> Matches! This is bizarre. A Jacobian counterexample has been sitting here in a prompt? Wait... is this map a known "fake" counterexample from the literature? Many mathematicians have tried and failed. This specific map might come from a paper or a forum where it was proposed and then debunked. Or... is it actually correct?

Gemma's having trouble accepting it too. A solution?! At this time of year? At this time of day? In this part of the country? Localized entirely within my own prompt?