Measure-zero conjecture for non-unique sparse phase-retrieval solutions

Let $K$ be the sparsity level and let $a_x$ denote the periodic auto-correlation of a $K$-sparse signal $x$. Measure-zero conjecture. If $K/N<1/2$, then the set of $K$-sparse signals having the same periodic auto-correlation $a_x$ as a given signal is of measure zero. This conjecture asserts that even when additional solutions exist, they are exceptional rather than generic; the source gives no resolution, so it remains open.