theorem MathlibNt.SieveTheory.LiLiuOnePlusOneNine.GoldbachBig.goldbachB8MainIntegral_eight_mul_le_60962 : 8 * goldbachB8MainIntegral ≤ 60962 / 100000

Pure analytic scalar estimate for the actual production double integral I8.

theorem MathlibNt.SieveTheory.LiLiuOnePlusOneNine.GoldbachBig.goldbachS4_normalized_upper_60962 (δ ε : ℝ) (hδ : 0 < δ) (hε : 0 < ε) (hεu : ε < 2 / 15) : ∃ (N₀ : ℕ), 4 ≤ N₀ ∧ ∀ (N : ℕ), N₀ ≤ N → Even N → ↑(goldbachS4 (goldbachDifferenceCarrier N ε) N (↑N ^ (3 / 11))) ≤ (60962 / 100000 + δ) * (SingularSeries.liuSingularSeries N * ↑N / Real.log ↑N ^ 2)

The unchanged actual S4 count, with all upstream analytic errors already paid.