Not evaluated
Quasi-Riemann hypothesis: zero-free half-plane Re(s) > 7/8 (family 003)
The gist
On October 6, 2026, OpenAI announced, for family 003, a “quasi-Riemann hypothesis”: a half-plane Re(s) > 7/8 free of zeros of the Riemann zeta function.
DiscoverIA status on October 11, 2026: not evaluated, meaning no third-party evaluation found.
AI draft, not reviewedWhat has not been reviewed?
Text written by an AI (DiscoverIA pipeline), on . The status and its sources come from the registry; only the explanatory text has not been reviewed. A reported error is corrected, then the text is reviewed.
Cite this entry
A single status snapshot since Oct 11, 2026: a citation always points to a dated snapshot.
Cite snapshot 1, Oct 11, 2026
APA citation with the dated link
BibTeX @misc, key discoveria-oai-fam-003-quasi-riemann-r1
@misc{discoveria-oai-fam-003-quasi-riemann-r1,
author = {{DiscoverIA}},
title = {Quasi-Riemann hypothesis: zero-free half-plane Re(s) > 7/8 (family 003)},
howpublished = {DiscoverIA registry, entry oai-fam-003-quasi-riemann},
note = {Status “Not evaluated”, snapshot 1, recorded on October 11, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-003-quasi-riemann#releve-1},
urldate = {2026-10-11}
}Dated link opens this snapshot in the history
To understand ≈ 30 s reading time, estimated
What it changes
Re(s) is the real part of a complex number s, and the Riemann hypothesis concerns the location of the zeros of the zeta function. If the result held, those zeros could not lie in the half-plane Re(s) > 7/8: this would be a weakened (“quasi”) version of the hypothesis, not the full hypothesis. According to an article in Nature, none of the 5 remaining millennium problems has been solved.
What remains unclear
The sources read give two values: Re(s) > 7/8, and Re(s) > 11/12, which the README cites separately. The Lean (a language in which a computer checks every step of a proof) is supplied by OpenAI only, and no third-party assessment is recorded.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · raw.githubusercontent.com
Step 1 of 4 on the scale: not evaluated. Next step: under review.
- Announced
- Recordednot evaluated
- nextTo follow
What this status means
Source reading : Source read word for word (level 3 of 3)
The result is declared neither right nor wrong.
To move to “Under review”: a public review under way. To “Peer reviewed”: a journal publication or a review by named experts.
Sources
- Main sourcegithub.comlink only, reading not recorded
Method
OpenAI publishes a manuscript (preprint) and a Lean configuration named QuasiRiemannHypothesis (formalization.yaml, line 777); according to a blog, its challenge is 9 lines long. The README carries the note “human edited for readability”. DiscoverIA status: not evaluated, meaning that no third-party evaluation has been found in the sources read. Set on October 11, 2026 from github.com (page read, quotation checked word for word).
Limits
The claimant supplies a Lean proof; as of this date, DiscoverIA has found no independent verification of this proof or of the result.
Key facts
- Claimed by
- OpenAI
announced on Oct 6, 2026 - Nature
- new result
- Field
- Mathematics (analytic number theory)
- Checked by
- claimant
- Sources
- 1 : 1 link only
- This entry
- AI draft, not reviewed
Status history
Only one observation so far.
An observation is added; none is ever erased.
In the same set
openai/math: 719 manuscripts in 372 families from an unreleased internal model · entry 3 of 372, by family number
- Not evaluated : Milne's rationality conjecture (family 001)
- Not evaluated : Full BSD formula for Selmer corank 0 or 1 (family 002)
- Not evaluated : Quasi-Riemann hypothesis: zero-free half-plane Re(s) > 7/8 (family 003)
- Not evaluated : Hilbert's tenth problem over Q (family 004)
- Not evaluated : Irrationality of Catalan's constant (family 005)
- Not evaluated : Goldfeld's conjecture (family 006)
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