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Frid, On the frequency of factors in a D0L word, Journal of Automata, Languages and Combinatorics 3 (1998), 29-41 and the study of generalized Thue-Morse words by S. Starosta, Generalized Thue-Morse words and palindromic richness, arXiv:1104.2476v2 [math.CO]."},"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":"1107.5033","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-07-25T19:52:50Z","cross_cats_sorted":[],"title_canon_sha256":"163f7750d75fbc2c39559bab3128f9c32f1772aef67040692a65f97e6c19123f","abstract_canon_sha256":"fde9ddc7775a6901165ff3534e94e10e23c2d408bc10f55671e9582a88b85764"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:34:46.379299Z","signature_b64":"EECbKw78rDNHJ1F9NELyys4DhKzZnJQdOCmwtrF0SSYzxi7BNU943az20abytcf438AZ6euAFK3WlqJjx1WVAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f41d3ddbafc2f8f9f43b98988e7896c34c2a99eab9b006a3610b8001e4ebc2df","last_reissued_at":"2026-05-18T03:34:46.378605Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:34:46.378605Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Factor frequencies in generalized Thue-Morse words","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Lubomira Balkova","submitted_at":"2011-07-25T19:52:50Z","abstract_excerpt":"We describe factor frequencies of the generalized Thue-Morse word t_{b,m} defined for integers b greater than 1, m greater than 0 as the fixed point starting in 0 of the morphism \\phi_{b,m} given by \\phi_{b,m}(k)=k(k+1)...(k+b-1), where k = 0,1,..., m-1 and where the letters are expressed modulo m. 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Starosta, Generalized Thue-Morse words and palindromic richness, arXiv:1104.2476v2 [math.CO]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.5033","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1107.5033","created_at":"2026-05-18T03:34:46.378718+00:00"},{"alias_kind":"arxiv_version","alias_value":"1107.5033v1","created_at":"2026-05-18T03:34:46.378718+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.5033","created_at":"2026-05-18T03:34:46.378718+00:00"},{"alias_kind":"pith_short_12","alias_value":"6QOT3W5PYL4P","created_at":"2026-05-18T12:26:22.705136+00:00"},{"alias_kind":"pith_short_16","alias_value":"6QOT3W5PYL4PT5B3","created_at":"2026-05-18T12:26:22.705136+00:00"},{"alias_kind":"pith_short_8","alias_value":"6QOT3W5P","created_at":"2026-05-18T12:26:22.705136+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/6QOT3W5PYL4PT5B3TCMI46EWYN","json":"https://pith.science/pith/6QOT3W5PYL4PT5B3TCMI46EWYN.json","graph_json":"https://pith.science/api/pith-number/6QOT3W5PYL4PT5B3TCMI46EWYN/graph.json","events_json":"https://pith.science/api/pith-number/6QOT3W5PYL4PT5B3TCMI46EWYN/events.json","paper":"https://pith.science/paper/6QOT3W5P"},"agent_actions":{"view_html":"https://pith.science/pith/6QOT3W5PYL4PT5B3TCMI46EWYN","download_json":"https://pith.science/pith/6QOT3W5PYL4PT5B3TCMI46EWYN.json","view_paper":"https://pith.science/paper/6QOT3W5P","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1107.5033&json=true","fetch_graph":"https://pith.science/api/pith-number/6QOT3W5PYL4PT5B3TCMI46EWYN/graph.json","fetch_events":"https://pith.science/api/pith-number/6QOT3W5PYL4PT5B3TCMI46EWYN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6QOT3W5PYL4PT5B3TCMI46EWYN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6QOT3W5PYL4PT5B3TCMI46EWYN/action/storage_attestation","attest_author":"https://pith.science/pith/6QOT3W5PYL4PT5B3TCMI46EWYN/action/author_attestation","sign_citation":"https://pith.science/pith/6QOT3W5PYL4PT5B3TCMI46EWYN/action/citation_signature","submit_replication":"https://pith.science/pith/6QOT3W5PYL4PT5B3TCMI46EWYN/action/replication_record"}},"created_at":"2026-05-18T03:34:46.378718+00:00","updated_at":"2026-05-18T03:34:46.378718+00:00"}