Fibonacci Direct Product Variation Tilings

The paper’s main theorem explicitly states that the 28 inflation tiling dynamical systems with polygonal windows form a single topological conjugacy class, and proves it by (i) showing each parallelogram-window DPV is MLD to a sheared DP tiling (Fact 5.1), (ii) establishing a common cut-and-project scheme with a torus parametrization, and (iii) constructing a conjugacy via matching torus points and extending by continuity (Proposition 5.12), culminating in Theorem 5.13 . The candidate solution follows the same strategy: same CPS, same use of the torus factor, define the conjugacy on a dense set via sections, and extend using regularity (boundary measure zero). Minor differences are expository (e.g., the candidate compresses the extension step using general results on continuity of sections), but mathematically it aligns with the paper’s construction and conclusions.