In previous work we introduced a Khovanov multicurve invariant $\operatorname{ \widetilde{ Kh}}$ associated with Conway tangles. Applying ideas from homological mirror symmetry we show that $\operatorname{ \widetilde{ Kh}}$ 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.
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