Resolves the Heesch problem by showing unbounded Heesch numbers for homogeneous tilings and convex monotiles in the hyperbolic plane, with first examples of weakly aperiodic convex monotiles from dual homogeneous tilings.
Maiti, Pseud-homogeneous tilings of the hyperbolic plane, arxiv:2302.05661 (2023)
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Unboundedness of the Heesch Number for Hyperbolic Convex Monotiles
Resolves the Heesch problem by showing unbounded Heesch numbers for homogeneous tilings and convex monotiles in the hyperbolic plane, with first examples of weakly aperiodic convex monotiles from dual homogeneous tilings.
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Networks as the fundamental constituents of the universe
Binary relations on random networks constitute the universe, with space and matter as phases of a statistical model whose Ollivier-Ricci curvature produces emergent 3D geometry, Einstein equations, and relativistic quantum mechanics at large scales.