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b224933 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 | 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
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