Nonexistence conjecture for generically universal Cantor sets

Let $d$ be a positive integer. A set is generically universal if every generic set—meaning a dense $G_{\delta}$ set whose complement has Lebesgue measure zero—contains a linear and translated copy of it. Nonexistence conjecture. There are no generically universal Cantor sets on $\mathbb{R}^d$. The paper proves non-universality for Cantor sets with positive Newhouse thickness in dimension one and for Newhouse projectively thick Cantor sets in higher dimensions; the general conjecture remains open.