{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:RX6NT7U35IMIRHVOEZX5SXVOS4","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"c1b00786334ed61a11260db9a7492290fc45f69f98c668e45cfdf2645cb2ade9","cross_cats_sorted":["cs.DM","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2014-02-24T14:49:22Z","title_canon_sha256":"f069beee27c04a17e81a9e05dcd6ef4943c2cebd6af4e779150eff87814d8963"},"schema_version":"1.0","source":{"id":"1402.5843","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.5843","created_at":"2026-05-18T01:11:51Z"},{"alias_kind":"arxiv_version","alias_value":"1402.5843v5","created_at":"2026-05-18T01:11:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.5843","created_at":"2026-05-18T01:11:51Z"},{"alias_kind":"pith_short_12","alias_value":"RX6NT7U35IMI","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"RX6NT7U35IMIRHVO","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"RX6NT7U3","created_at":"2026-05-18T12:28:46Z"}],"graph_snapshots":[{"event_id":"sha256:36aa756264cbf70184f4cb15a37e5cc31191b6549ee866c904559cc91eca459f","target":"graph","created_at":"2026-05-18T01:11:51Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We introduce and study a complexity function on words $c_x(n),$ called \\emph{cyclic complexity}, which counts the number of conjugacy classes of factors of length $n$ of an infinite word $x.$ We extend the well-known Morse-Hedlund theorem to the setting of cyclic complexity by showing that a word is ultimately periodic if and only if it has bounded cyclic complexity. Unlike most complexity functions, cyclic complexity distinguishes between Sturmian words of different slopes. We prove that if $x$ is a Sturmian word and $y$ is a word having the same cyclic complexity of $x,$ then up to renaming ","authors_text":"Gabriele Fici, Julien Cassaigne, Luca Q. Zamboni, Marinella Sciortino","cross_cats":["cs.DM","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2014-02-24T14:49:22Z","title":"Cyclic Complexity of Words"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.5843","kind":"arxiv","version":5},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:64bf5cf690555c07c4689add1b9d149f2828dfd6f5a71cc0de200c4ccbb3b28d","target":"record","created_at":"2026-05-18T01:11:51Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"c1b00786334ed61a11260db9a7492290fc45f69f98c668e45cfdf2645cb2ade9","cross_cats_sorted":["cs.DM","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2014-02-24T14:49:22Z","title_canon_sha256":"f069beee27c04a17e81a9e05dcd6ef4943c2cebd6af4e779150eff87814d8963"},"schema_version":"1.0","source":{"id":"1402.5843","kind":"arxiv","version":5}},"canonical_sha256":"8dfcd9fe9bea18889eae266fd95eae972ffc0778d6e7f17a25d5fb02a120e72f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8dfcd9fe9bea18889eae266fd95eae972ffc0778d6e7f17a25d5fb02a120e72f","first_computed_at":"2026-05-18T01:11:51.924807Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:51.924807Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TwNX8g1oYlZ54KOcD5PQ2j/aJtC7N+BbA7svZX4ieI/w+uYjgSvekIm0DOGevWzFBW6j7/1aJGRirP3Xb632DA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:51.925141Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.5843","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:64bf5cf690555c07c4689add1b9d149f2828dfd6f5a71cc0de200c4ccbb3b28d","sha256:36aa756264cbf70184f4cb15a37e5cc31191b6549ee866c904559cc91eca459f"],"state_sha256":"f557339296cb449e008853e5d66054933e3bc0a0857be67f680ce949f6fb9ac8"}