Super lambda-length conjecture for peripheral arcs in an annulus

Let $p_n$ be the sequence used in the source and define $w_n=p_{2n-4}$. In the annulus with a marked point on each boundary, consider the peripheral arcs described in the source: an arc starts at the marked point on the inner boundary, winds around $(n-1)$ times, and ends at the same marked point. Super lambda-length conjecture for peripheral arcs. If $w_1=w_2=1$, or if $w_1=a$ and $w_2=b$, then the values $w_n=p_{2n-4}$ correspond to the super $\lambda$-lengths of these peripheral arcs in the decorated super-Teichmüller space. The source identifies the obstruction to a proof as the lack of super skein relations for resolving crossings, so the conjecture remains open.