{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:7PTFY72DCWGYJ6CDVUPWH2OVK5","short_pith_number":"pith:7PTFY72D","schema_version":"1.0","canonical_sha256":"fbe65c7f43158d84f843ad1f63e9d55757ae726e6d9b69a1c58c899b0c777977","source":{"kind":"arxiv","id":"1312.4350","version":1},"attestation_state":"computed","paper":{"title":"Extensions of rich words","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jetro Vesti","submitted_at":"2013-12-16T13:31:57Z","abstract_excerpt":"In [X. Droubay et al, Episturmian words and some constructions of de Luca and Rauzy, Theoret. Comput. Sci. 255 (2001)], it was proved that every word w has at most |w|+1 many distinct palindromic factors, including the empty word. The unified study of words which achieve this limit was initiated in [A. Glen et al, Palindromic richness, Eur. Jour. of Comb. 30 (2009)]. They called these words rich (in palindromes).\n  This article contains several results about rich words and especially extending them. We say that a rich word w can be extended richly with a word u if wu is rich. Some notions are "},"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":"1312.4350","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-12-16T13:31:57Z","cross_cats_sorted":[],"title_canon_sha256":"7a925d6703097bacba133f261b3af106a1e1aa8e9c1e382f82ece669e217f275","abstract_canon_sha256":"39c61a183b4ed33f521933dc200f301861deb8a9dc06fb20aa390268e1c79075"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:30:08.557511Z","signature_b64":"RGRzW/Et05aFgAblgqq8zBW/ycbp+mBTEejX7HIVpvNVXk0rX3kCaIXSzbr5ctskV/RNthj42vG7wOtZJ3O1Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fbe65c7f43158d84f843ad1f63e9d55757ae726e6d9b69a1c58c899b0c777977","last_reissued_at":"2026-05-18T02:30:08.556850Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:30:08.556850Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Extensions of rich words","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jetro Vesti","submitted_at":"2013-12-16T13:31:57Z","abstract_excerpt":"In [X. Droubay et al, Episturmian words and some constructions of de Luca and Rauzy, Theoret. Comput. Sci. 255 (2001)], it was proved that every word w has at most |w|+1 many distinct palindromic factors, including the empty word. The unified study of words which achieve this limit was initiated in [A. Glen et al, Palindromic richness, Eur. Jour. of Comb. 30 (2009)]. They called these words rich (in palindromes).\n  This article contains several results about rich words and especially extending them. We say that a rich word w can be extended richly with a word u if wu is rich. Some notions are "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.4350","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":"1312.4350","created_at":"2026-05-18T02:30:08.556950+00:00"},{"alias_kind":"arxiv_version","alias_value":"1312.4350v1","created_at":"2026-05-18T02:30:08.556950+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.4350","created_at":"2026-05-18T02:30:08.556950+00:00"},{"alias_kind":"pith_short_12","alias_value":"7PTFY72DCWGY","created_at":"2026-05-18T12:27:36.564083+00:00"},{"alias_kind":"pith_short_16","alias_value":"7PTFY72DCWGYJ6CD","created_at":"2026-05-18T12:27:36.564083+00:00"},{"alias_kind":"pith_short_8","alias_value":"7PTFY72D","created_at":"2026-05-18T12:27:36.564083+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/7PTFY72DCWGYJ6CDVUPWH2OVK5","json":"https://pith.science/pith/7PTFY72DCWGYJ6CDVUPWH2OVK5.json","graph_json":"https://pith.science/api/pith-number/7PTFY72DCWGYJ6CDVUPWH2OVK5/graph.json","events_json":"https://pith.science/api/pith-number/7PTFY72DCWGYJ6CDVUPWH2OVK5/events.json","paper":"https://pith.science/paper/7PTFY72D"},"agent_actions":{"view_html":"https://pith.science/pith/7PTFY72DCWGYJ6CDVUPWH2OVK5","download_json":"https://pith.science/pith/7PTFY72DCWGYJ6CDVUPWH2OVK5.json","view_paper":"https://pith.science/paper/7PTFY72D","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1312.4350&json=true","fetch_graph":"https://pith.science/api/pith-number/7PTFY72DCWGYJ6CDVUPWH2OVK5/graph.json","fetch_events":"https://pith.science/api/pith-number/7PTFY72DCWGYJ6CDVUPWH2OVK5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7PTFY72DCWGYJ6CDVUPWH2OVK5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7PTFY72DCWGYJ6CDVUPWH2OVK5/action/storage_attestation","attest_author":"https://pith.science/pith/7PTFY72DCWGYJ6CDVUPWH2OVK5/action/author_attestation","sign_citation":"https://pith.science/pith/7PTFY72DCWGYJ6CDVUPWH2OVK5/action/citation_signature","submit_replication":"https://pith.science/pith/7PTFY72DCWGYJ6CDVUPWH2OVK5/action/replication_record"}},"created_at":"2026-05-18T02:30:08.556950+00:00","updated_at":"2026-05-18T02:30:08.556950+00:00"}