Numerical analysis reports nine consecutive Riemann-Siegel zeros near height 3 × 10^12, highlighting reproducible precision benchmarks beyond verified bounds.
This technical note reports a reproducible arbitrary-precision computation of nine consecutive sign-changing zeros of the Riemann-Siegel function between heights 3,000,175,333,800 and 3,000,175,333,802. The first ordinate is 3,000,175,333,800.08525171240694953081383928693..., numerically identified as zero number 12,363,153,441,418. The interval begins 1,000 units above the endpoint of the rigorous Platt-Trudgian verification. Direct residual evaluations, sign-change checks, endpoint zero counts, and full reproduction code are included. Scope: this is a reproducible computational data record. It does not provide interval-arithmetic certification, extend the rigorously verified Riemann-hypothesis height, or assert that the ordinates have never been computed privately or in an unindexed dataset.
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Zeraoulia Rafik (2026) studied this question.
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