{"paper":{"title":"Self-Similar One-Dimensional Quasilattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mtrl-sci","hep-th","math.MP"],"primary_cat":"math-ph","authors_text":"Latham Boyle, Paul J. Steinhardt","submitted_at":"2016-08-29T20:00:03Z","abstract_excerpt":"We study 1D quasilattices, especially self-similar ones that can be used to generate two-, three- and higher-dimensional quasicrystalline tessellations that have matching rules and invertible self-similar substitution rules (also known as inflation rules) analogous to the rules for generating Penrose tilings. The lattice positions can be expressed in a closed-form expression we call {\\it floor form}: $x_{n}=S(n-\\alpha)+(L-S)\\lfloor \\kappa(n-\\beta)\\rfloor$, where $L >S>0$ and $0<\\kappa<1$ is an irrational number. We describe two equivalent geometric constructions of these quasilattices and show"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.08220","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1608.08220/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}