theorem MathlibNt.SieveTheory.LiLiuOnePlusOneNine.GoldbachBig.goldbach_upperRosserDensity_fortyFiveEighths_audit (K ρ : ℝ) : 1 < K → 0 < ρ → ∃ (z₀ : ℝ), ∀ (S : BoundingSieve) (z Δ : ℝ), z₀ ≤ z → 2 ≤ z → 0 < Δ → SwitchingPrinciple.HasDimensionOneLocalProductBound S K → (∀ p ∈ S.prodPrimes.primeFactors, ↑p ≤ z) → 45 / 8 = Real.log Δ / Real.log z → BoundingSieve.mainSum (LinearSieve.upperRosserWeight S.prodPrimes (⌊Δ⌋₊ + 1)) ≤ (suzukiContinuousUpperFactor (45 / 8) + ρ) * AnalyticNumberTheory.Sieve.sieveProductPrimeFactors S

The actual 45/8 > 5 endpoint is an instance of the full six-window result.