…appears to be four (an infinite improvement). I coauthored a paper with Gary Greaves, whose recent paper Edge-signed graphs with smallest eigenvalue greater than -2 also saw contributions from Jack Koolen and Akhiro Munemasa. They both have an Erdős number of two (each via Chris Godsil, who is an Erdős coauthor), making Gary a three and myself a four.

If I do not publish any more papers, the best I can hope for is three, if Gary later collaborates with a one. But for now my goal should be to obtain a Bacon number…