{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:RXMC2JYJKYPQDVM4A4QYCJPOXS","short_pith_number":"pith:RXMC2JYJ","schema_version":"1.0","canonical_sha256":"8dd82d2709561f01d59c07218125eebcb34284386b0bbf6d852babae13a95cb6","source":{"kind":"arxiv","id":"1408.0451","version":2},"attestation_state":"computed","paper":{"title":"Generalized trapezoidal words","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Amy Glen, Florence Lev\\'e","submitted_at":"2014-08-03T03:18:45Z","abstract_excerpt":"The factor complexity function $C_w(n)$ of a finite or infinite word $w$ counts the number of distinct factors of $w$ of length $n$ for each $n \\ge 0$. A finite word $w$ of length $|w|$ is said to be trapezoidal if the graph of its factor complexity $C_w(n)$ as a function of $n$ (for $0 \\leq n \\leq |w|$) is that of a regular trapezoid (or possibly an isosceles triangle); that is, $C_w(n)$ increases by 1 with each $n$ on some interval of length $r$, then $C_w(n)$ is constant on some interval of length $s$, and finally $C_w(n)$ decreases by 1 with each $n$ on an interval of the same length $r$. "},"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":"1408.0451","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-08-03T03:18:45Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"c737429d3c543c604dff99e2364f30c2d7139c98c7247cbe43c52ac34ca7cd1f","abstract_canon_sha256":"07094501c1e3402b6c6b08f75edf2fcf82e674f960c00e60010a21447166dd07"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:26:31.678780Z","signature_b64":"JrVAqWOA4NbWYBTYU8Ydkxva6Bflz1pcQouWoq7tDOTn4nsa0NknZ3H7Fmwo9sNUZGih7dFq6QdPQ1A04BvNAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8dd82d2709561f01d59c07218125eebcb34284386b0bbf6d852babae13a95cb6","last_reissued_at":"2026-05-18T02:26:31.678393Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:26:31.678393Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Generalized trapezoidal words","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Amy Glen, Florence Lev\\'e","submitted_at":"2014-08-03T03:18:45Z","abstract_excerpt":"The factor complexity function $C_w(n)$ of a finite or infinite word $w$ counts the number of distinct factors of $w$ of length $n$ for each $n \\ge 0$. A finite word $w$ of length $|w|$ is said to be trapezoidal if the graph of its factor complexity $C_w(n)$ as a function of $n$ (for $0 \\leq n \\leq |w|$) is that of a regular trapezoid (or possibly an isosceles triangle); that is, $C_w(n)$ increases by 1 with each $n$ on some interval of length $r$, then $C_w(n)$ is constant on some interval of length $s$, and finally $C_w(n)$ decreases by 1 with each $n$ on an interval of the same length $r$. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.0451","kind":"arxiv","version":2},"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":"1408.0451","created_at":"2026-05-18T02:26:31.678459+00:00"},{"alias_kind":"arxiv_version","alias_value":"1408.0451v2","created_at":"2026-05-18T02:26:31.678459+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.0451","created_at":"2026-05-18T02:26:31.678459+00:00"},{"alias_kind":"pith_short_12","alias_value":"RXMC2JYJKYPQ","created_at":"2026-05-18T12:28:46.137349+00:00"},{"alias_kind":"pith_short_16","alias_value":"RXMC2JYJKYPQDVM4","created_at":"2026-05-18T12:28:46.137349+00:00"},{"alias_kind":"pith_short_8","alias_value":"RXMC2JYJ","created_at":"2026-05-18T12:28:46.137349+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/RXMC2JYJKYPQDVM4A4QYCJPOXS","json":"https://pith.science/pith/RXMC2JYJKYPQDVM4A4QYCJPOXS.json","graph_json":"https://pith.science/api/pith-number/RXMC2JYJKYPQDVM4A4QYCJPOXS/graph.json","events_json":"https://pith.science/api/pith-number/RXMC2JYJKYPQDVM4A4QYCJPOXS/events.json","paper":"https://pith.science/paper/RXMC2JYJ"},"agent_actions":{"view_html":"https://pith.science/pith/RXMC2JYJKYPQDVM4A4QYCJPOXS","download_json":"https://pith.science/pith/RXMC2JYJKYPQDVM4A4QYCJPOXS.json","view_paper":"https://pith.science/paper/RXMC2JYJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1408.0451&json=true","fetch_graph":"https://pith.science/api/pith-number/RXMC2JYJKYPQDVM4A4QYCJPOXS/graph.json","fetch_events":"https://pith.science/api/pith-number/RXMC2JYJKYPQDVM4A4QYCJPOXS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RXMC2JYJKYPQDVM4A4QYCJPOXS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RXMC2JYJKYPQDVM4A4QYCJPOXS/action/storage_attestation","attest_author":"https://pith.science/pith/RXMC2JYJKYPQDVM4A4QYCJPOXS/action/author_attestation","sign_citation":"https://pith.science/pith/RXMC2JYJKYPQDVM4A4QYCJPOXS/action/citation_signature","submit_replication":"https://pith.science/pith/RXMC2JYJKYPQDVM4A4QYCJPOXS/action/replication_record"}},"created_at":"2026-05-18T02:26:31.678459+00:00","updated_at":"2026-05-18T02:26:31.678459+00:00"}