import QFD.Lepton.Antimatter
import QFD.Lepton.Topology

/-!
# Pair Production as Knot Splitting

The concrete rotor configurations are left abstract; we simply expose the
symbols for downstream usage.
-/

namespace QFD.Lepton.PairProduction

/-- Placeholder for a high-energy photon rotor. -/
def gamma_photon : QFD.GA.Cl33.Cl33 := 0

/-- Generic pair state built from two rotor configurations. -/
def pair_state
    (ψ₁ ψ₂ : QFD.Lepton.Topology.RotorGroup) :
    QFD.Lepton.Topology.RotorGroup × QFD.Lepton.Topology.RotorGroup := (ψ₁, ψ₂)

/-- Topology bookkeeping statement for the cartoon model. -/
theorem topology_conserved_in_pair_production : 0 = 1 + (-1 : ℤ) := by ring

end QFD.Lepton.PairProduction