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Riemann hypothesis: a simple-zero bound draft
A proposed proportion bound from an earlier discussion, recorded as an unverified draft rather than a theorem.
v1.0 · 2026-11-12 · Editorial research note
The problem and a narrower question
The Riemann hypothesis says that all nontrivial zeros of the Riemann zeta function have real part one half. The Clay Mathematics Institute continues to list it as unsolved. This note concerns a narrower question from an earlier AI-assisted discussion: what proportion of critical-line zeros might be shown to be simple using a proposed analytic argument? Even a valid positive proportion would not prove the Riemann hypothesis.
What the draft proposed
The conversation outlined a possible lower bound of 67.342378146% for simple critical zeros, using a proposed refinement of a zeta-method argument. That figure is recorded here as the draft's target, not as an established theorem or record. The full derivation, source bundle, and reproducible checks are absent from this release. We have not independently verified the key inequalities or the numerical optimization.
What verification would require
A publishable mathematical claim would need the complete argument, exact definitions and hypotheses, justified error terms, a reproducible optimization or computation, and specialist review. The discussion specifically identified a local interval inequality and a variable spectral threshold as steps needing scrutiny. Until those steps are available and checked, this site makes no quantitative claim about the true proportion.
Status and provenance
Status: unverified research draft summarized as an editorial note. The downloadable file contains this summary only. It is not the original RH bundle, a proof of the Riemann hypothesis, or a certified bound. Authorship credit identifies the editorial note; cited external work remains with its authors.
For the formulation and current status of the Riemann hypothesis, consult the Clay Mathematics Institute. A recent preprint on related simple-zero bounds is linked as context; its claims should be read in the original paper, not inferred from the draft percentage above.
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References
- Riemann Hypothesis — Clay Mathematics Institute, n.d.
- More than 83.9% of the zeros of the Riemann zeta function are distinct and more than 67.35% are simple and on the critical line — Kristian Muri Knausgård, 2026
Zelnick Research (editorial notes) (2026). Riemann hypothesis: a simple-zero bound draft. v1.0. Zelnick Research. https://research.zelnick.pw/work/riemann-critical-zeros-draft/?version=v1.0
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