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Anderson4D.Parametrix.L2GoodEventClosure

Closed one-sided good-event estimate #

This module removes the final Proposition 3.4 interface from the one-sided numerical good-event theorem. The pairing/graded coefficient agreement is automatic on every positive-scale continuous-noise event.

theorem Anderson4D.PartialPairing.eventually_measureReal_compl_canonicalConstructedOneSidedGoodEvent_le_two_mul_sq_closed {M : NoiseModel} {ρ : SmoothCutoff} {outerConstant powerConstant Crenorm lam : ℝ} (houter : 0 ≤ outerConstant) (hpower : 0 ≤ powerConstant) (hCrenorm : 0 ≤ Crenorm) (hlam : 0 ≤ lam) (hlamle : lam ≤ 1) (hpowerRatio : powerConstant * lam ≤ boundaryGeometricRatio) (hrenormRatio : Crenorm * lam ≤ boundaryGeometricRatio) (hdet : ∀ᶠ (ε : ℝ) in nhdsWithin 0 (Set.Ioi 0), ∀ (m : ℕ), 1 ≤ m → m ≤ truncOrder ε → ∀ (α β : Z4), ‖deterministicMomentPairingSum ρ lam ε m α β‖ ≤ deterministicMomentRHS outerConstant powerConstant lam ε m α β) (hcounter : ∀ᶠ (ε : ℝ) in nhdsWithin 0 (Set.Ioi 0), ∀ q ∈ Finset.Icc 1 (truncOrder ε), |renormC2q ρ lam ε q| ≤ ε⁻¹ ^ 2 / |Real.log ε| * (Crenorm * lam) ^ (2 * q)) :

The exact 2 ε² exceptional-set bound with all Proposition 3.4 inputs discharged. Only the deterministic P-3.5b estimate and the renormalization-constant estimate remain as quantitative inputs.