Not evaluated
A quasi-Riemann hypothesis for Dedekind zeta functions (Cureton and Thorner, with AxiomProver)
The gist
Dean Cureton and Jesse Thorner posted on Hexagon, on October 12, 2026, a proof obtained with the AxiomProver system that no Dedekind zeta function would vanish when the real part exceeds 31/32 (version of October 14).
DiscoverIA status on October 24, 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 24, 2026: a citation always points to a dated snapshot.
Cite snapshot 1, Oct 24, 2026
APA citation with the dated link
BibTeX @misc, key discoveria-cureton-thorner-qrh-dedekind-2026-10-12-r1
@misc{discoveria-cureton-thorner-qrh-dedekind-2026-10-12-r1,
author = {{DiscoverIA}},
title = {A quasi-Riemann hypothesis for Dedekind zeta functions (Cureton and Thorner, with AxiomProver)},
howpublished = {DiscoverIA registry, entry cureton-thorner-qrh-dedekind-2026-10-12},
note = {Status “Not evaluated”, snapshot 1, recorded on October 24, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/cureton-thorner-qrh-dedekind-2026-10-12#releve-1},
urldate = {2026-10-24}
}Dated link opens this snapshot in the history
To understand ≈ 30 s reading time, estimated
What it changes
Dedekind zeta functions extend the Riemann zeta function to number fields. If the result held, none of them would have a zero in the half-plane where the real part exceeds 31/32, a weakened form of the Riemann hypothesis known as a quasi-Riemann hypothesis. The work follows the strategy of an OpenAI preprint on Artin's conjecture, which obtained a narrower region of this kind for certain Hecke L-functions and for the zeta functions of certain fields; OpenAI had also announced the bounds 7/8 and 11/12 for Dirichlet L-functions, including the Riemann zeta function.
What remains unclear
Hexagon does not carry out peer review, and no third party has checked the proof yet: Iwao Kimura cites it while stating that he has not checked it. The Lean formalisation comes from the authors.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · hexagonmath.org · 2610.00200v2
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 sourcehexagonmath.org · 2610.00200v2page read word for word · consulted on Oct 24, 2026 ·
If K is any number field, then ζ_K(s) ≠ 0 when Re s > 31/32 and s ≠ 1.
- Paperhexagonmath.org · 2610.00200v1page read word for word · consulted on Oct 24, 2026 ·
If K is any number field, then ζ_K(s) ≠ 0 when Re s > 1 − 1/6000.
- Lean proofgithub.compage read word for word · consulted on Oct 24, 2026 ·
AxiomProver generated the proofs and Lean formalization.
- Corroborationarxiv.orgpage read word for word · consulted on Oct 24, 2026 ·
These preprints have not been refereed, and we have not checked their proofs
Method
Axiom Math's AxiomProver system generated the proofs and their Lean formalisation; the two researchers set the direction and take responsibility for the results. The first version, of October 12, gave the bound 1 − 1/6000, and the second, of October 14, widens the region to a width of 1/32; on Hexagon, the version 1 page nonetheless already shows 31/32. The formalisation is published in the AxiomMath/DedekindZetaZeroFree repository. DiscoverIA status: not evaluated, meaning that no third-party evaluation has been found in the sources read. Set on October 24, 2026 from hexagonmath.org (page read, quotation checked word for word: “If K is any number field, then ζ_K(s) ≠ 0 when Re s > 31/32 and s ≠ 1.”).
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
- Dean Cureton et Jesse Thorner, with AxiomProver (Axiom Math)
announced on Oct 12, 2026 - Nature
- new result
- Field
- Mathematics (number theory / Dedekind zeta functions)
- Checked by
- no verifier identified
- Sources
- 4 : 4 read word for word
- This entry
- AI draft, not reviewed
Status history
Only one observation so far.
- 01
First observation:Not evaluatedCurrent status
preprint on Hexagon, a platform without peer review; Lean supplied by the authors only; Iwao Kimura (arXiv 2610.21511v2, October 22) cites it without having checked it; no…
Read the full reason
preprint on Hexagon, a platform without peer review; Lean supplied by the authors only; Iwao Kimura (arXiv 2610.21511v2, October 22) cites it without having checked it; no third-party evaluation found
Source: hexagonmath.orgread word for word
An observation is added; none is ever erased.
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