| import Mathlib | |
| import OAI.MathematicalPhysics.RecorderFlows.Model | |
| import OAI.Computability.SolenoidalRecorder.Machines | |
| namespace OAI | |
| /-! Fixed-label material trajectories and the machine observation specification. -/ | |
| namespace Solenoidal | |
| namespace Fluid | |
| noncomputable def label : Space := ![1 / 8, 3 / 8, 1 / 2] | |
| def InStrip (x : Space) : Prop := (1 / 2 : ℝ) < Int.fract (x 0) ∧ Int.fract (x 0) < 1 | |
| def Trajectory (U : Field) (X : ℝ → Space) : Prop := | |
| X 0 = label ∧ ∀ t : ℝ, 0 ≤ t → | |
| HasDerivWithinAt X (U (point t (X t))) (Set.Ici 0) t | |
| def ObservationAssertion (M : Machine) (w : List M.Symbol) (U : Field) : Prop := | |
| ∃ X : ℝ → Space, Trajectory U X ∧ | |
| (∀ Y : ℝ → Space, Trajectory U Y → ∀ t : ℝ, 0 ≤ t → Y t = X t) ∧ | |
| ((∃ t : ℝ, 0 ≤ t ∧ InStrip (X t)) ↔ M.Halts w) | |
| end Fluid | |
| end Solenoidal | |
| end OAI | |