theorem
MathlibNt.SieveTheory.caseII_rounded_transportErr_le_positiveDelta_relative_packet_sourceLarge_coefficients
(S : BoundingSieve)
(H : SwitchingPrinciple.SuzukiLemma144KappaOne.Section13HatLayers)
{N D z : ℕ}
{yr zr d Δ σ C K B0 s : ℝ}
(hH : SwitchingPrinciple.SuzukiLemma144KappaOne.Section13HatContract H 2)
(hN : Odd N)
(hD : Real.exp 1 ≤ ↑D)
(hΔ0 : 0 < Δ)
(hΔ1 : Δ < 1)
(hσ : 3 ≤ σ)
(hs1 : 1 < s)
(hK : 0 ≤ K)
(_hC : 0 ≤ C)
(hsmall : 3 ^ d ≤ Real.log ↑D)
(hE : 1 / 3 ≤ SwitchingPrinciple.SuzukiLemma144KappaOne.errorEnvelope H N (↑D) d s)
(hP : 3 ≤ C * Real.exp √K)
(hyr : yr = ↑D ^ (1 / 3))
(_hzr : zr = ↑D ^ (1 / s))
(hz : z = ⌈zr⌉₊)
:
caseIIRoundedTransportErr S H N (↑D) yr zr d Δ σ C K B0 s + SwitchingPrinciple.suzukiVProduct S ↑z * (K * 3 ^ 2 / (s * Real.log ↑D)) ≤ B0 + SwitchingPrinciple.suzukiVProduct S ↑z * (caseIIPositiveDeltaIntegralPart H N (↑D) yr d Δ σ C K s + C * Real.exp √K * SwitchingPrinciple.SuzukiLemma144KappaOne.errorEnvelope H N (↑D) d s * Real.log ↑D ^ (-Δ) * caseIIEndpointRelativeCoeffSourceLarge N (↑D) Δ σ K)
Exact-ratio, scale-free rounded transport packet for the source-large branch.