{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:OQHW7SPENC5WO5XJERBL5U3ZNI","short_pith_number":"pith:OQHW7SPE","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"},"canonical_sha256":"740f6fc9e468bb6776e92442bed3796a3d564d187d4a6895ab6ac8a9fc7bd42b","source":{"kind":"arxiv","id":"math/0501420","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0501420","created_at":"2026-05-18T04:02:36Z"},{"alias_kind":"arxiv_version","alias_value":"math/0501420v3","created_at":"2026-05-18T04:02:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0501420","created_at":"2026-05-18T04:02:36Z"},{"alias_kind":"pith_short_12","alias_value":"OQHW7SPENC5W","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"OQHW7SPENC5WO5XJ","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"OQHW7SPE","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:OQHW7SPENC5WO5XJERBL5U3ZNI","target":"record","payload":{"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"},"canonical_sha256":"740f6fc9e468bb6776e92442bed3796a3d564d187d4a6895ab6ac8a9fc7bd42b","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"},"source_kind":"arxiv","source_id":"math/0501420","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:02:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Jy7tJ9CTUdrK3l91S6NTpyDiyDRtjictZ7Z6i2iQ/CvjmKtSwbxOL+vIIFxu9MbI5zt+Ny6gSTSj1Feh9oSCCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T06:20:49.268534Z"},"content_sha256":"5f40f8e38f364f62c1f45768b248b250810323b417027483a7691b61bf0bc58a","schema_version":"1.0","event_id":"sha256:5f40f8e38f364f62c1f45768b248b250810323b417027483a7691b61bf0bc58a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:OQHW7SPENC5WO5XJERBL5U3ZNI","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:02:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zc10hxKDYgr4J3lxtnFCUDCsMBt7ZSJfjch82OQuLxj0tIN/+y06dvgbff+YI8r2raFlN2qwv296+3u7n4X0Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T06:20:49.268879Z"},"content_sha256":"5408f55b4b3383be064b2a2dd78ea973d9d89bd5d5e9992532cbd99360809abf","schema_version":"1.0","event_id":"sha256:5408f55b4b3383be064b2a2dd78ea973d9d89bd5d5e9992532cbd99360809abf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OQHW7SPENC5WO5XJERBL5U3ZNI/bundle.json","state_url":"https://pith.science/pith/OQHW7SPENC5WO5XJERBL5U3ZNI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OQHW7SPENC5WO5XJERBL5U3ZNI/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-23T06:20:49Z","links":{"resolver":"https://pith.science/pith/OQHW7SPENC5WO5XJERBL5U3ZNI","bundle":"https://pith.science/pith/OQHW7SPENC5WO5XJERBL5U3ZNI/bundle.json","state":"https://pith.science/pith/OQHW7SPENC5WO5XJERBL5U3ZNI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OQHW7SPENC5WO5XJERBL5U3ZNI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:OQHW7SPENC5WO5XJERBL5U3ZNI","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"804b8d43daa8c8bba22859fd9889a2e99483cce45000cbcbbf3a9f67b56dcdea","cross_cats_sorted":["math.NT"],"license":"","primary_cat":"math.CO","submitted_at":"2005-01-24T18:44:05Z","title_canon_sha256":"cd001049e2dac9e86ed7674fcae4d186f4d04ee42bdc914c010b1c00fb83e466"},"schema_version":"1.0","source":{"id":"math/0501420","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0501420","created_at":"2026-05-18T04:02:36Z"},{"alias_kind":"arxiv_version","alias_value":"math/0501420v3","created_at":"2026-05-18T04:02:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0501420","created_at":"2026-05-18T04:02:36Z"},{"alias_kind":"pith_short_12","alias_value":"OQHW7SPENC5W","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"OQHW7SPENC5WO5XJ","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"OQHW7SPE","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:5408f55b4b3383be064b2a2dd78ea973d9d89bd5d5e9992532cbd99360809abf","target":"graph","created_at":"2026-05-18T04:02:36Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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.","authors_text":"St\\'ephane Fischler","cross_cats":["math.NT"],"headline":"","license":"","primary_cat":"math.CO","submitted_at":"2005-01-24T18:44:05Z","title":"Palindromic Prefixes and Episturmian Words"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0501420","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:5f40f8e38f364f62c1f45768b248b250810323b417027483a7691b61bf0bc58a","target":"record","created_at":"2026-05-18T04:02:36Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"804b8d43daa8c8bba22859fd9889a2e99483cce45000cbcbbf3a9f67b56dcdea","cross_cats_sorted":["math.NT"],"license":"","primary_cat":"math.CO","submitted_at":"2005-01-24T18:44:05Z","title_canon_sha256":"cd001049e2dac9e86ed7674fcae4d186f4d04ee42bdc914c010b1c00fb83e466"},"schema_version":"1.0","source":{"id":"math/0501420","kind":"arxiv","version":3}},"canonical_sha256":"740f6fc9e468bb6776e92442bed3796a3d564d187d4a6895ab6ac8a9fc7bd42b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"740f6fc9e468bb6776e92442bed3796a3d564d187d4a6895ab6ac8a9fc7bd42b","first_computed_at":"2026-05-18T04:02:36.574529Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:02:36.574529Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+oO4/Aeu38ngoG+cmLO4FdqUzEF9HgoMkepjnZXIkVEltbyXLz7DJWwhbnhzs2lxxv3HYZgqHeOI5KBIS0mWAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:02:36.575200Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0501420","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5f40f8e38f364f62c1f45768b248b250810323b417027483a7691b61bf0bc58a","sha256:5408f55b4b3383be064b2a2dd78ea973d9d89bd5d5e9992532cbd99360809abf"],"state_sha256":"5c0e473c916445fc14bef6dc6bd8d064a07ad139def1a58bd3fb723130b61874"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dJKmLoJhUm0IJI9EtGm/prL6GPtLuz8xV9sXDKxKwRLDMm7Zhq3bzL4d2pvlRR3jAnZu3Ukt+o3hW2CsyCL5CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T06:20:49.270884Z","bundle_sha256":"0c5fc98f42a70211be6b5bf2782079e7d8406a339544bcbe1bdd33b3b4a540fe"}}