What was already known
Earlier smooth nonembeddable CR 3-manifolds lacked a closed canonical section; analogous examples with that section existed in dimension seven.
AI involvement
Sean Curry reports discovering the counterexample while experimenting with ChatGPT Plus. He selected the problem, revised the manuscript, independently checked all arguments and explains the obstruction.
The original paper ties the central counterexample construction to experimentation with ChatGPT, with substantial human direction and proof development; the exact model-generated step is unavailable.
- Supporting source (arxiv.org) — Submission history, v1 only as of review
- Supporting source (vibemathed.com) — Registry entry and source link
- Supporting source (whataifound.org) — Parallel listing of the same arXiv paper
Importance
Gives a counterexample to the proposed smooth three-dimensional implication.
Limitations
The paper also globalizes the example to a small perturbation on S³, without separately crediting that step to ChatGPT. The model conversation is unavailable, so its precise construction step is unknown.
Technical verification
Curry explicitly reports independently checking all calculations and arguments of the presented counterexample; under the site policy this is a completed, source-reported human proof check, though no external referee or machine check is documented.
Independent checking
independent human check of all manuscript calculations and arguments
- Checker
- Sean N. Curry, author
- Scope
- Theorem 1.1 smooth closed-section counterexample and its presented supporting arguments
- Basis
- Reported by the linked checker
Human understanding
Curry's explanation identifies the preserving Hamiltonian perturbation and the weighted-moment nonembeddability mechanism, and he substantially rewrote the proof.
Correction and publication history
Gives a counterexample to the proposed smooth three-dimensional implication.
Read this published revision