Distinctness conjecture for frayed ribbon Schur Q-functions

Let $D$ and $E$ be shifted skew shapes. A frayed ribbon is a shifted near-ribbon containing two squares on the staircase, and let $D^a$ denote the antipodal reflection of $D$ across the northeast-southwest diagonal. Write $Q_D$ for the Schur $Q$-function associated with $D$. Frayed ribbon distinctness conjecture. If $D$ and $E$ are frayed ribbons such that $Q_D=Q_E$, then either $D=E$ or $D=E^a$. The claim concerns the unresolved equality problem for skew Schur $Q$-functions; the paper reports computational and theoretical evidence but does not establish the conjecture.