The $2M$ phase-transition conjecture for almost-injective complex phase retrieval

Let $\Phi$ be the measurement matrix for signals in $\mathbb{C}^M$, with $N$ intensity measurements, and write $\mathrm{AlmInj}[\Phi,\mathbb{C}^{M\times N}]$ for almost injectivity, meaning injectivity on an appropriate open set modulo the unit-circle action. The $2M$ conjecture. $\mathrm{AlmInj}[\Phi,\mathbb{C}^{M\times N}]$ exhibits a phase transition at $N=2M$. The source states that part (b) was proved by Balan, Casazza, and Edidin and that a proof sketch of part (a) was given by Flammia, Silberfarb, and Caves, so this conjecture is resolved.