| import OAI.Analysis.IrrationalRotation.Model.ParameterCircleWeights | |
| import OAI.Analysis.IrrationalRotation.Model.CompactTransfer | |
| import Mathlib.MeasureTheory.Measure.FiniteMeasure | |
| namespace OAI | |
| noncomputable section | |
| open MeasureTheory | |
| namespace Invariant233 | |
| def circleTranslationGraph (t : Circle) : FiniteMeasure (Circle × Circle) := | |
| ⟨circleMeasure.map (fun x => (x, x + t)), by | |
| change IsFiniteMeasure ((volume : Measure Circle).map (fun x => (x, x + t))) | |
| infer_instance⟩ | |
| namespace CircleParameterData | |
| def rationalTranslation (p : CircleParameterData) (A : ℕ) (r : ℤ) : Circle := | |
| (((r : ℝ) / (p.q A : ℝ) : ℝ) : Circle) | |
| def rationalRatioBound (p : CircleParameterData) (A : ℕ) : ℝ := | |
| Real.exp (∑ i ∈ Finset.range (A - 1), p.flattenedCost i) | |
| def RationalGraphIdentities (p : CircleParameterData) (θ : ℝ) | |
| (P : Circle → SequenceHilbert ℤ →L[ℂ] SequenceHilbert ℤ) : Prop := | |
| ∀ᵐ x ∂circleMeasure, ∀ A : ℕ, 1 ≤ A → ∀ r : ℤ, | |
| (1 - P (x + p.rationalTranslation A r)) * | |
| ratioDiagonal (p.floorCocycle θ) (x, x + p.rationalTranslation A r) * P x = 0 | |
| end CircleParameterData | |
| end Invariant233 | |
| end | |
| end OAI | |