The twisted Fukaya-category conjecture for normal crossings surfaces

Let $X$ be a proper normal crossings surface with graph-like singular locus described by a trivalent graph $G(X)$ and orientable dual intersection complex. For each edge $e$ whose component $C_e$ of the singular locus is isomorphic to $\mathbb{P}^1$, set

$$n_e=-\deg(\mathfrak{Sing}(X))|_{C_e}.$$

Let $Z$ be a Riemann surface with a pants decomposition whose graph is $G(X)$, and let $P(\{n_e\})$ be the graded symplectic manifold obtained by the stated cut-and-reglue construction. Twisted Fukaya-category conjecture. There is an equivalence

$$\operatorname{DSing}(X)\simeq \mathrm{RFuk}^{\mathrm{gr}}(P(\{n_e\}),\Omega_Z).$$

The right-hand category carries an autoequivalence $\Lambda$ and a natural isomorphism $t:\mathrm{id}\to\Lambda^{-1}[2]$, giving a $\Lambda$-twisted $2$-periodic structure. This conjecturally extends the mirror description to nonzero degrees along the singular components.