{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:BWPBNLLQ6KEBQTPHUE44PK75M2","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":"602fbc7effcba6b58cb38da625ec4954ebcd89062cf4cd20686fb3c679377440","cross_cats_sorted":["cs.DM","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2012-06-23T01:50:56Z","title_canon_sha256":"b1cf72ee13619ef46cc81e02ec3996fc5897e20063886c1a547023c2f6c1deaa"},"schema_version":"1.0","source":{"id":"1206.5352","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.5352","created_at":"2026-05-18T03:45:31Z"},{"alias_kind":"arxiv_version","alias_value":"1206.5352v4","created_at":"2026-05-18T03:45:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.5352","created_at":"2026-05-18T03:45:31Z"},{"alias_kind":"pith_short_12","alias_value":"BWPBNLLQ6KEB","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"BWPBNLLQ6KEBQTPH","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"BWPBNLLQ","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:84ab5f40618613466943f75fa1e60a3986d80bca59a7f03b81bec6deabca3389","target":"graph","created_at":"2026-05-18T03:45:31Z","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 show that the subword complexity function p_x(n), which counts the number of distinct factors of length n of a sequence x, is k-synchronized in the sense of Carpi if x is k-automatic. As an application, we generalize recent results of Goldstein. We give analogous results for the number of distinct factors of length n that are primitive words or powers. In contrast, we show that the function that counts the number of unbordered factors of length n is not necessarily k-synchronized for k-automatic sequences.","authors_text":"Daniel Goc, Jeffrey Shallit, Luke Schaeffer","cross_cats":["cs.DM","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2012-06-23T01:50:56Z","title":"Subword Complexity and k-Synchronization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.5352","kind":"arxiv","version":4},"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:ce1e3272c1de5c586768b9a64119e8c3a509ebc0864e7ddcaf69f9f281014044","target":"record","created_at":"2026-05-18T03:45:31Z","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":"602fbc7effcba6b58cb38da625ec4954ebcd89062cf4cd20686fb3c679377440","cross_cats_sorted":["cs.DM","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2012-06-23T01:50:56Z","title_canon_sha256":"b1cf72ee13619ef46cc81e02ec3996fc5897e20063886c1a547023c2f6c1deaa"},"schema_version":"1.0","source":{"id":"1206.5352","kind":"arxiv","version":4}},"canonical_sha256":"0d9e16ad70f288184de7a139c7abfd66952c839f7a4f0ff7f140f255cb251ba0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0d9e16ad70f288184de7a139c7abfd66952c839f7a4f0ff7f140f255cb251ba0","first_computed_at":"2026-05-18T03:45:31.481985Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:45:31.481985Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zY6JJhtGdlxQlXOKGLI6UrHnp9PdsC06KQgSy1HnXDIvnGpUe2Jr0irSZQ0hhwB7TwBCjLpbLk+yNne8eQvjAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:45:31.482404Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.5352","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ce1e3272c1de5c586768b9a64119e8c3a509ebc0864e7ddcaf69f9f281014044","sha256:84ab5f40618613466943f75fa1e60a3986d80bca59a7f03b81bec6deabca3389"],"state_sha256":"7379d8f56ccb58843c49c4818faac6384b41d3e3cfbd15ef9272a41d112d8d95"}