theorem MathlibNt.SieveTheory.LiLiuOnePlusOneNine.GoldbachBig.goldbachWeight_uniformCrossIntegralLedger (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 - 8 * (564383 / 1000000) * goldbachG12PrimeIntegral fun (x : ℝ) => 1) - δ) * (SingularSeries.liuSingularSeries N * ↑N / Real.log ↑N ^ 2) ≤ 4 * ↑(D19 N)

A fixed integral ledger after the actual G12 output sieve and cross quadrature. The uniform-level upper integral is retained literally; no final positive margin is asserted.