| 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 | |