6 problems

Nonexistence conjecture. There are no self-extremal sets in $\ell_p$ for $1<p<2$.

Prime-cardinality frequency conjecture. Extreme sets with prime cardinality appear more frequently than sets whose cardinality is neither prime nor a perfect square.

Differing-Sidon-constant conjecture. Under these assumptions, $A$ and $B$ are extreme.

Prime-cyclic uniqueness conjecture. All extreme $n$-element subsets of $\mathbb Z_p$ are equivalent.

Six-element classification conjecture. The only six-element extreme sets in cyclic groups are $\mathbb Z_6$, the set $\{0,1,2,3,4,7\}\subset\mathbb Z_{10}$, and their images under…

Extremality criterion. An $(n-1)$-element subset of $\mathbb Z_n$ is extreme if and only if $n$ is not congruent to $3$ modulo $4$.