Not evaluated
Counterexamples to the ordinary Fried conjecture near hyperbolic metrics (Becker and Lawton, with GPT-6.1 Sol and Claude Code)
The gist
On October 15, 2026, Simon Becker and Benjamin Lawton posted on arXiv counterexamples to the ordinary Fried conjecture in dimension 3, built with GPT-6.1 Sol and partly formalised in Lean with Claude Code.
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-becker-lawton-fried-2026-10-15-r1
@misc{discoveria-becker-lawton-fried-2026-10-15-r1,
author = {{DiscoverIA}},
title = {Counterexamples to the ordinary Fried conjecture near hyperbolic metrics (Becker and Lawton, with GPT-6.1 Sol and Claude Code)},
howpublished = {DiscoverIA registry, entry becker-lawton-fried-2026-10-15},
note = {Status “Not evaluated”, snapshot 1, recorded on October 24, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/becker-lawton-fried-2026-10-15#releve-1},
urldate = {2026-10-24}
}Dated link opens this snapshot in the history
To understand ≈ 30 s reading time, estimated
What it changes
On a negatively curved manifold, the Fried conjecture relates the value at zero of a zeta function built from closed geodesics to an invariant called torsion. If the counterexamples held, this identity would fail for some real analytic metrics arbitrarily close to a hyperbolic metric in dimension 3. "Ordinary" refers to the value of the zeta function itself at zero, which the paper distinguishes from a corrected invariant, Chaubet and Dang's dynamical torsion.
What remains unclear
The Lean formalisation covers only conditional algebraic and limiting steps: the geometric and spectral inputs are not formalised. No third party has reviewed the work yet.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · arxiv.org · abs/2610.22281
Step 1 of 4 on the scale: not evaluated. Next step: under review.
- Announced
- Recordednot evaluated
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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 sourcearxiv.org · abs/2610.22281page read word for word · consulted on Oct 24, 2026 ·
We give an LLM-assisted construction of counterexamples to the ordinary Fried conjecture
- Paperarxiv.org · html/2610.22281page read word for word · consulted on Oct 24, 2026 ·
The Lean verification covers conditional algebraic and limiting steps. The geometric and spectral inputs are not formalized.
- Lean proofgithub.comlink only, reading not recorded
Method
Simon Becker asked GPT-6.1 Sol, in Codex, to prove M. Zworski's Conjecture 9; the resulting argument led to the counterexample instead. Benjamin Lawton used Claude and Claude Code for research, derivations, writing, checks and the partial Lean formalisation, published in the blawton/fried-conj-lean repository. DiscoverIA status: not evaluated, meaning that no third-party evaluation has been found in the sources read. Set on October 24, 2026 from arxiv.org (page read, quotation checked word for word: “We give an LLM-assisted construction of counterexamples to the ordinary Fried conjecture”).
Limits
The claimant supplies Lean proofs for the conditional algebraic and limiting steps only; DiscoverIA has found no independent verification of them.
Key facts
- Claimed by
- Simon Becker et Benjamin Lawton, with GPT-6.1 Sol (OpenAI) et Claude Code (Anthropic)
announced on Oct 15, 2026 - Nature
- new result
- Field
- Mathematics (spectral geometry / dynamical zeta functions)
- Checked by
- no verifier identified
- Sources
- 3 : 2 read word for word, 1 link only
- This entry
- AI draft, not reviewed
Status history
Only one observation so far.
- 01
First observation:Not evaluatedCurrent status
arXiv preprint, not peer-reviewed; partial Lean supplied by the authors; no third-party evaluation found
Source: arxiv.orgread word for word
An observation is added; none is ever erased.
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