The duality between book thickness and convex antithickness

For a graph, book thickness is the minimum number of pages in a book embedding, and convex antithickness is the minimum number of convex geometric thrackles in a straight-line drawing. Book–convex-antithickness duality conjecture. Book thickness and convex antithickness are tied. This is stated alongside the proposed geometric thickness–geometric antithickness duality; no resolution is supplied in the paper excerpt.