Not evaluated
Central limit theorem for the high-temperature SYK model: announced proof, obtained with ChatGPT and partly formalised in Lean (Kamijima, Nakajima, Noda, Sasaya)
The gist
On October 13, 2026, four probabilists posted on arXiv a central limit theorem for the high-temperature SYK model, proved with ChatGPT 5.5 Pro and 5.6 Pro and then formalised in Lean under one assumption.
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-syk-tcl-haute-temperature-2026-10-13-r1
@misc{discoveria-syk-tcl-haute-temperature-2026-10-13-r1,
author = {{DiscoverIA}},
title = {Central limit theorem for the high-temperature SYK model: announced proof, obtained with ChatGPT and partly formalised in Lean (Kamijima, Nakajima, Noda, Sasaya)},
howpublished = {DiscoverIA registry, entry syk-tcl-haute-temperature-2026-10-13},
note = {Status “Not evaluated”, snapshot 1, recorded on October 24, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/syk-tcl-haute-temperature-2026-10-13#releve-1},
urldate = {2026-10-24}
}Dated link opens this snapshot in the history
To understand ≈ 20 s reading time, estimated
What it changes
The SYK model describes particles with random interactions and serves as a testing ground in theoretical physics. If the result held, the fluctuations of the logarithm of its partition function would follow a normal distribution at high temperature, that is, for small values of the inverse temperature β.
What remains unclear
The Lean formalisation, whose code was generated by the AI and reviewed by the authors, leaves Proposition 4.2 as an assumption. No third party has reviewed the proof yet, and the result covers high temperatures only.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · arxiv.org · abs/2610.18440
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 sourcearxiv.org · abs/2610.18440page read word for word · consulted on Oct 24, 2026 ·
We prove that for all sufficiently small inverse temperatures
- Paperarxiv.org · html/2610.18440page read word for word · consulted on Oct 24, 2026 ·
We have formalized the proofs of our main results in Lean 4, conditional on Proposition 4.2.
- Lean proofgithub.comlink only, reading not recorded
Method
A first attempt with ChatGPT 5.5 Pro, aimed directly at the free energy, did not succeed; the authors then proposed going through the partition function instead, which led to proofs produced by the AI that they examined and refined, and then, with ChatGPT 5.6 Pro, to a simpler combinatorial argument for a key estimate. The formalisation is published in the TokyoProbabilityGroup/SYK_CLT 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 prove that for all sufficiently small inverse temperatures”).
Limits
The claimant supplies Lean proofs conditional on Proposition 4.2; DiscoverIA has found no independent verification of them.
Key facts
- Claimed by
- Yoshinori Kamijima, Shuta Nakajima, Ryoichiro Noda et Kôhei Sasaya, with ChatGPT 5.5 Pro et 5.6 Pro (OpenAI)
announced on Oct 13, 2026 - Nature
- new result
- Field
- Mathematics (probability / mathematical physics)
- 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; Lean supplied by the authors, conditional on Proposition 4.2; no third-party evaluation found
Source: arxiv.orgread word for word
An observation is added; none is ever erased.
Report an error or suggest a source
Thank you, your message was sent.
Sending failed. Try again, or write to contact@discoveria.ai.
Is your result listed?What each status requires, correcting this entry, replying to it.