{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:QG7SSDBR2W2DP4QP7KCFGSI3NW","short_pith_number":"pith:QG7SSDBR","schema_version":"1.0","canonical_sha256":"81bf290c31d5b437f20ffa8453491b6d967e72a6c56d4831a40134928ee9c21e","source":{"kind":"arxiv","id":"1108.3618","version":1},"attestation_state":"computed","paper":{"title":"Circular words and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.FL","authors_text":"Beno\\^it Rittaud (Laboratoire Analyse, G\\'eom\\'etrie et Applications, Institut Galil\\'ee, Laurent Vivier (Laboratoire de Didactique Andr\\'e Revuz, Universit\\'e Paris-13), Universit\\'e Paris Diderot)","submitted_at":"2011-08-18T03:52:14Z","abstract_excerpt":"We define the notion of circular words, then consider on such words a constraint derived from the Fibonacci condition. We give several results on the structure of these circular words, then mention possible applications to various situations: periodic expansion of numbers in numeration systems, \"gcd-property\" of integer sequences, partition of the prefix of the fixed point of the Fibonacci substitution, spanning trees of a wheel. Eventually, we mention some open questions."},"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":"1108.3618","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2011-08-18T03:52:14Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"8cb9c0f92894c50abc6919db564b49f7471c14cfcde3490877a9eddf9c446460","abstract_canon_sha256":"89821dfc7028ee77ec8228ecb2a472f9edbd8b98d7fd86ddb9582b218b7e4e91"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:15:15.762379Z","signature_b64":"6MD/tid2eiBlLJzJkgMhgLLuUhX+X4wg3O6VYPZQY05OECjJVkH4DiXugpcQZWcOZSP8v1NColXuWeNQToLfDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"81bf290c31d5b437f20ffa8453491b6d967e72a6c56d4831a40134928ee9c21e","last_reissued_at":"2026-05-18T04:15:15.761595Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:15:15.761595Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Circular words and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.FL","authors_text":"Beno\\^it Rittaud (Laboratoire Analyse, G\\'eom\\'etrie et Applications, Institut Galil\\'ee, Laurent Vivier (Laboratoire de Didactique Andr\\'e Revuz, Universit\\'e Paris-13), Universit\\'e Paris Diderot)","submitted_at":"2011-08-18T03:52:14Z","abstract_excerpt":"We define the notion of circular words, then consider on such words a constraint derived from the Fibonacci condition. We give several results on the structure of these circular words, then mention possible applications to various situations: periodic expansion of numbers in numeration systems, \"gcd-property\" of integer sequences, partition of the prefix of the fixed point of the Fibonacci substitution, spanning trees of a wheel. Eventually, we mention some open questions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.3618","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":"1108.3618","created_at":"2026-05-18T04:15:15.761725+00:00"},{"alias_kind":"arxiv_version","alias_value":"1108.3618v1","created_at":"2026-05-18T04:15:15.761725+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.3618","created_at":"2026-05-18T04:15:15.761725+00:00"},{"alias_kind":"pith_short_12","alias_value":"QG7SSDBR2W2D","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_16","alias_value":"QG7SSDBR2W2DP4QP","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_8","alias_value":"QG7SSDBR","created_at":"2026-05-18T12:26:39.201973+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/QG7SSDBR2W2DP4QP7KCFGSI3NW","json":"https://pith.science/pith/QG7SSDBR2W2DP4QP7KCFGSI3NW.json","graph_json":"https://pith.science/api/pith-number/QG7SSDBR2W2DP4QP7KCFGSI3NW/graph.json","events_json":"https://pith.science/api/pith-number/QG7SSDBR2W2DP4QP7KCFGSI3NW/events.json","paper":"https://pith.science/paper/QG7SSDBR"},"agent_actions":{"view_html":"https://pith.science/pith/QG7SSDBR2W2DP4QP7KCFGSI3NW","download_json":"https://pith.science/pith/QG7SSDBR2W2DP4QP7KCFGSI3NW.json","view_paper":"https://pith.science/paper/QG7SSDBR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1108.3618&json=true","fetch_graph":"https://pith.science/api/pith-number/QG7SSDBR2W2DP4QP7KCFGSI3NW/graph.json","fetch_events":"https://pith.science/api/pith-number/QG7SSDBR2W2DP4QP7KCFGSI3NW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QG7SSDBR2W2DP4QP7KCFGSI3NW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QG7SSDBR2W2DP4QP7KCFGSI3NW/action/storage_attestation","attest_author":"https://pith.science/pith/QG7SSDBR2W2DP4QP7KCFGSI3NW/action/author_attestation","sign_citation":"https://pith.science/pith/QG7SSDBR2W2DP4QP7KCFGSI3NW/action/citation_signature","submit_replication":"https://pith.science/pith/QG7SSDBR2W2DP4QP7KCFGSI3NW/action/replication_record"}},"created_at":"2026-05-18T04:15:15.761725+00:00","updated_at":"2026-05-18T04:15:15.761725+00:00"}