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.


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