| import OAI.MathematicalPhysics.RapidForcing.NSUniqueness |
| import OAI.MathematicalPhysics.RapidForcing.SchwartzRestriction |
|
|
| namespace OAI |
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|
|
| namespace RapidForcing |
|
|
| theorem addressed_analytic_realization (ν : ℝ) (hν : 0 < ν) (M : Machine) (w : M.Input) : |
| let u := addressedVelocity M w |
| let f := addressedForce ν M w |
| Smooth f ∧ Supported f ∧ Rapid f ∧ RapidSpaceTime f ∧ |
| Smooth u ∧ Supported u ∧ Rapid u ∧ RapidSpaceTime u ∧ |
| UniqueEnergySolution ν f u (fun _ _ => 0) ∧ |
| ∃ X : ℝ → Space → Space, MaterialFlow u X ∧ |
| (M.Halts w ↔ ∃ t : ℝ, 0 ≤ t ∧ (X t 0) 0 < -1) := by |
| obtain ⟨hfS, hfK, huS, huK, _⟩ := addressed_classical_solution ν M w |
| obtain ⟨huR, huRX, hfR, hfRX⟩ := addressed_fields_rapid ν M w |
| exact ⟨hfS, hfK, hfR, hfRX, huS, huK, huR, huRX, |
| addressed_uniqueEnergySolution hν.le M w, addressed_particle_detection M w⟩ |
|
|
| end RapidForcing |
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|
| end OAI |
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|
