| import OAI.Analysis.IrrationalRotation.Model.CircleDigitMarginals |
| import OAI.Analysis.IrrationalRotation.Model.ParameterCircleOperator |
| import OAI.Analysis.IrrationalRotation.Model.CircleRationalGraphs |
|
|
| namespace OAI |
|
|
| noncomputable section |
| open MeasureTheory |
| namespace Invariant233.CircleCoupling |
|
|
| def finiteHybridChoice (N i : ℕ) : Bool := decide (i < N + 1) |
|
|
| def finiteHybridPoint (p : CircleParameterData) |
| (hr : ∀ i, 0 < MixedRadix.radices p.q i) (N : ℕ) : Sample → Circle := |
| hybridPoint p hr (finiteHybridChoice N) |
|
|
| def OrderedCouplingIdentities (p : CircleParameterData) (θ : ℝ) |
| (hr : ∀ i, 0 < MixedRadix.radices p.q i) |
| (F : Circle → Rotation.Fiber →L[ℂ] Rotation.Fiber) : Prop := |
| ∀ j : ℕ, ∀ᵐ ω ∂law p j, |
| (1 - F (point p hr true ω)) * |
| ratioDiagonal (p.floorCocycle θ) (point p hr false ω, point p hr true ω) * |
| F (point p hr false ω) = 0 ∧ |
| ∀ k : ℤ, 0 < p.floorCocycle θ k (point p hr true ω) / |
| p.floorCocycle θ k (point p hr false ω) ∧ |
| p.floorCocycle θ k (point p hr true ω) / |
| p.floorCocycle θ k (point p hr false ω) ≤ 1 |
|
|
| end Invariant233.CircleCoupling |
|
|
| end |
|
|
| end OAI |
|
|
