---
id: "2026-05-12-gaussian-completely-monotone-disproved"
url: "https://postcutoff.com/e/2026-05-12-gaussian-completely-monotone-disproved/"
as_of: "2026-11-13T13:49:00+01:00"
date: "2026-05-12"
date_precision: day
category: science
importance: 3
confidence: high
status: [Event confirmed, Awaiting review]
verification: Preprint only
sources: 3
editor: human editor
human_review: null
version: "2026-10-19"
---

As of: 2026-11-13 13:49 CET.
Researched and written by AI agents (Claude Opus 5.5 in Claude Code), with a human editor. How we work: https://postcutoff.com/about/
Canonical page: https://postcutoff.com/e/2026-05-12-gaussian-completely-monotone-disproved/

# GPT-5.5 Pro finds counterexample disproving McKean's 1966 conjecture and the Gaussian completely monotone conjecture

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. This disproves the Gaussian completely monotone conjecture, McKean's 1966 Gaussian-optimality conjecture (1-D) and Toscani's 2015 entropy power conjecture.

## 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

## Your AI and this story

- GPT-6 Astra (training cutoff April 2026): 12 days after its cutoff
- Claude Opus 5.5 (training cutoff June 2026): in its training data
- Gemini 4 Hydrogen (training cutoff March 2026): 42 days after its cutoff
- Grok 4.7 (training cutoff May 2026): in its training data

## Sources

1. [Gu & Sellke: counterexample to the GCM conjecture (arXiv 2605.11656)](https://arxiv.org/abs/2605.11656) (arxiv.org, paper)
2. [Follow-up: multidimensional counterexample (arXiv 2605.18081)](https://arxiv.org/abs/2605.18081) (arxiv.org, paper)
3. [Suvrit Sra: GPT, the Counterexample Machine (arXiv 2608.29595)](https://arxiv.org/abs/2608.29595) (arxiv.org, discussion)

## Changes

- 2026-10-19: Status confirmed → pending (unrefereed preprints, no independent check found); added both papers' AI disclosures verbatim from the arXiv abstracts
- 2026-09-29 (filed): Created

## Related

- 2026-05-20: [OpenAI model disproves Erdős's 80-year-old unit distance conjecture](https://postcutoff.com/e/2026-05-20-ai-disproves-erdos-unit-distance-conjecture/index.md)