Palis's conjecture on arithmetic differences of affine Cantor sets

A regular Cantor set $K$ is called affine if its defining map has constant derivative on every interval $K_i$. For two affine Cantor sets $K$ and $K'$, consider their arithmetic difference $K-K'$ under nonzero scaling parameters. Palis's conjecture. The arithmetic difference of two affine Cantor sets generically, if not always, contains an interval or has zero Lebesgue measure. This conjecture concerns the dichotomy between interval formation and measure-zero arithmetic differences; it remains open.