Final assembly from deterministic estimates #
This module removes the abstract MainGoodEventInput interface. Given the
moving deterministic P-3.5b estimate and the R-322 counterterm estimate, the
measurable event is constructed internally and the characteristic-function
argument is completed at one common coupling threshold.
theorem
Anderson4D.mainConditional_of_secondMoment_and_deterministic_bounds
{M : NoiseModel}
{ρ : SmoothCutoff}
{K secondPower outerConstant goodPower Crenorm : ℝ}
(hK : 0 ≤ K)
(hsecondPower : 0 < secondPower)
(houter : 0 ≤ outerConstant)
(hgoodPower : 0 < goodPower)
(hCrenorm : 0 < Crenorm)
(hsecond : MainSecondMomentInput M ρ K secondPower)
(hdet :
∀ (lam : ℝ),
0 < lam →
∀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 goodPower lam ε m α β)
(hcounter :
∀ (lam : ℝ),
0 < lam →
∀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))
:
MainConditional M ρ
Complete quantifier assembly from the second-moment estimate and the two deterministic inputs to the one-sided operator good event.