{"paper":{"title":"Deterministic 2-Dimensional Temperature-1 Tile Assembly Systems Cannot Compute","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["cs.CG","cs.DS"],"primary_cat":"cs.CC","authors_text":"Hendrik Jan Hoogeboom, J\\'er\\^ome Durand-Lose, Nata\\v{s}a Jonoska","submitted_at":"2019-01-24T18:47:33Z","abstract_excerpt":"We consider non cooperative binding in so called `temperature 1', in deterministic (here called {\\it confluent}) tile self-assembly systems (1-TAS) and prove the standing conjecture that such systems do not have universal computational power. We call a TAS whose maximal assemblies contain at least one ultimately periodic assembly path {\\it para-periodic}. We observe that a confluent 1-TAS has at most one maximal producible assembly, $\\alpha_{max}$, that can be considered a union of path assemblies, and we show that such a system is always para-periodic. This result is obtained through a superp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.08575","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}