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MathlibNt.SieveTheory.LinearSieve.Suzuki.SuzukiUpperRosserFiniteToContinuousFinalProducer

Unconditional upper Rosser finite-to-continuous producers #

The boundary/source successor identity is now produced internally, so the finite-prefix comparison no longer exposes it as an input.

Finite continuous upper Rosser boundary factors are bounded by Suzuki's continuous upper factor, with the layer identity supplied internally.

theorem MathlibNt.SieveTheory.SwitchingPrinciple.exists_upperRosserBoundaryPrefix_le_suzukiContinuousUpperFactor_sub_one_add_of_source (H : SuzukiLemma144KappaOne.Section13HatLayers) (hH : SuzukiLemma144KappaOne.Section13HatSourceContract H) (L : ) (K ρ : ) (hK : 1 K) ( : 0 < ρ) :
∃ (z₀ : ), 2 z₀ ∀ (S : BoundingSieve) (z Δ s : ), z₀ z0 < ΔHasDimensionOneLocalProductBound S K(∀ pS.prodPrimes.primeFactors, p z)s = Real.log Δ / Real.log z3 / 2 ss 4kFinset.range L, qS.prodPrimes.primeFactors, S.nu q / (1 - S.nu q) * LinearSieve.upperRosserBoundaryChainsFixedDepthDensity (fun (p : ) => S.nu p / (1 - S.nu p)) (Δ⌋₊ + 1) q ({pS.prodPrimes.primeFactors | q < p}) k suzukiContinuousUpperFactor s - 1 + ρ

Fixed-depth mesh comparison landing below the genuine Suzuki upper factor; the source-layer producer is no longer a caller premise.

Jurkat--Richert rewrite of the unconditional finite-prefix producer.