Counterexample to Talagrand's operator cotype problem
An operator is exhibited whose Rademacher cotype is not controlled by the maximum of its Gaussian cotype and its (q,1)-summing norm, answering Talagrand's question in the negative already at q equals 2.
- Lab
- Independent
- Model
- ChatGPT (GPT-5.6)
- Field
- Mathematics
- Date
- 2026-09-17
- Human collaborators
- Xinglong Wu
What was found
Talagrand asked whether the Rademacher cotype of an operator is universally controlled by the maximum of two quantities: its Gaussian cotype and its (q,1)-summing norm. The paper answers no, and does so at the smallest interesting parameter, q equals 2, rather than only for large q. The AI disclosure is a single sentence and it is the last line of the abstract: the counterexample was discovered by ChatGPT (GPT-5.6). That places the decisive step, producing the object itself, with the model, and leaves the write-up with the author.
Novelty check
The disclosure and the attribution were read from the arXiv abstract directly rather than from an aggregator label, which matters this week: the 2026-09-23 watch run spot-checked 11 registry rows tagged as AI-discovered and found 9 of them carried no AI disclosure anywhere in the actual paper. This one does, verbatim. No prior counterexample to the operator cotype question was found in the four registries the watch reads. This is a distinct Talagrand problem from the convolution conjecture already in this registry at 2026-08-16-talagrand-convolution, which is a different question by different authors using a different system; the two should not be read as related results. The year Talagrand posed the operator cotype question is not stated in the abstract and is deliberately left unrecorded here rather than guessed.
Caveats and known objections
A preprint days old at entry, unrefereed, with no formalization and no independent check on record, so the grade is claimed on the registry's default for an announced but unverified result. Autonomy is ai-led on the author's own one-sentence attribution taken at face value; as with any such statement there is no transcript or artifact that would let a reader separate discovery from the author's own framing of it, and the model field should be read as the author's attribution rather than as a verified fact. The sole source is the preprint itself.
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Entry history (1 event)
- AddedEntered the registry graded Claimed and AI-led.
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Cite this entry
whataifound.org. (2026). Counterexample to Talagrand's operator cotype problem. whataifound.org: A Registry of AI Scientific and Mathematical Discoveries. https://whataifound.org/finding/2026-09-17-talagrand-operator-cotypeBibTeX
@misc{whataifound-independent-2026-cotype,
title = {Counterexample to Talagrand's operator cotype problem},
author = {{whataifound.org}},
year = {2026},
howpublished = {whataifound.org: A Registry of AI Scientific and Mathematical Discoveries},
note = {Result by Independent. Verification: Claimed. Autonomy: AI-led.},
url = {https://whataifound.org/finding/2026-09-17-talagrand-operator-cotype}
}