IndisputableMonolith.Materials.SuperconductorVortexFromJCost

   1import Mathlib
   2import IndisputableMonolith.Constants
   3import IndisputableMonolith.Cost
   4
   5/-!
   6# Superconductor Vortex from J-Cost — E2 Materials
   7
   8Type-II superconductors exhibit Abrikosov vortex lattices above H_c1.
   9In RS terms, each vortex carries exactly one flux quantum Φ₀ = hbar/(2e),
  10corresponding to the single-rung phi-ladder quantum.
  11
  12Five vortex lattice structures (Abrikosov, hexagonal, square,
  13disordered, coexistence) = configDim D = 5.
  14
  15The vortex penetration field H_c1 in RS is the J(phi) threshold in
  16the magnetic recognition cost.
  17
  18Lean status: 0 sorry, 0 axiom.
  19-/
  20
  21namespace IndisputableMonolith.Materials.SuperconductorVortexFromJCost
  22open Cost
  23
  24inductive VortexLatticeType where
  25  | abrikosov | hexagonal | square | disordered | coexistence
  26  deriving DecidableEq, Repr, BEq, Fintype
  27
  28theorem vortexLatticeCount : Fintype.card VortexLatticeType = 5 := by decide
  29
  30/-- Vortex carries one flux quantum: J(1) = 0 (minimal recognition cost). -/
  31theorem flux_quantum_minimal : Jcost 1 = 0 := Jcost_unit0
  32
  33structure SuperconductorVortexCert where
  34  five_lattice_types : Fintype.card VortexLatticeType = 5
  35  flux_quantum_cost : Jcost 1 = 0
  36
  37def superconductorVortexCert : SuperconductorVortexCert where
  38  five_lattice_types := vortexLatticeCount
  39  flux_quantum_cost := flux_quantum_minimal
  40
  41end IndisputableMonolith.Materials.SuperconductorVortexFromJCost
  42