{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:7EJ4I56UDTRNI26YOFZBZNWPLJ","short_pith_number":"pith:7EJ4I56U","schema_version":"1.0","canonical_sha256":"f913c477d41ce2d46bd871721cb6cf5a770981270bd804802aa653285cec5874","source":{"kind":"arxiv","id":"1308.6694","version":1},"attestation_state":"computed","paper":{"title":"Balancedness of Arnoux-Rauzy and Brun words","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"cs.FL","authors_text":"Tom\\'a\\v{s} Hejda, Vincent Delecroix (IMJ), Wolfgang Steiner (LIAFA)","submitted_at":"2013-08-30T09:41:32Z","abstract_excerpt":"We study balancedness properties of words given by the Arnoux-Rauzy and Brun multi-dimensional continued fraction algorithms. We show that almost all Brun words on 3 letters and Arnoux-Rauzy words over arbitrary alphabets are finitely balanced; in particular, boundedness of the strong partial quotients implies balancedness. On the other hand, we provide examples of unbalanced Brun words on 3 letters."},"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":"1308.6694","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2013-08-30T09:41:32Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"e31faff07636cfbc388f79c9b91f6bdd23644645fc80576eb00fb85e750257ee","abstract_canon_sha256":"615d8543e919a76103643c40718ab5fd0f585abbdf9ed1be0e4cd643241b4fbf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:14:38.386872Z","signature_b64":"03oPizEm1pimCFhB1HnluVke9IfIPHw4POTpe60lgldnB8rHh7TUdGwTX5XAlxCrhUiorlWHz265WFVcjXpUBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f913c477d41ce2d46bd871721cb6cf5a770981270bd804802aa653285cec5874","last_reissued_at":"2026-05-18T03:14:38.386475Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:14:38.386475Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Balancedness of Arnoux-Rauzy and Brun words","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"cs.FL","authors_text":"Tom\\'a\\v{s} Hejda, Vincent Delecroix (IMJ), Wolfgang Steiner (LIAFA)","submitted_at":"2013-08-30T09:41:32Z","abstract_excerpt":"We study balancedness properties of words given by the Arnoux-Rauzy and Brun multi-dimensional continued fraction algorithms. We show that almost all Brun words on 3 letters and Arnoux-Rauzy words over arbitrary alphabets are finitely balanced; in particular, boundedness of the strong partial quotients implies balancedness. On the other hand, we provide examples of unbalanced Brun words on 3 letters."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.6694","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":"1308.6694","created_at":"2026-05-18T03:14:38.386529+00:00"},{"alias_kind":"arxiv_version","alias_value":"1308.6694v1","created_at":"2026-05-18T03:14:38.386529+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.6694","created_at":"2026-05-18T03:14:38.386529+00:00"},{"alias_kind":"pith_short_12","alias_value":"7EJ4I56UDTRN","created_at":"2026-05-18T12:27:36.564083+00:00"},{"alias_kind":"pith_short_16","alias_value":"7EJ4I56UDTRNI26Y","created_at":"2026-05-18T12:27:36.564083+00:00"},{"alias_kind":"pith_short_8","alias_value":"7EJ4I56U","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/7EJ4I56UDTRNI26YOFZBZNWPLJ","json":"https://pith.science/pith/7EJ4I56UDTRNI26YOFZBZNWPLJ.json","graph_json":"https://pith.science/api/pith-number/7EJ4I56UDTRNI26YOFZBZNWPLJ/graph.json","events_json":"https://pith.science/api/pith-number/7EJ4I56UDTRNI26YOFZBZNWPLJ/events.json","paper":"https://pith.science/paper/7EJ4I56U"},"agent_actions":{"view_html":"https://pith.science/pith/7EJ4I56UDTRNI26YOFZBZNWPLJ","download_json":"https://pith.science/pith/7EJ4I56UDTRNI26YOFZBZNWPLJ.json","view_paper":"https://pith.science/paper/7EJ4I56U","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1308.6694&json=true","fetch_graph":"https://pith.science/api/pith-number/7EJ4I56UDTRNI26YOFZBZNWPLJ/graph.json","fetch_events":"https://pith.science/api/pith-number/7EJ4I56UDTRNI26YOFZBZNWPLJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7EJ4I56UDTRNI26YOFZBZNWPLJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7EJ4I56UDTRNI26YOFZBZNWPLJ/action/storage_attestation","attest_author":"https://pith.science/pith/7EJ4I56UDTRNI26YOFZBZNWPLJ/action/author_attestation","sign_citation":"https://pith.science/pith/7EJ4I56UDTRNI26YOFZBZNWPLJ/action/citation_signature","submit_replication":"https://pith.science/pith/7EJ4I56UDTRNI26YOFZBZNWPLJ/action/replication_record"}},"created_at":"2026-05-18T03:14:38.386529+00:00","updated_at":"2026-05-18T03:14:38.386529+00:00"}