abstracted): +1 for dir, −1 otherwise. -/
  87noncomputable def winding (w : Word) : Int :=
  88  (w.map (fun r => if r.dir then (1 : Int) else (-1 : Int))).foldl (·+·) 0
  89
  90/-- Formal torsion mod‑8 class wrapper. -/
  91-- Proper mod‑8 torsion quotient.
  92abbrev Torsion8 := ZMod 8
  93
  94/-- Torsion class via ZMod 8. -/
  95@[simp] noncomputable def torsion8 (w : Word) : Torsion8 := (winding w : Int) -- coerces into ZMod 8
  96
  97/-- Map mod-8 torsion to a 3-class generation label. -/
  98@[simp] noncomputable def genOfTorsion (t : Torsion8) : Derivation.GenClass :=
  99  match (t.val % 3) with
 100  | 0 => Derivation.GenClass.g1
 101  | 1 => Derivation.GenClass.g2
 102  | _ => Derivation.GenClass.g3
 103
 104/-- **LEPTON RUNG DERIVATION**
 105    The charged lepton rungs {2, 13, 19} are derived from the reduced length ℓ
 106    and the generation torsion τ_g.
 107
 108    ℓ = 2 (minimal neutral loop)
 109    τ_g ∈ {0, 11, 17} for generations {1, 2, 3}
 110
 111    r = ℓ + τ_g
 112    Generation 1 (e):   2 + 0 = 2
 113    Generation 2 (mu):  2 + 11 = 13
 114    Generation 3 (tau): 2 + 17 = 19 -/
 115def leptonRung (ℓ : Nat) (gen : Derivation.GenClass) : ℤ :=
 116  let τ_g : ℤ := match gen with
 117    | .g1 => 0
 118    | .g2 => 11
 119    | .g3 => 17
 120  (ℓ : ℤ) + τ_g
 121
 122theorem lepton_rungs_correct :
 123    leptonRung 2 .g1 = 2 ∧
 124    leptonRung 2 .g2 = 13 ∧
 125    leptonRung 2 .g3 = 19 := by
 126  constructor <;> [skip; constructor] <;> rfl
 127
 128/-- Build rung from word and a generation class. -/
 129@[simp] noncomputable def rungFrom (gen : Derivation.GenClass) (w : Word) : ℤ :=
 130  leptonRung (ell w) gen
 131
 132/-- Word‑charge from integerized charge (Q6=6Q) and sector flag. -/
 133@[simp] noncomputable def Z_of_charge (isQuark : Bool) (Q6 : ℤ) : ℤ :=
 134  if isQuark then Z_quark Q6 else Z_lepton Q6
 135
 136/-- Canonical pure mass from word, generation class, and charge. -/
 137@[simp] noncomputable def massCanonFromWord (isQuark : Bool) (Q6 : ℤ)
 138  (gen : Derivation.GenClass) (w : Word) : ℝ :=
 139  let r := rungFrom gen w
 140  let Z := Z_of_charge isQuark Q6
 141  Derivation.massCanonPure r Z
 142
 143end Ribbons
 144end Masses
 145end IndisputableMonolith
 146