Tick

formal source

  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