What was already known
Talagrand proposed universal control by Gaussian cotype and the (q,1)-summing norm; Kwapień’s related decomposition problem was also open.
AI involvement
Xinglong Wu says ChatGPT (GPT-5.6) discovered the counterexample during discussions. Wu independently checked all arguments and explains the central estimates.
The central counterexample is explicitly model-discovered in human discussions; autonomous development is not documented.
Importance
Provides an unbounded counterexample and refutes the related universal decomposition bound.
Limitations
The result concerns operator cotype at q=2; the Kwapień consequence follows from the paper’s argument. No separate machine certificate or third-party complete review is documented.
Technical verification
The named author explicitly reports independently verifying all arguments; this is a source-reported completed human check.
Independent checking
independent human verification of all paper arguments
- Checker
- Xinglong Wu
- Scope
- Theorem 1.1 operator-cotype counterexample and its arguments
- Basis
- Reported by the linked checker
Human understanding
Wu lays out every central estimate in §2 and the decomposition implication in §1.
Correction and publication history
Provides an unbounded counterexample and refutes the related universal decomposition bound.
Read this published revision