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))
:
∀ᶠ (ε : ℝ) in nhdsWithin 0 (Set.Ioi 0), MeasureTheory.volume.real
(canonicalOneSidedL2ParametrixGoodEvent M ρ lam ε (truncOrder ε)
(canonicalGradedTruncatedParametrixL2Factor M ρ lam ε (truncOrder ε))
(canonicalPerrLeftRemainder M ρ lam ε (truncOrder ε)))ᶜ ≤ 2 * ε ^ 2
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.