theorem MathlibNt.SieveTheory.LiLiuOnePlusOneNine.GoldbachBig.goldbachWeight_twelve_base_I10_consumed_eventually (δ : ℝ) (hδ : 0 < δ) (ε : ℝ) : 0 < ε → ε < 2 / 15 → ∃ (N₀ : ℕ), 4 ≤ N₀ ∧ ∀ (N : ℕ), N₀ ≤ N → Even N → ∀ (α : ℝ), 1 / 18 < α → α < goldbachB10Beta → ↑(goldbachWeightTwelveBase (goldbachDifferenceCarrier N ε) N (↑N ^ α) (↑N ^ goldbachB10Beta) (↑N ^ goldbachB10Gamma) (↑N ^ (9 / 19 - ε))) - (8 * (1 - ε) * goldbachB10I10 + δ) * (SingularSeries.liuSingularSeries N * ↑N / Real.log ↑N ^ 2) ≤ 4 * ↑(D19 N)

Consume the proved I10 upper bound into the actual signed eleven-term base expression, keeping the literal goldbachWeightTwelveBase rather than asserting any separate positivity of that base.