# The 4M-4 conjecture is false!

Cynthia Vinzant just disproved part (a) of the ${4M-4}$ conjecture, see here!

We posed the ${4M-4}$ conjecture two years ago, and there was even a monetary motivation for it! I will not go into details regarding the conjecture, you can read more about it either on a previous blog post of mine or a post of Dustin Mixon. In a nutshell it tries to predict how many phaseless measurements are needed to identify a complex vector of $M$ dimensions. The conjecture was that (a) ${4M-4}$ measurements are always needed and (b) ${4M-4}$ measurements suffice (as long as sufficiently generic).

Part (b) had been solved (positively) around a year ago Aldo Conca, Dan Edidin, Milena Hering, and Cynthia Vinzant (see the paper here) and part (a) was just disproved by Cynthia with an example in four dimensions.