Uniform Suzuki lower density for Chen's varying source family #
This is the first production consumer of the uniform-in-sieve Lemma 14.7. Its
constant is chosen before the varying family
jurkatRichertSourceBoundingSieve N; the proof then uses the literal Chen
floor level, adaptive supported-carrier depth, and the exact Euler/main-sum
bridges. No conclusion-shaped comparison premise is used.
Increasing the displayed dimension-one constant preserves the local-product
bound. This lets the source witness, which is stated with 1 < K, meet the
literal all-depth consumer's harmless normalization 2 ≤ K.
On Chen's interval, the natural Suzuki cutoff is no larger than the natural
floor level. This is the missing finite-carrier bridge needed by the exact
mainSum theorem.
Chen's varying source family satisfies the eventual lower-density estimate
with one Suzuki constant selected before the family varies. The fixed source
parameters are exactly (d, Δ, Θ) = (16, 1/2, 7).
The conclusion is at Chen's literal floor level and uses the production lower
Rosser weight. The arbitrary positive ρ absorbs the complete adaptive-depth
Suzuki error uniformly in the growing supported carrier.
The source-contract-relative Chen/Jurkat--Richert base lower-density fundamental lemma, obtained directly from the natural-ceiling varying-family producer rather than through the stronger generic real-parameter comparison.
The exact finite lower-Rosser expansion turns the density theorem above into Chen's base lower-sieve fundamental lemma, still retaining the genuine finite Goldbach remainder.
Chen's base lower asymptotic after the Suzuki source contract and the genuine standard Bombieri--Vinogradov input. The former now supplies the complete lower sieve; the only remaining premise here is the named distribution theorem.