theorem MathlibNt.SieveTheory.LiLiuOnePlusOneNine.GoldbachBig.fouvryG9Mother_analytic_upper : ∃ (C : ℝ), 0 < C ∧ ∃ (K : ℝ), 1 < K ∧ ∀ (A : ℕ) (e ε δ η ρ : ℝ), 0 < e → e ≤ 1 → 0 < ε → ε < 4 / 53 → ε < δ → δ < 1 / 4 → 0 < η → η < 1 / 8 → 1 < ρ → ρ ≤ 5 / 4 → ∃ (N₀ : ℝ), ∀ (N : ℕ), N₀ ≤ ↑N → Even N → fouvryG9MotherSifted N e (fouvryG9SievePrimes N √↑N) ≤ ∑ k ∈ fouvryG9GridUsed N e ρ, fouvryG9UpperFactor N (↑N ^ (5 / 9 - δ) / (2 / 3 * ρ ^ k.1) ^ (5 / 9)) C K η * fouvryG9RectangleEulerMass N ρ k (fouvryG9SievePrimes N √↑N) + ↑N / Real.log ↑N ^ A

Actual mother upper sieving with the analytic extended F-factor. Both the prime-density hypotheses and all distribution/transport errors are supplied by proved producers. The still-visible Euler mass is to be estimated next.