What question did this study set out to answer?

To establish an improved lower bound for the proportion of simple zeros of the Riemann zeta function located on the critical line.

August 16, 2026Open Access

A two-certificate trace-energy deduction for simple zeros of the Riemann zeta function

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To establish an improved lower bound for the proportion of simple zeros of the Riemann zeta function located on the critical line.
Retained certified seven-point and nine-point gap inequalities simultaneously across the same window.
Absorbed the gap inequalities into a supporting plane for the finite-dimensional trace-energy envelope.
Utilized exact arithmetic checks and pinned upstream interval certificates representing 2,168,370-node and 116,272,426-node computational runs.
Established a research-draft candidate asymptotic lower bound of liminf_{T->infinity} N_0^s(T,2T)/N(T,2T) >= 0.6733169771424713... (> 0.673316977).
Provided an open-source archive enabling independent reproducibility of the local deduction and exact arithmetic comparisons.

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Implication

Mathematical analysis demonstrates a lower bound exceeding 67.33% for simple zeros of the Riemann zeta function, indicating progress in understanding critical line zero distributions.

Cite This Study

Yuhang Shi (2026) studied this question.

synapsesocial.com/papers/6a8179cbf2fb91fc834ad1b3 https://doi.org/10.5281/zenodo.21926962

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Implication

Mathematical analysis demonstrates a lower bound exceeding 67.33% for simple zeros of the Riemann zeta function, indicating progress in understanding critical line zero distributions.

A two-certificate trace-energy deduction for simple zeros of the Riemann zeta function

Key Points

Discussion

Implication

Cite This Study

A two-certificate trace-energy deduction for simple zeros of the Riemann zeta function

Key Points

Discussion

Implication

Cite This Study

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