GPT-5.5 Pro finds counterexample disproving McKean’s 1966 conjecture and the Gaussian completely monotone conjecture
Event confirmedAwaiting review
The takeaway
Gu and Sellke (arXiv 2605.11656) presented an explicit probability measure, found by GPT-5.5 Pro, for which the 5th time-derivative of entropy along the heat flow is positive.
Status
- Claim
Event confirmedAwaiting review
- Our reporting
- High confidence
- Verification
- Preprint only
- Importance
- 3 of 5
- Last verified
- 19 October 2026
Your AI and this story
- GPT-6 Astra12 days after its cutoff
- Claude Opus 5.5In its training data
- Gemini 4 Hydrogen42 days after its cutoff
- Grok 4.7In its training data
It is after the cutoff of GPT-6 Astra and Gemini 4 Hydrogen, and can be in the training data of Claude Opus 5.5 and Grok 4.7.
Key facts
- arXiv 2605.11656 (12 May 2026)
- Counterexample found by GPT-5.5 Pro; proof written by the human authors
- Follow-ups: a hexagonal multidimensional counterexample (arXiv 2605.18081) and log-concave families (2608.30275)
- AI disclosure (Gu–Sellke abstract, arXiv 2605.11656): ‘The explicit counterexample was found by GPT-5.5 Pro.’
- AI disclosure (Zou–Fan–Gao–Wang abstract, arXiv 2605.18081, which disproves the Cheng–Geng log-convexity conjecture in dimension ≥ 2): ‘The explicit two-dimensional counterexample was found by GPT-5.5 Pro.’
What happened
OpenAI researcher Mark Sellke and a co-author used GPT-5.5 Pro to search for a distribution violating a 60-year-old monotonicity conjecture, and it produced one.
Why it matters
It is part of 2026’s striking pattern of AI counterexamples: models proved especially good at finding objects that break long-believed conjectures. Suvrit Sra documented 15+ such counterexamples in “GPT, the Counterexample Machine”.
What is disputed or not yet verified
| Verification | Unrefereed preprint (Gu & Sellke, arXiv 2605.11656) with a human-written proof; the multidimensional disproof by Zou, Fan, Gao and Wang (arXiv 2605.18081) is also an unrefereed preprint; no formal proof |
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Sources
3 sources from 1 site. Numbers match the chips in the text.
3 sources: 2 primary, 1 reaction
Primary
- Gu & Sellke: counterexample to the GCM conjecture (arXiv 2605.11656)arxiv.org, paper
- Follow-up: multidimensional counterexample (arXiv 2605.18081)arxiv.org, paper
Reactions
- Suvrit Sra: GPT, the Counterexample Machine (arXiv 2608.29595)arxiv.org, discussion
Changes
- Status confirmed → pending (unrefereed preprints, no independent check found); added both papers’ AI disclosures verbatim from the arXiv abstracts
- Filed