Publications & Preprints

On the Quantitative Sieve Parity Bypass under the Siegel Zero Hypothesis

This paper develops a quantitative form of the “exceptional-character bypass” of the sieve parity barrier for the binary Goldbach problem. The main statement is explicitly conditional: if a Siegel zero $\beta_1 = 1 - \delta_1$ of $L(s, \chi_D)$ exists, then the number of representations satisfies

with an effective constant $C$. Thus the paper does not prove the Goldbach conjecture; it shows that in the presence of an exceptional zero — the scenario usually regarded as an obstruction to sieve methods — the parity barrier can be bypassed, with an explicit dependence of the threshold on $\delta_1$.

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The Bilinear Minor-Arcs Hypothesis as the Unifying Isomorphism of the Sieve Parity Barrier

A meta-theoretic survey. Ten historically distinct formulations of the parity barrier — from classical sieve-theoretic ones to statements in the language of bilinear sums — are presented as projections of a single hypothesis, which the author calls the Bilinear Minor-Arcs Hypothesis (BMAH).

The main isomorphism theorem between these formulations is given in sketch form only: its proof is not complete, and the BMAH itself remains a conjecture. The text should be read as a map of the landscape, not as a summary of established facts.

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A Balanced Divisor-Weight Orthogonality Problem Arising from Additive Goldbach Witnesses

This note derives exact second-moment identities for shifted Möbius sums — sums of the shape $\sum_{n \le x} \mu(n)\,\mu(n+h)$ — arising from additive Goldbach witnesses. Eight rigid statements are proved. The central estimate $\mathrm{CWC}_3$ itself is stated as a conjecture — a theorem-card target — not a theorem, and it is not used as an input for any claim about the binary Goldbach problem.

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