Bound · version 1
Earlier version 1. View current version 2 →
The source claims ζ(s) ≠ 0 for Re(s) > 7/8, and the same region for every Dirichlet L-function, with principal-character poles at s = 1 excluded. It also claims this for finite-order Hecke L-functions over Q(√−3).
A claimed fixed half-plane, stronger than a region shrinking toward 1, but weaker than RH.
This source presents a theorem with a proposed proof. Its wording does not establish acceptance or independent mathematical review.
Proposed
Only the exact statement, domain and revision cited by this Claim; this is not a resolution of classical RH or independent OpenMath expert assessment.
Source dated Sep 30, 2026 · Observed Oct 10, 2026
In this problem · publication v3 · Selected context
Bound · Proposed
If validated, this would exclude zeros to the right of 7/8 at every height; it would still leave 1/2 < Re(s) ≤ 7/8 unresolved. This proposed Claim is not included in established progress.
Relationship not independently reviewed. This concerns its use in this problem.
In this problem · publication v4
Bound · Proposed
If validated, this would exclude zeros to the right of 7/8 at every height; it would still leave 1/2 < Re(s) ≤ 7/8 unresolved. This proposed Claim is not included in established progress.
Relationship not independently reviewed. This concerns its use in this problem.
OpenAI claims a fixed zero-free half-plane Re(s) > 7/8 for zeta and all Dirichlet L-functions.
paraphrase · No upstream full text or code is republished by this record.
OpenAI · Preprint
Preprint released in the 6 October 2026 collection. The repository’s formalization metadata marks review status unchecked. Recorded here as a proposed result awaiting assessment; formal checking and mathematical faithfulness are separate.
Source revision: git-fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb. Observed Oct 10, 2026.
OpenAI attributes this collection to an unreleased internal model. The zero-free-region work is an exception to the usual fixed evaluation procedure; the alternate 11/12 writeup was human-edited for readability. Do not infer a public model version or attribute individual GPT-6 submissions to this company release.
Source updated Sep 30, 2026.
Statement versions and problem publication versions are separate. A new publication can update context or sources while retaining the same statement.
Assessments retained in these publication records. Earlier statement versions retain their own source histories.
Proposed
Only the exact statement, domain and revision cited by this Claim; this is not a resolution of classical RH or independent OpenMath expert assessment.
Source dated Sep 30, 2026 · Observed Oct 10, 2026 · Source passage →