Cantarini–Kac classification conjecture for simple Jordan superalgebras

Let $F$ be a field of zero characteristic, and let $J$ be a simple Jordan superalgebra over $F$ with nonzero odd part. The possible superalgebras include $H(A,*)$, where $(A,*)$ is a $*$-simple associative superalgebra with a superinvolution $*$ and noncommutative even part; Jordan superalgebras of a superform, $k_3$, $D_t$, or $K_{10}$ over an extension of $F$; Kantor doubles $Kan(A,[,])$ and twisted Kantor doubles; and Jordan Cheng–Kac superalgebras $JCK(A,d)$ and twisted subsuperalgebras of $JCK(A,d)$. Cantarini–Kac classification conjecture. Every such $J$ is isomorphic to one of these superalgebras. The conjecture is known for linearly compact simple Jordan superalgebras and for superconformal Jordan algebras, but remains open in the general finite- or infinite-dimensional setting.