lci and Gorenstein equivalence conjecture for $(p,2)$-clans

Let $\gamma$ be any $(p,2)$-clan with $p\geq 2$, and let $Y_{\gamma}$ be its orbit closure. lci–Gorenstein equivalence conjecture. $Y_{\gamma}$ is a local complete intersection if and only if $\gamma$ avoids the patterns $1++-1$, $1-++1$, $1++221$, $122++1$, $1+212$, and $121+2$. Equivalently, $Y_{\gamma}$ is a local complete intersection if and only if it is Gorenstein. The source presents this as the $q=2$ case of the broader conjectural pattern-avoidance program; the statement is computationally supported but remains open.