noncomputable def MathlibNt.SieveTheory.LiLiuOnePlusOneNine.GoldbachBig.goldbachWeightFiveNegativeScalarCoefficient : ℝ

The five certified negative scalar entries; the positive lower factors remain literal.

Equations

• MathlibNt.SieveTheory.LiLiuOnePlusOneNine.GoldbachBig.goldbachWeightFiveNegativeScalarCoefficient = Real.exp (-Real.eulerMascheroniConstant) * (159 / 2 * MathlibNt.SieveTheory.SwitchingPrinciple.dimensionOneLowerLinearSieveFactor 6 + 33 / 2 * MathlibNt.SieveTheory.SwitchingPrinciple.dimensionOneLowerLinearSieveFactor (33 / 8)) - 2360636 / 100000 - 1951976 / 100000 - 4 * (84289 / 100000) - 540996 / 100000 - 2 * (60962 / 100000)

theorem MathlibNt.SieveTheory.LiLiuOnePlusOneNine.GoldbachBig.goldbachWeightFiveNegativeScalarCoefficient_le : goldbachWeightFiveNegativeScalarCoefficient ≤ goldbachWeightThreeNegativeScalarCoefficient

theorem MathlibNt.SieveTheory.LiLiuOnePlusOneNine.GoldbachBig.goldbachWeight_remainingFive_fiveNegativeScalars_small_epsilon (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 → ↑(goldbachWeightRemainingFive (goldbachDifferenceCarrier N ε) N (↑N ^ (4 / 53)) (↑N ^ (4 / 33)) (↑N ^ (3 / 11))) + (goldbachWeightFiveNegativeScalarCoefficient - δ) * (SingularSeries.liuSingularSeries N * ↑N / Real.log ↑N ^ 2) ≤ 4 * ↑(D19 N)

The actual signed D19 inequality; no positivity of the coefficient or remaining count asserted.