import Mathlib.Data.Real.Basic
import Mathlib.Topology.Order.LocalExtr
import QFD.Hydrogen.PhotonSolitonEmergentConstants

noncomputable section

namespace QFD

universe u
variable {Point : Type u}

/--
Lepton model extends the emergent constants with the winding profile `Q_star`
and the stability potential.
-/
structure LeptonModel (Point : Type u) extends EmergentConstants Point where
  Q_star : Config → ℝ
  StabilityPotential : ℝ → ℝ
  h_Qstar_nonneg : ∀ c, Q_star c ≥ 0
  h_V_bounded : ∃ V_min : ℝ, ∀ Q, StabilityPotential Q ≥ V_min

/-- Stable isomer configurations sit at local minima of the stability potential. -/
def IsStableIsomer (M : LeptonModel Point) (c : Config) : Prop :=
  IsLocalMin M.StabilityPotential (M.Q_star c)

/--
The electron, muon, and tau predicates (placeholders awaiting refined intervals).
-/
def IsElectron (M : LeptonModel Point) (c : Config) : Prop :=
  IsStableIsomer M c ∧
  M.Q_star c > 2.1 ∧ M.Q_star c < 2.25 ∧
  c.charge = -1

def IsMuon (M : LeptonModel Point) (c : Config) : Prop :=
  IsStableIsomer M c ∧
  M.Q_star c ≥ 2.25 ∧ M.Q_star c < 2.4 ∧
  c.charge = -1

def IsTau (M : LeptonModel Point) (c : Config) : Prop :=
  IsStableIsomer M c ∧
  M.Q_star c > 1000 ∧
  c.charge = -1

/--
Generation number assignment based on Q* ordering:
- Generation 1 (electron): Q* ≈ 2.2
- Generation 2 (muon): Q* ≈ 2.3
- Generation 3 (tau): Q* >> 1
- Generation 0: Invalid/composite state
-/
def GenerationNumber (M : LeptonModel Point) (c : Config)
    [Decidable (IsElectron M c)] [Decidable (IsMuon M c)] [Decidable (IsTau M c)] : ℕ :=
  if IsElectron M c then 1
  else if IsMuon M c then 2
  else if IsTau M c then 3
  else 0

end QFD