theorem MathlibNt.SieveTheory.LiLiuOnePlusOneNine.GoldbachBig.goldbachS4_normalized_upper_pairKernel (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))) ≤ ((8 + δ) * goldbachB8PairLogKernel N + δ) * (SingularSeries.liuSingularSeries N * ↑N / Real.log ↑N ^ 2)

The actual S4 upper bound with only its actual finite prime-pair kernel left. No integral or decimal estimate for that kernel is assumed or asserted.