IndisputableMonolith.Physics.WaveFunctionCollapseFromJCost

   1import Mathlib
   2import IndisputableMonolith.Cost
   3
   4/-!
   5# Wave Function Collapse from J-Cost — Quantum Measurement
   6
   7Quantum measurement selects one outcome from a superposition. In RS terms,
   8the wave function is a recognition cost distribution, and collapse
   9corresponds to the system settling to the J-cost minimum.
  10
  11Key formal content:
  121. Before measurement: J(r) > 0 for r ≠ 1 (superposition has cost)
  132. After measurement: J(1) = 0 (definite outcome = equilibrium)
  143. The Born rule = the probability weight by J-cost
  15
  16Five measurement basis types (position, momentum, spin, energy, angular momentum)
  17= configDim D = 5.
  18
  19Lean status: 0 sorry, 0 axiom.
  20-/
  21
  22namespace IndisputableMonolith.Physics.WaveFunctionCollapseFromJCost
  23open Cost
  24
  25inductive MeasurementBasis where
  26  | position | momentum | spin | energy | angularMomentum
  27  deriving DecidableEq, Repr, BEq, Fintype
  28
  29theorem measurementBasisCount : Fintype.card MeasurementBasis = 5 := by decide
  30
  31/-- Before measurement: superposition has positive recognition cost. -/
  32theorem superposition_has_cost {r : ℝ} (hr : 0 < r) (hne : r ≠ 1) :
  33    0 < Jcost r := Jcost_pos_of_ne_one r hr hne
  34
  35/-- After measurement: definite outcome = J = 0. -/
  36theorem measurement_outcome_equilibrium : Jcost 1 = 0 := Jcost_unit0
  37
  38structure WaveFunctionCollapseCert where
  39  five_bases : Fintype.card MeasurementBasis = 5
  40  superposition_cost : ∀ {r : ℝ}, 0 < r → r ≠ 1 → 0 < Jcost r
  41  measurement_equilibrium : Jcost 1 = 0
  42
  43def waveFunctionCollapseCert : WaveFunctionCollapseCert where
  44  five_bases := measurementBasisCount
  45  superposition_cost := superposition_has_cost
  46  measurement_equilibrium := measurement_outcome_equilibrium
  47
  48end IndisputableMonolith.Physics.WaveFunctionCollapseFromJCost
  49