{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:FM4BFUKNWWQZBGUHYVWHR5HFHH","short_pith_number":"pith:FM4BFUKN","schema_version":"1.0","canonical_sha256":"2b3812d14db5a1909a87c56c78f4e539caf677b493e22c975d3cc0dd885bba54","source":{"kind":"arxiv","id":"1601.06480","version":2},"attestation_state":"computed","paper":{"title":"Congruences and recursions for the cubic partition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Manosij Ghosh Dastidar, Shane Chern","submitted_at":"2016-01-25T05:19:20Z","abstract_excerpt":"Let $p_2(n)$ denote the number of cubic partitions. In this paper, we shall present two new congruences modulo $11$ for $p_2(n)$. We also provide an elementary alternative proof of a congruence established by Chan. Furthermore, we will establish a recursion for $p_2(n)$, which is a special case of a broader class of recursions."},"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":"1601.06480","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-01-25T05:19:20Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"bd6035c6130bbe089a2dd8f4a9fa2dbfbfd6eef73ce637bfb900faea9c3a486c","abstract_canon_sha256":"94d465ccbdc7abff0b1e0d866ec983214247790cc3b992584fbef8d2ba08fbe0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:50:57.424769Z","signature_b64":"fFslss9Aq3bV1jSCm7UKRx5bn/MjQN8xvjHJaJyLZco+yZKbbcW7y9AMAri8QjkrJi59oXg68dYth8iMKHm6Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2b3812d14db5a1909a87c56c78f4e539caf677b493e22c975d3cc0dd885bba54","last_reissued_at":"2026-05-18T00:50:57.423939Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:50:57.423939Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Congruences and recursions for the cubic partition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Manosij Ghosh Dastidar, Shane Chern","submitted_at":"2016-01-25T05:19:20Z","abstract_excerpt":"Let $p_2(n)$ denote the number of cubic partitions. In this paper, we shall present two new congruences modulo $11$ for $p_2(n)$. We also provide an elementary alternative proof of a congruence established by Chan. Furthermore, we will establish a recursion for $p_2(n)$, which is a special case of a broader class of recursions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.06480","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":"1601.06480","created_at":"2026-05-18T00:50:57.424078+00:00"},{"alias_kind":"arxiv_version","alias_value":"1601.06480v2","created_at":"2026-05-18T00:50:57.424078+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.06480","created_at":"2026-05-18T00:50:57.424078+00:00"},{"alias_kind":"pith_short_12","alias_value":"FM4BFUKNWWQZ","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_16","alias_value":"FM4BFUKNWWQZBGUH","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_8","alias_value":"FM4BFUKN","created_at":"2026-05-18T12:30:15.759754+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/FM4BFUKNWWQZBGUHYVWHR5HFHH","json":"https://pith.science/pith/FM4BFUKNWWQZBGUHYVWHR5HFHH.json","graph_json":"https://pith.science/api/pith-number/FM4BFUKNWWQZBGUHYVWHR5HFHH/graph.json","events_json":"https://pith.science/api/pith-number/FM4BFUKNWWQZBGUHYVWHR5HFHH/events.json","paper":"https://pith.science/paper/FM4BFUKN"},"agent_actions":{"view_html":"https://pith.science/pith/FM4BFUKNWWQZBGUHYVWHR5HFHH","download_json":"https://pith.science/pith/FM4BFUKNWWQZBGUHYVWHR5HFHH.json","view_paper":"https://pith.science/paper/FM4BFUKN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1601.06480&json=true","fetch_graph":"https://pith.science/api/pith-number/FM4BFUKNWWQZBGUHYVWHR5HFHH/graph.json","fetch_events":"https://pith.science/api/pith-number/FM4BFUKNWWQZBGUHYVWHR5HFHH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FM4BFUKNWWQZBGUHYVWHR5HFHH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FM4BFUKNWWQZBGUHYVWHR5HFHH/action/storage_attestation","attest_author":"https://pith.science/pith/FM4BFUKNWWQZBGUHYVWHR5HFHH/action/author_attestation","sign_citation":"https://pith.science/pith/FM4BFUKNWWQZBGUHYVWHR5HFHH/action/citation_signature","submit_replication":"https://pith.science/pith/FM4BFUKNWWQZBGUHYVWHR5HFHH/action/replication_record"}},"created_at":"2026-05-18T00:50:57.424078+00:00","updated_at":"2026-05-18T00:50:57.424078+00:00"}