| import Mathlib |
| import OAI.MeasureTheory.Falconer.Model |
| import OAI.MeasureTheory.Falconer.Recursion.InteriorPolicy |
| import OAI.MeasureTheory.Falconer.Recursion.Ledger |
| import OAI.MeasureTheory.FalconerCompletion.Graphs.GraphCapScaleInvCrude |
| import OAI.MeasureTheory.FalconerCompletion.Shells.TransportedAngularField |
|
|
| namespace OAI |
|
|
| /-! Recursive policies and quantitative depth estimates. -/ |
|
|
| open _root_.OAI.PlanarFalconer |
|
|
| section |
| section |
| open Set MeasureTheory |
| open scoped ComplexConjugate RealInnerProductSpace |
| namespace GraphLiteralSupport.CurrentFalconer.TreeND |
| open Set MeasureTheory PlanarFalconer |
| open scoped ContDiff |
| variable {n : ℕ} |
| namespace PositiveDistanceState |
| variable (e : PositiveDistanceState (n+1)) |
|
|
| noncomputable def sourcePrefixDepth : ℕ := |
| policyDepth (adjustedProfile (d:=n+1) e.mass e.N) e.N e.q e.a e.t |
|
|
| noncomputable def prefixPhasedLeft (z : PrefixAssignment n) |
| (ξ : EuclideanSpace ℝ (Fin (n+1))) (x w : EuclideanSpace ℝ (Fin (n+1))) : ℂ := |
| Attempt4PrefixShell.SpatialFourierND.spatialFourierPhase (n+1) ((2:ℝ)^e.a)⁻¹ ξ x * e.prefixInverseLeft z x w |
| noncomputable def prefixPhasedRight (z : PrefixAssignment n) |
| (ξ : EuclideanSpace ℝ (Fin (n+1))) (x w : EuclideanSpace ℝ (Fin (n+1))) : ℂ := |
| Attempt4PrefixShell.SpatialFourierND.spatialFourierPhase (n+1) ((2:ℝ)^e.a)⁻¹ ξ x * e.prefixInverseRight z x w |
|
|
| noncomputable def prefixGraphChildMax (v : ℝ) (Ψ : ℝ → ℝ) |
| (z : PrefixAssignment n) (ξ : EuclideanSpace ℝ (Fin (n+1))) : ℝ := |
| _root_.OAI.CurrentFalconer.TreeND.graphSourceChildMax e.ρ e.ρ e.a e.sourcePrefixDepth v e.X e.Y |
| (((2:ℝ)^e.N)^(-e.mass e.sourcePrefixDepth)) |
| (((2:ℝ)^e.N)^(-e.mass e.sourcePrefixDepth)) Ψ |
| (e.prefixPhasedLeft z ξ) (e.prefixPhasedRight z ξ) |
|
|
| noncomputable def prefixGraphFactor : ℝ := |
| let A := adjustedProfile (d:=n+1) e.mass e.N |
| ((2:ℝ)^e.N)^(-2*(A e.sourcePrefixDepth-A e.a)+height A e.a e.sourcePrefixDepth+ |
| (e.C+36*(n+1:ℝ)+5)*e.sig) |
| end PositiveDistanceState |
| end GraphLiteralSupport.CurrentFalconer.TreeND |
| end |
| end |
|
|
| end OAI |
|
|
