{"paper":{"title":"An example of degenerate hyperbolicity in a cellular automaton with 3 states","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.CG","authors_text":"Henryk Fuk\\'s, Joel Midgley-Volpato","submitted_at":"2015-06-22T15:25:43Z","abstract_excerpt":"We show that a behaviour analogous to degenerate hyperbolicity can occur in nearest-neighbour cellular automata (CA) with three states. We construct a 3-state rule by \"lifting\" elementary CA rule 140. Such \"lifted\" rule is equivalent to rule 140 when arguments are restricted to two symbols, otherwise it behaves as identity. We analyze the structure of multi-step preimages of 0, 1 and 2 under this rule by using minimal finite state machines (FSM), and exploit regularities found in these FSM. This allows to construct explicit expressions for densities of 0s and 1s after $n$ iterations of the rul"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.06649","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"}