The classical-pattern basis conjecture for the union of dihedral subgroups

Let $D_n$ be the dihedral subgroup of the symmetric group on $n$ letters, and let $D$ denote the union of the groups $D_n$. For a set $P$ of classical patterns, write $\operatorname{Av}(P)$ for the permutations avoiding every pattern in $P$. Dihedral subgroup basis conjecture. The union of the dihedral subgroups consists of permutations avoiding the classical patterns $3142$, $1342$, $2314$, $2134$, $3241$, $4231$, $3421$, $4213$, $2413$, $1324$, $3124$, $1423$, $2431$, $4312$, $4132$, and $1243$. This would provide the classical-pattern basis not given by the cited classification of pattern-defined subgroups; the paper presents it as a result discovered computationally by $\mathsf{BiSC}$, with no resolution stated.