OpenAI · reported seven-eighths half-plane
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.
1 cited passage ↓1 problem ↓Record git-fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb ↓
The exact passages cited in OpenMath. Each passage identifies how its wording was recorded.
OpenAI claims a fixed zero-free half-plane Re(s) > 7/8 for zeta and all Dirichlet L-functions.
Passage ID: riemann-hypothesis:rh-openai-seven-eighths:v1
Source item: openai-quasi-rh#rh-openai-seven-eighths
Source record: openai-quasi-rh@git-fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb
Explicit citations in versioned problem publications. A citation records a use; it does not confer proof or independent verification.
Problem publication v13
Source assessment
Proposed
Proposed bound · external formalization reported; review unchecked
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 date Sep 30, 2026 · Observed Oct 10, 2026
Research activity
Recent AI-related proposals awaiting assessment
OpenAI reports a seven-eighths zero-free half-plane with Lean artifacts; Gomila reports an improved positive Newman upper bound with interval certificates. Each proposed Claim has its own scope and pinned source evidence.
These are proposals in this publication, excluded from established progress. No cited source establishes the full classical RH here.
History
OpenAI’s proposed seven-eighths half-plane
Linked manuscripts, code and data. External proof reports, statement correspondence and OpenMath execution are separate checks.
Source-reported evidence
Manuscript claims a fixed Re(s) > 7/8 region. Its proof and faithfulness to the formal target have not been independently assessed by OpenMath.
Resource revision: fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb
Source-reported evidence
Weaker fixed region Re(s) > 11/12; an alternate argument within the same source family, not a duplicate new RH Problem.
Resource revision: fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb
Formal code
Source-reported evidence
The formalization catalogue maps actual Mathlib riemannZeta and Dirichlet L-function targets to this file. Comparator target files contain intentional sorry placeholders. No local compilation, axiom audit or statement-faithfulness review is asserted here.
Resource revision: fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb
Project notes
Source-reported evidence
Scope includes zeta, all positive Dirichlet moduli and finite-order Hecke L-functions over Q(√−3); excludes principal poles and later arithmetic applications.
Resource revision: fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb
Project notes
Source-reported evidence
Metadata declares review.status unchecked for the collection. Exact pin preserves later correction history.
Resource revision: fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb
Recorded authorship
OpenAI
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.
OpenMath source records preserve exact citations. Observation dates order these records; they do not establish the latest upstream paper or proof.
OpenAI · reported seven-eighths half-plane
No upstream full text or code is republished by this record.
Source terms ↗