theorem MathlibNt.SieveTheory.LiLiuOnePlusOneNine.GoldbachBig.goldbachWeight_sharpCrossIntegralLedger (δ : ℝ) (hδ : 0 < δ) : ∃ (ε₀ : ℝ), 0 < ε₀ ∧ ε₀ ≤ 2 / 15 ∧ ∀ (ε : ℝ), 0 < ε → ε < ε₀ → ∃ (N₀ : ℕ), 4 ≤ N₀ ∧ ∀ (N : ℕ), N₀ ≤ N → Even N → (goldbachG67IntegralConstant + 124341093 / 200000000 - goldbachB9PaperSplitIntegral - 10385101 / 100000000 - goldbachG12SharpIntegralConstant - δ) * (SingularSeries.liuSingularSeries N * ↑N / Real.log ↑N ^ 2) ≤ 4 * ↑(D19 N)

Fixed author-weighted G12 ledger. The full actual JR positive constant is retained; this does not assert a rational numerical estimate or net positivity.