Eleven probabilists construct the Critical 2D KPZ process, a solution of the critical two-dimensional KPZ equation, ‘through extensive interactions’ with ChatGPT 5.5, 5.6 and 6

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Key facts

• Result: centred log partition functions of 2D Gaussian directed polymers at criticality converge in law to a unique limit, which is a measurable function of the Critical 2D Stochastic Heat Flow via a renormalised Cole–Hopf transform; the limit is non-Gaussian, its covariance has a log-log blow-up near the diagonal, and Gaussian fluctuations appear when averaging on shrinking scales
• Authors include the groups behind the Critical 2D Stochastic Heat Flow (Caravenna, Sun, Zygouras) and KPZ specialists (Yu Gu, Li-Cheng Tsai, Alexander Dunlap, Quentin Berger, Shuta Nakajima)
• AI statement (verbatim): ‘The results presented here were obtained through extensive interactions with generative AI (ChatGPT 5.5, 5.6 and 6) … The proof builds on key recent and older advances in our field, combined in novel ways with substantial AI input.’
• Appendix C: AI ‘contributed to the tightness argument, the proof of convergence to a unique limit, and its non-Gaussianity’. From a Gaussian convexity theorem supplied by the authors, ‘AI derived a covariance bound’ giving tightness; an AI ‘sparse switch-off construction’ ‘initially appeared to close the remaining estimate, but a subsequent audit identified a gap’ and was abandoned; asked for simpler arguments, AI ‘proposed a simpler use of conditional Gaussian convexity’ that completed the convergence proof; AI ‘developed a proof using Gaussian rigidity’ for non-Gaussianity
• Division of labour (Appendix C): ‘We supplied structural ideas, assessed the proposed arguments, and guided the choice and revision of approaches. AI developed these suggestions and generated further proof ideas that were not contained in the original prompts. Some proposals were fruitful; others contained errors or introduced unnecessary complications.’