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SRBRD: The Symmetric Root-Bounded Relation Domain and the Sieve–Parity Boundary SRBRD-09 · The moment-polytope dual Author line in the source: Neo.K; Aletheia (GPT-5.6 Sol)

Lattice Sparsity and the Moment-Polytope Dual: Finite Occupancy Caps, Polynomial Majorants, Even-Degree Certificates and Layered Moment LP Duality

Because occupancy is capped, union upper bounds can be certified by polynomial majorants or a layered moment-polytope LP with rational dual certificates, which allows even degrees (m = 5000: degree 4 vs Bonferroni 5; m = 10⁶: degree 6 vs 7).

A finite-moment certificate family strictly stronger than Bonferroni; still finite certificates per m. Verdict: UNIFORM GOLDBACH CLOSURE STILL OPEN. This is the classical binomial-moment LP (Prékopa / Boros–Prékopa type), not cited in the paper; the m = 10⁶ control comes with no code or data and cannot be reproduced from the file.

Connections · Connections

PreviousSRBRD-03 · Center–frontier occupancy · Center–Frontier Occupancy: The Exact Bonferroni Remainder and a Cap-Corrected Non-Cover Certificate

NextSRBRD-10 · The first uniformization barrier · Uniform Moment Envelopes and Dual Polynomials: Phase-Free Envelopes Fail and the Bottleneck Is the CRT Phase Discrepancy

This is a full-text translation of the Chinese source, which remains authoritative for its research claims. Translation is not independent mathematical verification and does not upgrade the original evidence level.

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