Haddley and Worsley's conjecture on monohedral tilings of the circular disc

A monohedral tiling of the closed circular unit disc $\mathcal{B}^2$ is a finite family of congruent compact Jordan regions with mutually disjoint interiors whose union is $\mathcal{B}^2$. A tiling is radially generated if every tile is radially generated, meaning that its boundary is a continuous simple curve consisting of a circular arc of length $\alpha$ and two other curves, one of which is the rotation of the other about their common point by angle $\alpha$. A tiling is a subtiling of another tiling if it is obtained by subdividing tiles of the latter.

Haddley and Worsley's conjecture. Every monohedral tiling is a subtiling of a radially generated tiling.

This conjecture proposes that all monohedral tilings of the circular disc are structurally subordinate to radially generated tilings, providing a broad framework for understanding such tilings. The source gives no resolution, so the conjecture remains open.