{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:BWPBNLLQ6KEBQTPHUE44PK75M2","short_pith_number":"pith:BWPBNLLQ","schema_version":"1.0","canonical_sha256":"0d9e16ad70f288184de7a139c7abfd66952c839f7a4f0ff7f140f255cb251ba0","source":{"kind":"arxiv","id":"1206.5352","version":4},"attestation_state":"computed","paper":{"title":"Subword Complexity and k-Synchronization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.CO"],"primary_cat":"cs.FL","authors_text":"Daniel Goc, Jeffrey Shallit, Luke Schaeffer","submitted_at":"2012-06-23T01:50:56Z","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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1206.5352","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2012-06-23T01:50:56Z","cross_cats_sorted":["cs.DM","math.CO"],"title_canon_sha256":"b1cf72ee13619ef46cc81e02ec3996fc5897e20063886c1a547023c2f6c1deaa","abstract_canon_sha256":"602fbc7effcba6b58cb38da625ec4954ebcd89062cf4cd20686fb3c679377440"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:45:31.482404Z","signature_b64":"zY6JJhtGdlxQlXOKGLI6UrHnp9PdsC06KQgSy1HnXDIvnGpUe2Jr0irSZQ0hhwB7TwBCjLpbLk+yNne8eQvjAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0d9e16ad70f288184de7a139c7abfd66952c839f7a4f0ff7f140f255cb251ba0","last_reissued_at":"2026-05-18T03:45:31.481985Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:45:31.481985Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Subword Complexity and k-Synchronization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.CO"],"primary_cat":"cs.FL","authors_text":"Daniel Goc, Jeffrey Shallit, Luke Schaeffer","submitted_at":"2012-06-23T01:50:56Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.5352","kind":"arxiv","version":4},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1206.5352","created_at":"2026-05-18T03:45:31.482043+00:00"},{"alias_kind":"arxiv_version","alias_value":"1206.5352v4","created_at":"2026-05-18T03:45:31.482043+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.5352","created_at":"2026-05-18T03:45:31.482043+00:00"},{"alias_kind":"pith_short_12","alias_value":"BWPBNLLQ6KEB","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_16","alias_value":"BWPBNLLQ6KEBQTPH","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_8","alias_value":"BWPBNLLQ","created_at":"2026-05-18T12:27:01.376967+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BWPBNLLQ6KEBQTPHUE44PK75M2","json":"https://pith.science/pith/BWPBNLLQ6KEBQTPHUE44PK75M2.json","graph_json":"https://pith.science/api/pith-number/BWPBNLLQ6KEBQTPHUE44PK75M2/graph.json","events_json":"https://pith.science/api/pith-number/BWPBNLLQ6KEBQTPHUE44PK75M2/events.json","paper":"https://pith.science/paper/BWPBNLLQ"},"agent_actions":{"view_html":"https://pith.science/pith/BWPBNLLQ6KEBQTPHUE44PK75M2","download_json":"https://pith.science/pith/BWPBNLLQ6KEBQTPHUE44PK75M2.json","view_paper":"https://pith.science/paper/BWPBNLLQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1206.5352&json=true","fetch_graph":"https://pith.science/api/pith-number/BWPBNLLQ6KEBQTPHUE44PK75M2/graph.json","fetch_events":"https://pith.science/api/pith-number/BWPBNLLQ6KEBQTPHUE44PK75M2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BWPBNLLQ6KEBQTPHUE44PK75M2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BWPBNLLQ6KEBQTPHUE44PK75M2/action/storage_attestation","attest_author":"https://pith.science/pith/BWPBNLLQ6KEBQTPHUE44PK75M2/action/author_attestation","sign_citation":"https://pith.science/pith/BWPBNLLQ6KEBQTPHUE44PK75M2/action/citation_signature","submit_replication":"https://pith.science/pith/BWPBNLLQ6KEBQTPHUE44PK75M2/action/replication_record"}},"created_at":"2026-05-18T03:45:31.482043+00:00","updated_at":"2026-05-18T03:45:31.482043+00:00"}