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Research / Sep 17, 2026

Talagrand's operator cotype problem

Is the Rademacher cotype of a bounded linear operator between Banach spaces universally bounded by the maximum of its Gaussian cotype and its (q,1)-summing norm?

Model / AI: ChatGPT (GPT-5.6)

self-reported (counterexample)
Sep 17, 2026

Negative resolution for cotype-2 operators

Model / AI: ChatGPT (GPT-5.6)

self-reported (counterexample)

Xinglong Wu resolves Michel Talagrand's operator cotype problem in the negative, demonstrating that the Rademacher cotype cannot be controlled by the Gaussian cotype and (q,1)-summing norm even in the fundamental case q = 2. The author reports that ChatGPT (GPT-5.6) discovered the counterexample structure during interactive experimentation.

Source read 2026-10-08. Read the arXiv v1 abstract, theorem statement, and AI-attribution section. The operator norm calculations were not independently audited.