← SRBRD: The Symmetric Root-Bounded Relation Domain and the Sieve–Parity Boundary / SRBRD-11 · The sieve–parity audit

SRBRD: The Symmetric Root-Bounded Relation Domain and the Sieve–Parity Boundary SRBRD-11 · The sieve–parity audit Author line in the source: Neo.K; Aletheia (GPT-5.6 Sol)

Square-Root Completion and the Sieve–Parity Interface: Fixed Cutoffs, Root-Complete Prime Certification, Bulk–Frontier Geometry and a Parity-Barrier Audit

The fixed-cutoff bulk of SRBRD is exactly a two-linear-form residue sieve; no fixed cutoff gives both a positive bulk radius and double-endpoint root completeness (T07); separating primes from rough P₂ is the classical parity problem; a Chen-type result serves only as an external benchmark.

Verdict 'SIEVE-PARITY BOUNDARY IDENTIFIED'; the paper says outright 'this round is not an SRBRD-11 PROOF PASS'; Chen's theorem is 'not a theorem of this document but an external benchmark'; whether SRBRD's extra structure escapes the parity barrier is answered 'currently unknown'. The rough predicate wrongly treats primes ≤ z as obstructions; this is corrected in SRBRD-13 (see the download table below).

Connections · Connections

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

NextSRBRD-14 · The transport identity and parity correlation · Aggregate Semiprime-Cell Coupling: Diagonal / Off-Diagonal Transport Matrix, the Prime-Majority Criterion, a Recursive Diagonal Lower Bound and the Parity-Correlation Identity

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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