{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:LODY6N3YRATEYR4OBG7BAEQEMQ","short_pith_number":"pith:LODY6N3Y","schema_version":"1.0","canonical_sha256":"5b878f377888264c478e09be1012046414352d3f16cf824946def0840346817a","source":{"kind":"arxiv","id":"1809.07523","version":1},"attestation_state":"computed","paper":{"title":"Catalan-like numbers and Hausdorff moment sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hayoung Choi, Seonguk Yoo, Yeong-Nan Yeh","submitted_at":"2018-09-20T08:25:54Z","abstract_excerpt":"In this paper we show that many well-known counting coefficients, including the Catalan numbers, the Motzkin numbers, the central binomial coefficients, the central Delannoy numbers are Hausdorff moment sequences in a unified approach. In particular we answer a conjecture of Liang at al. which such numbers have unique representing measures. The smallest interval including the support of representing measure is explicitly found. Subsequences of Catalan-like numbers are also considered. We provide a necessary and sufficient condition for a pattern of subsequences that if sequences are the Stielt"},"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":"1809.07523","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-20T08:25:54Z","cross_cats_sorted":[],"title_canon_sha256":"71f06fa5d7482251f1751634889a43261bd9fd5bca3d6957c486a5f268afa544","abstract_canon_sha256":"73a5c05ec641d2162c03b73089236b565d0f452b61a8cdc5be36200748b3f3db"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:16.033223Z","signature_b64":"p9zeV938o0V7dgQ7TBr6xGPP++Pobw0oTMu4kKtkWNMM0FUYiiIFFBql5UidrL67VWso0kFfnF+phGzkVEOWDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5b878f377888264c478e09be1012046414352d3f16cf824946def0840346817a","last_reissued_at":"2026-05-18T00:05:16.032707Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:16.032707Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Catalan-like numbers and Hausdorff moment sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hayoung Choi, Seonguk Yoo, Yeong-Nan Yeh","submitted_at":"2018-09-20T08:25:54Z","abstract_excerpt":"In this paper we show that many well-known counting coefficients, including the Catalan numbers, the Motzkin numbers, the central binomial coefficients, the central Delannoy numbers are Hausdorff moment sequences in a unified approach. In particular we answer a conjecture of Liang at al. which such numbers have unique representing measures. The smallest interval including the support of representing measure is explicitly found. Subsequences of Catalan-like numbers are also considered. We provide a necessary and sufficient condition for a pattern of subsequences that if sequences are the Stielt"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.07523","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":"1809.07523","created_at":"2026-05-18T00:05:16.032790+00:00"},{"alias_kind":"arxiv_version","alias_value":"1809.07523v1","created_at":"2026-05-18T00:05:16.032790+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.07523","created_at":"2026-05-18T00:05:16.032790+00:00"},{"alias_kind":"pith_short_12","alias_value":"LODY6N3YRATE","created_at":"2026-05-18T12:32:37.024351+00:00"},{"alias_kind":"pith_short_16","alias_value":"LODY6N3YRATEYR4O","created_at":"2026-05-18T12:32:37.024351+00:00"},{"alias_kind":"pith_short_8","alias_value":"LODY6N3Y","created_at":"2026-05-18T12:32:37.024351+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/LODY6N3YRATEYR4OBG7BAEQEMQ","json":"https://pith.science/pith/LODY6N3YRATEYR4OBG7BAEQEMQ.json","graph_json":"https://pith.science/api/pith-number/LODY6N3YRATEYR4OBG7BAEQEMQ/graph.json","events_json":"https://pith.science/api/pith-number/LODY6N3YRATEYR4OBG7BAEQEMQ/events.json","paper":"https://pith.science/paper/LODY6N3Y"},"agent_actions":{"view_html":"https://pith.science/pith/LODY6N3YRATEYR4OBG7BAEQEMQ","download_json":"https://pith.science/pith/LODY6N3YRATEYR4OBG7BAEQEMQ.json","view_paper":"https://pith.science/paper/LODY6N3Y","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1809.07523&json=true","fetch_graph":"https://pith.science/api/pith-number/LODY6N3YRATEYR4OBG7BAEQEMQ/graph.json","fetch_events":"https://pith.science/api/pith-number/LODY6N3YRATEYR4OBG7BAEQEMQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LODY6N3YRATEYR4OBG7BAEQEMQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LODY6N3YRATEYR4OBG7BAEQEMQ/action/storage_attestation","attest_author":"https://pith.science/pith/LODY6N3YRATEYR4OBG7BAEQEMQ/action/author_attestation","sign_citation":"https://pith.science/pith/LODY6N3YRATEYR4OBG7BAEQEMQ/action/citation_signature","submit_replication":"https://pith.science/pith/LODY6N3YRATEYR4OBG7BAEQEMQ/action/replication_record"}},"created_at":"2026-05-18T00:05:16.032790+00:00","updated_at":"2026-05-18T00:05:16.032790+00:00"}