{"id":"palomar/PALOMAR-2026-10-07-000006","url":"https://github.com/jconorgrogan/palomar-chair-verification/tree/5f5ceedee770b76c21e8f1105e5e4e3b84b8d676","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-07-000006-v1.json","repo":"https://github.com/jconorgrogan/palomar-chair-verification","tags":["math.MG","math.CO","discrete-geometry","aperiodic-tiling","tilings"],"score":0,"title":"The CLARK Tile: An Aperiodic Monotile in Five Dimensions","trust":"high","domain":"math.MG","source":"palomar","authors":["Conor Grogan"],"reviews":0,"subject":"math.MG","summary":"We give an explicit compact tile, called CLARK (Chair with Local Asymmetric Registration Keys), in five-dimensional Euclidean space. It modifies a chair of 31 unit five-cubes with 256 rational pyramidal keys. Copies may be translated, rotated or reflected. The selected theorem proves tiling existence, no nonzero translation period in any physical tiling, and a finite full Euclidean symmetry group of cardinality at most 3840 for every such tiling. No registration, matching-rule or hierarchy assumption is imposed. A trivial symmetry group is not asserted.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-07","reactions":{},"formalized":true,"formalizes":[{"title":"S54 exact final sparse-key T5 specification","identifier":"","relationship":"formalizes"},{"title":"Uniform prime-dimensional framed chair hierarchy manuscripts, 2026-10-05","identifier":"","relationship":"adapts"},{"title":"Five-dimensional physical right-symmetry quotient hierarchy, 2026-10-05","identifier":"","relationship":"adapts"}]}