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Quasi-Riemann: a conditional 0.8733 target
An exact final-stage certificate for a possible zero-free boundary, contingent on an unproved arithmetic counting estimate.
v1.0 · 2026-11-12 · Editorial research note
A different zero-free problem
A quasi-Riemann zero-free bound asks for a constant θ < 1 such that the relevant Dirichlet L-functions have no zeros when Re(s) > θ, with the principal pole handled separately. A smaller θ is stronger, but any such bound above one half remains weaker than the Riemann hypothesis. The shared research conversation treats this as a separate project from its simple-zero proportion work.
The baseline reviewed
The conversation reports reviewing a public QuasiRiemannTracker formal development and a related preprint with a zero-free boundary near 0.8733819666. It says the author did not rebuild the full formal development locally or reprove its analytic foundations. That baseline and its scope belong to the cited external work; this note makes no independent validation claim about it.
The proposed conditional target
The conversation tested whether the final comparison system could reach θ = 0.8733. Its exact-arithmetic certificate says that stage is feasible if a new counting estimate saves an exponent of 1/1500 on a specified parameter rectangle. The certificate checks final margins and admission conditions; it does not prove the required arithmetic estimate. Without that missing input, 0.8733 is a target, not a new zero-free theorem.
What the negative control showed
The discussion also ran the parameters without the hypothetical saving. They failed the final comparison as expected. A seemingly favorable branch was unusable because it violated a length condition. This is a useful check against optimizing a displayed number while ignoring the theorem's conditions, but it does not supply the missing counting result.
Status and next mathematical step
Status: editorial summary of a conditional numerical target. The next substantive task is to prove the new estimate for the actual arithmetic family, with its required uniformity, and then integrate it into the analytic argument. Neither step is established by this note. The original verifier, replay certificate, and research bundle linked in the conversation are not included in this release. No reuse license has been specified.
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References
- Innovative Riemann Hypothesis Approach: shared research conversation — Zelnick Research and ChatGPT discussion, 2026
- QuasiRiemannTracker public source — GTimG and contributors, 2026
- Slightly improved zero-free half-planes for the quasi-Riemann hypothesis — Baiying Liu, 2026
- Riemann Hypothesis — Clay Mathematics Institute, n.d.
Zelnick Research (editorial notes) (2026). Quasi-Riemann: a conditional 0.8733 target. v1.0. Zelnick Research. https://research.zelnick.pw/work/quasi-riemann-conditional-target/?version=v1.0
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