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SRBRD: The Symmetric Root-Bounded Relation Domain and the Sieve–Parity Boundary SRBRD-10 · The first uniformization barrier Author line in the source: Neo.K; Aletheia (GPT-5.6 Sol)

Uniform Moment Envelopes and Dual Polynomials: Phase-Free Envelopes Fail and the Bottleneck Is the CRT Phase Discrepancy

Builds a rigorous signed-moment-envelope interface (exact B_1, uniform lower and upper moment providers), but phase-free envelopes are too loose ('PHASE-FREE UNIFORM CLOSURE FAILS'); the barrier is localised to the CRT phase-hit discrepancy of positive moments.

A negative result: the authors' own verdict is 'PHASE-FREE UNIFORM CLOSURE FAILS; UNIFORM GOLDBACH CLOSURE STILL OPEN'. The next round announced here (CRT phase-hit / lattice packing) is not what SRBRD-11 does: the series turns to sieves and parity at this point. The numerics of this paper were not reproduced in the pre-publication read-through.

Connections · Connections

PreviousSRBRD-09 · The moment-polytope dual · Lattice Sparsity and the Moment-Polytope Dual: Finite Occupancy Caps, Polynomial Majorants, Even-Degree Certificates and Layered Moment LP Duality
NextSRBRD-11 · The sieve–parity audit · Square-Root Completion and the Sieve–Parity Interface: Fixed Cutoffs, Root-Complete Prime Certification, Bulk–Frontier Geometry and a Parity-Barrier Audit

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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