Khovanov multicurves are linear

In previous work we introduced a Khovanov multicurve invariant $\mathrm{}$ associated with Conway tangles. Applying ideas from homological mirror symmetry we show that $\mathrm{}$ is subject to strong geography restrictions: Every component of the invariant is linear, in the sense that it admits a lift to a curve homotopic to a straight line in an appropriate planar cover of the tangle boundary.