{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:5RUJV3KR4DFRXPX35YQPGJQWFS","short_pith_number":"pith:5RUJV3KR","schema_version":"1.0","canonical_sha256":"ec689aed51e0cb1bbefbee20f326162ca743c59929ad1329a4ad9c0eee089ba9","source":{"kind":"arxiv","id":"1407.5430","version":1},"attestation_state":"computed","paper":{"title":"A short Proof of a conjecture by Hirschhorn and Sellers on Overpartitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Liuquan Wang","submitted_at":"2014-07-21T09:30:29Z","abstract_excerpt":"Let $\\overline{p}(n)$ be the number of overpartitions of $n$, we establish and give a short elementary proof of the following congruence \\[\\overline{p}({{4}^{\\alpha }}(40n+35))\\equiv 0 \\, (\\bmod \\, 40),\\] where $\\alpha ,n $ are nonnegative integers. By letting $\\alpha =0$ we proved a conjecture of Hirschhorn and Sellers. Some new congruences for $\\overline{p}(n)$ modulo 3 and 5 have also been found, including the following two infinite families of Ramanujan-type congruences: for any integers $n\\ge 0$ and $\\alpha \\ge 1$, \\[\\overline{p}({{5}^{2\\alpha +1}}(5n+1))\\equiv \\overline{p}({{5}^{2\\alpha "},"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":"1407.5430","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-07-21T09:30:29Z","cross_cats_sorted":[],"title_canon_sha256":"271b569efe4f933fa336e84602af11b00a70a897f0fbd6aa4137dbda70e8cd79","abstract_canon_sha256":"8cb82832361845111d87a1c363784b341c97a07be613c9d41331cee9072c5214"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:47:13.996283Z","signature_b64":"0429yYZ3r9mdr+ytUn4d5bUtXOOwhE0JETAiapadIUPQG15aHZRrZdZf1fZO4hr9IgsV8lVyVVBA5R525adVDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ec689aed51e0cb1bbefbee20f326162ca743c59929ad1329a4ad9c0eee089ba9","last_reissued_at":"2026-05-18T02:47:13.995751Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:47:13.995751Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A short Proof of a conjecture by Hirschhorn and Sellers on Overpartitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Liuquan Wang","submitted_at":"2014-07-21T09:30:29Z","abstract_excerpt":"Let $\\overline{p}(n)$ be the number of overpartitions of $n$, we establish and give a short elementary proof of the following congruence \\[\\overline{p}({{4}^{\\alpha }}(40n+35))\\equiv 0 \\, (\\bmod \\, 40),\\] where $\\alpha ,n $ are nonnegative integers. By letting $\\alpha =0$ we proved a conjecture of Hirschhorn and Sellers. Some new congruences for $\\overline{p}(n)$ modulo 3 and 5 have also been found, including the following two infinite families of Ramanujan-type congruences: for any integers $n\\ge 0$ and $\\alpha \\ge 1$, \\[\\overline{p}({{5}^{2\\alpha +1}}(5n+1))\\equiv \\overline{p}({{5}^{2\\alpha "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.5430","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":"1407.5430","created_at":"2026-05-18T02:47:13.995826+00:00"},{"alias_kind":"arxiv_version","alias_value":"1407.5430v1","created_at":"2026-05-18T02:47:13.995826+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.5430","created_at":"2026-05-18T02:47:13.995826+00:00"},{"alias_kind":"pith_short_12","alias_value":"5RUJV3KR4DFR","created_at":"2026-05-18T12:28:14.216126+00:00"},{"alias_kind":"pith_short_16","alias_value":"5RUJV3KR4DFRXPX3","created_at":"2026-05-18T12:28:14.216126+00:00"},{"alias_kind":"pith_short_8","alias_value":"5RUJV3KR","created_at":"2026-05-18T12:28:14.216126+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/5RUJV3KR4DFRXPX35YQPGJQWFS","json":"https://pith.science/pith/5RUJV3KR4DFRXPX35YQPGJQWFS.json","graph_json":"https://pith.science/api/pith-number/5RUJV3KR4DFRXPX35YQPGJQWFS/graph.json","events_json":"https://pith.science/api/pith-number/5RUJV3KR4DFRXPX35YQPGJQWFS/events.json","paper":"https://pith.science/paper/5RUJV3KR"},"agent_actions":{"view_html":"https://pith.science/pith/5RUJV3KR4DFRXPX35YQPGJQWFS","download_json":"https://pith.science/pith/5RUJV3KR4DFRXPX35YQPGJQWFS.json","view_paper":"https://pith.science/paper/5RUJV3KR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1407.5430&json=true","fetch_graph":"https://pith.science/api/pith-number/5RUJV3KR4DFRXPX35YQPGJQWFS/graph.json","fetch_events":"https://pith.science/api/pith-number/5RUJV3KR4DFRXPX35YQPGJQWFS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5RUJV3KR4DFRXPX35YQPGJQWFS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5RUJV3KR4DFRXPX35YQPGJQWFS/action/storage_attestation","attest_author":"https://pith.science/pith/5RUJV3KR4DFRXPX35YQPGJQWFS/action/author_attestation","sign_citation":"https://pith.science/pith/5RUJV3KR4DFRXPX35YQPGJQWFS/action/citation_signature","submit_replication":"https://pith.science/pith/5RUJV3KR4DFRXPX35YQPGJQWFS/action/replication_record"}},"created_at":"2026-05-18T02:47:13.995826+00:00","updated_at":"2026-05-18T02:47:13.995826+00:00"}