We found a proof of Roberson’s weak conjecture asserting that homomorphism indistinguishability over any proper minor-closed graph class is not the same as isomorphism. This conjecture has been on my mind for a long time and I’m very excited to see it resolved.

Given the OpenAI incident, we decided to publish the current write-up on Zenodo. We’ll put an accessible exposition of the result on arXiv soon. This is joint work with Arnar Ágúst Kristjánsson, Benjamin Moore, Daniel Neuen, David E. Roberson, and Ben Young.