{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2005:OQHW7SPENC5WO5XJERBL5U3ZNI","short_pith_number":"pith:OQHW7SPE","schema_version":"1.0","canonical_sha256":"740f6fc9e468bb6776e92442bed3796a3d564d187d4a6895ab6ac8a9fc7bd42b","source":{"kind":"arxiv","id":"math/0501420","version":3},"attestation_state":"computed","paper":{"title":"Palindromic Prefixes and Episturmian Words","license":"","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"St\\'ephane Fischler","submitted_at":"2005-01-24T18:44:05Z","abstract_excerpt":"Let $w$ be an infinite word on an alphabet $A$. We denote by $(n_i)_{i \\geq 1}$ the increasing sequence (assumed to be infinite) of all lengths of palindrome prefixes of $w$. In this text, we give an explicit construction of all words $w$ such that $n_{i+1} \\leq 2 n_i + 1$ for any $i$, and study these words. Special examples include characteristic Sturmian words, and more generally standard episturmian words. As an application, we study the values taken by the quantity $\\limsup n_{i+1}/n_i$, and prove that it is minimal (among all non-periodic words) for the Fibonacci word."},"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":"math/0501420","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.CO","submitted_at":"2005-01-24T18:44:05Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"cd001049e2dac9e86ed7674fcae4d186f4d04ee42bdc914c010b1c00fb83e466","abstract_canon_sha256":"804b8d43daa8c8bba22859fd9889a2e99483cce45000cbcbbf3a9f67b56dcdea"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:02:36.575200Z","signature_b64":"+oO4/Aeu38ngoG+cmLO4FdqUzEF9HgoMkepjnZXIkVEltbyXLz7DJWwhbnhzs2lxxv3HYZgqHeOI5KBIS0mWAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"740f6fc9e468bb6776e92442bed3796a3d564d187d4a6895ab6ac8a9fc7bd42b","last_reissued_at":"2026-05-18T04:02:36.574529Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:02:36.574529Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Palindromic Prefixes and Episturmian Words","license":"","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"St\\'ephane Fischler","submitted_at":"2005-01-24T18:44:05Z","abstract_excerpt":"Let $w$ be an infinite word on an alphabet $A$. We denote by $(n_i)_{i \\geq 1}$ the increasing sequence (assumed to be infinite) of all lengths of palindrome prefixes of $w$. In this text, we give an explicit construction of all words $w$ such that $n_{i+1} \\leq 2 n_i + 1$ for any $i$, and study these words. Special examples include characteristic Sturmian words, and more generally standard episturmian words. As an application, we study the values taken by the quantity $\\limsup n_{i+1}/n_i$, and prove that it is minimal (among all non-periodic words) for the Fibonacci word."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0501420","kind":"arxiv","version":3},"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":"math/0501420","created_at":"2026-05-18T04:02:36.574643+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0501420v3","created_at":"2026-05-18T04:02:36.574643+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0501420","created_at":"2026-05-18T04:02:36.574643+00:00"},{"alias_kind":"pith_short_12","alias_value":"OQHW7SPENC5W","created_at":"2026-05-18T12:25:53.335082+00:00"},{"alias_kind":"pith_short_16","alias_value":"OQHW7SPENC5WO5XJ","created_at":"2026-05-18T12:25:53.335082+00:00"},{"alias_kind":"pith_short_8","alias_value":"OQHW7SPE","created_at":"2026-05-18T12:25:53.335082+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/OQHW7SPENC5WO5XJERBL5U3ZNI","json":"https://pith.science/pith/OQHW7SPENC5WO5XJERBL5U3ZNI.json","graph_json":"https://pith.science/api/pith-number/OQHW7SPENC5WO5XJERBL5U3ZNI/graph.json","events_json":"https://pith.science/api/pith-number/OQHW7SPENC5WO5XJERBL5U3ZNI/events.json","paper":"https://pith.science/paper/OQHW7SPE"},"agent_actions":{"view_html":"https://pith.science/pith/OQHW7SPENC5WO5XJERBL5U3ZNI","download_json":"https://pith.science/pith/OQHW7SPENC5WO5XJERBL5U3ZNI.json","view_paper":"https://pith.science/paper/OQHW7SPE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0501420&json=true","fetch_graph":"https://pith.science/api/pith-number/OQHW7SPENC5WO5XJERBL5U3ZNI/graph.json","fetch_events":"https://pith.science/api/pith-number/OQHW7SPENC5WO5XJERBL5U3ZNI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OQHW7SPENC5WO5XJERBL5U3ZNI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OQHW7SPENC5WO5XJERBL5U3ZNI/action/storage_attestation","attest_author":"https://pith.science/pith/OQHW7SPENC5WO5XJERBL5U3ZNI/action/author_attestation","sign_citation":"https://pith.science/pith/OQHW7SPENC5WO5XJERBL5U3ZNI/action/citation_signature","submit_replication":"https://pith.science/pith/OQHW7SPENC5WO5XJERBL5U3ZNI/action/replication_record"}},"created_at":"2026-05-18T04:02:36.574643+00:00","updated_at":"2026-05-18T04:02:36.574643+00:00"}