{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:WWLQ26MPIXPRUQINMCBFESABCA","short_pith_number":"pith:WWLQ26MP","schema_version":"1.0","canonical_sha256":"b5970d798f45df1a410d6082524801103f84c72bcd37867bca1b45978ca78184","source":{"kind":"arxiv","id":"1301.4877","version":1},"attestation_state":"computed","paper":{"title":"Proof of Sun's conjecture on the divisibility of certain binomial sums","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Victor J. W. Guo","submitted_at":"2013-01-21T14:39:37Z","abstract_excerpt":"In this paper, we prove the following result conjectured by Z.-W. Sun: $$ (2n-1){3n\\choose n}| \\sum_{k=0}^{n}{6k\\choose 3k}{3k\\choose k}{6(n-k)\\choose 3(n-k)}{3(n-k)\\choose n-k}. $$ by showing that the left-hand side divides each summand on the right-hand side."},"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":"1301.4877","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-01-21T14:39:37Z","cross_cats_sorted":[],"title_canon_sha256":"36a9b5cf49595c1203d85d68ba62e204b3cedcd55ff8cbeb14e5d26a66e35563","abstract_canon_sha256":"fce54206f37ef4519b18a92c1873fbe6c6b83f3aa7a14e6e3d657881a6beb6c0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:35:55.285147Z","signature_b64":"XW2PvtdSjRIL3Tq9fLjpFLrWOLkJJnwz1dr+invesjmGVHKuNdw970wL6Z8uJN3KYts4xIS8uRs2TCbz7zudCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b5970d798f45df1a410d6082524801103f84c72bcd37867bca1b45978ca78184","last_reissued_at":"2026-05-18T03:35:55.284410Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:35:55.284410Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Proof of Sun's conjecture on the divisibility of certain binomial sums","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Victor J. W. Guo","submitted_at":"2013-01-21T14:39:37Z","abstract_excerpt":"In this paper, we prove the following result conjectured by Z.-W. Sun: $$ (2n-1){3n\\choose n}| \\sum_{k=0}^{n}{6k\\choose 3k}{3k\\choose k}{6(n-k)\\choose 3(n-k)}{3(n-k)\\choose n-k}. $$ by showing that the left-hand side divides each summand on the right-hand side."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.4877","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":"1301.4877","created_at":"2026-05-18T03:35:55.284552+00:00"},{"alias_kind":"arxiv_version","alias_value":"1301.4877v1","created_at":"2026-05-18T03:35:55.284552+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.4877","created_at":"2026-05-18T03:35:55.284552+00:00"},{"alias_kind":"pith_short_12","alias_value":"WWLQ26MPIXPR","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_16","alias_value":"WWLQ26MPIXPRUQIN","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_8","alias_value":"WWLQ26MP","created_at":"2026-05-18T12:28:06.772260+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/WWLQ26MPIXPRUQINMCBFESABCA","json":"https://pith.science/pith/WWLQ26MPIXPRUQINMCBFESABCA.json","graph_json":"https://pith.science/api/pith-number/WWLQ26MPIXPRUQINMCBFESABCA/graph.json","events_json":"https://pith.science/api/pith-number/WWLQ26MPIXPRUQINMCBFESABCA/events.json","paper":"https://pith.science/paper/WWLQ26MP"},"agent_actions":{"view_html":"https://pith.science/pith/WWLQ26MPIXPRUQINMCBFESABCA","download_json":"https://pith.science/pith/WWLQ26MPIXPRUQINMCBFESABCA.json","view_paper":"https://pith.science/paper/WWLQ26MP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1301.4877&json=true","fetch_graph":"https://pith.science/api/pith-number/WWLQ26MPIXPRUQINMCBFESABCA/graph.json","fetch_events":"https://pith.science/api/pith-number/WWLQ26MPIXPRUQINMCBFESABCA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WWLQ26MPIXPRUQINMCBFESABCA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WWLQ26MPIXPRUQINMCBFESABCA/action/storage_attestation","attest_author":"https://pith.science/pith/WWLQ26MPIXPRUQINMCBFESABCA/action/author_attestation","sign_citation":"https://pith.science/pith/WWLQ26MPIXPRUQINMCBFESABCA/action/citation_signature","submit_replication":"https://pith.science/pith/WWLQ26MPIXPRUQINMCBFESABCA/action/replication_record"}},"created_at":"2026-05-18T03:35:55.284552+00:00","updated_at":"2026-05-18T03:35:55.284552+00:00"}