Smooth counterexample to the Trautman conjecture

Does a smooth three-dimensional CR manifold with a nowhere-zero closed section of its canonical bundle have to be locally embeddable in complex two-space?

Sep 2, 2026

Strongly pseudoconvex counterexample

Model / AI: ChatGPT Plus

self-reported

Sean Curry states that experimentation with ChatGPT produced the counterexample construction and an initial draft. He substantially revised the text and independently checked the calculations and arguments. The result modifies standard nonembeddable CR three-manifolds while preserving a nowhere-zero closed canonical section.

Source read 2026-09-08. Read the abstract, main theorem and AI-use acknowledgement in arXiv v1. No model version, independent check or formal proof was found.

Paper — Paper