The Pin(2)-monopole Floer spectral sequence conjecture for branched double covers

Let $L\subset S^3$ be a link, let $\Sigma(L)$ denote its branched double cover, and let $\bar{L}$ be the mirror of $L$. Write $\widetilde{\mathrm{BN}}^3_{*,*}(\bar{L})$ for the relevant characteristic-two Bar-Natan homology and $\widetilde{\mathit{HS}}_*(\Sigma(L))$ for Pin(2)-monopole Floer homology. Pin(2)-monopole Floer spectral sequence conjecture. There exists a spectral sequence whose $E^2$-page is

$$\widetilde{\mathrm{BN}}^3_{*,*}(\bar{L})$$

which converges to

$$\widetilde{\mathit{HS}}_*(\Sigma(L)).$$

After setting $u$ equal to $Q$, this is a spectral sequence of $\mathbb{F}[Q]/Q^3$-modules. The conjecture proposes the Pin(2) analogue of the involutive monopole Floer spectral sequence established in the paper; the supplied text does not state that it has been resolved.