Congratulations to Cynthia Vinzant for disproving the 4M-4 conjecture! The main result of her 4-page paper is the existence of a matrix such that is injective modulo a global phase factor (indeed, ). This is not Cynthia’s first contribution to this problem—her recent paper with Conca, Edidin and Hering proves that the conjecture holds for infinitely many .

I wanted to briefly highlight the main idea behind this paper: She provides an algorithm that, on input of a matrix with complex rational entries, either outputs “not known to be injective” or outputs “injective” along with a certificate of injectivity. The algorithm is fundamentally based on the following characterization of injectivity: