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8fadf68 | 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 | import OAI.Geometry.NodalSets.Elliptic.SeedFrequencyDivergence
import OAI.Geometry.NodalSets.SmoothLimit.SphereIterationInterface
namespace OAI
namespace Yau.Target
open Manifold
open scoped ContDiff
noncomputable section
theorem sphere_persistent_limit_implies_main {r delta : ℝ}
(s : (k : ℕ) → SphereNodalStage r delta k) (hN : ∀ k, k+1 ≤ (s k).frequency)
(b : SphereEnergyData) (hb : ContMDiff (𝓡 4) 𝓘(ℝ,ℝ) ∞ b.density)
(hnear : ∀ k, sphereCoefficientDistance (s k).charts 8
(s k).energy.tensor (s k).energy.density b.tensor b.density < (s k).radius) :
MainTarget := by
have H (k : ℕ) := (s k).persistence b hb (hnear k)
choose mu v hwindow hmu hv hv0 he hlift hln hle hratio using H
exact mainTarget_of_seed_windows
(intrinsicWeightedMetric b.tensor b.smooth b.symm b.pos b.density hb b.positive)
(fun k ↦ (s k).frequency) mu (fun k ↦ circleLift (v k)) hN hmu
(fun k ↦ (hwindow k).1) hln hlift hle hratio
end
end Yau.Target
end OAI
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