{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:KJFAVBAJADUTRQQSKII5W6C36C","short_pith_number":"pith:KJFAVBAJ","schema_version":"1.0","canonical_sha256":"524a0a840900e938c2125211db785bf0bf9cb3baf8947925104d99924ff05f86","source":{"kind":"arxiv","id":"1702.03611","version":2},"attestation_state":"computed","paper":{"title":"Partitions and Sylvester waves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Cormac O'Sullivan","submitted_at":"2017-02-13T02:44:28Z","abstract_excerpt":"The restricted partition function $p_N(n)$ counts the partitions of the integer $n$ into at most $N$ parts. In the nineteenth century Sylvester described these partitions as a sum of waves. We give detailed descriptions of these waves and, for the first time, show the asymptotics of the initial waves as $N$ and $n$ both go to infinity at about the same rate. This allows us to see when the initial waves are a good approximation to $p_N(n)$ in this situation. Our proofs employ the saddle-point method of Perron and the dilogarithm."},"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":"1702.03611","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-02-13T02:44:28Z","cross_cats_sorted":[],"title_canon_sha256":"8b22de1db2659d3c072e32f4f181446004b1dfb93aed60687172a74002695079","abstract_canon_sha256":"dea928b35ed16ed4a8a98d03d5731fb63485745e5b6522726c6391d27d38382a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:19:47.693254Z","signature_b64":"QfejjO4dJObJkl3SRFvv4/OVOle0eAgWmD2mk/FUJ8ETjPzr+bC9LwfhJX9CjsVj3tUKEc66Rftcrg3af+2IDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"524a0a840900e938c2125211db785bf0bf9cb3baf8947925104d99924ff05f86","last_reissued_at":"2026-05-18T00:19:47.692564Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:19:47.692564Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Partitions and Sylvester waves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Cormac O'Sullivan","submitted_at":"2017-02-13T02:44:28Z","abstract_excerpt":"The restricted partition function $p_N(n)$ counts the partitions of the integer $n$ into at most $N$ parts. In the nineteenth century Sylvester described these partitions as a sum of waves. We give detailed descriptions of these waves and, for the first time, show the asymptotics of the initial waves as $N$ and $n$ both go to infinity at about the same rate. This allows us to see when the initial waves are a good approximation to $p_N(n)$ in this situation. Our proofs employ the saddle-point method of Perron and the dilogarithm."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.03611","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":"1702.03611","created_at":"2026-05-18T00:19:47.692669+00:00"},{"alias_kind":"arxiv_version","alias_value":"1702.03611v2","created_at":"2026-05-18T00:19:47.692669+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.03611","created_at":"2026-05-18T00:19:47.692669+00:00"},{"alias_kind":"pith_short_12","alias_value":"KJFAVBAJADUT","created_at":"2026-05-18T12:31:24.725408+00:00"},{"alias_kind":"pith_short_16","alias_value":"KJFAVBAJADUTRQQS","created_at":"2026-05-18T12:31:24.725408+00:00"},{"alias_kind":"pith_short_8","alias_value":"KJFAVBAJ","created_at":"2026-05-18T12:31:24.725408+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/KJFAVBAJADUTRQQSKII5W6C36C","json":"https://pith.science/pith/KJFAVBAJADUTRQQSKII5W6C36C.json","graph_json":"https://pith.science/api/pith-number/KJFAVBAJADUTRQQSKII5W6C36C/graph.json","events_json":"https://pith.science/api/pith-number/KJFAVBAJADUTRQQSKII5W6C36C/events.json","paper":"https://pith.science/paper/KJFAVBAJ"},"agent_actions":{"view_html":"https://pith.science/pith/KJFAVBAJADUTRQQSKII5W6C36C","download_json":"https://pith.science/pith/KJFAVBAJADUTRQQSKII5W6C36C.json","view_paper":"https://pith.science/paper/KJFAVBAJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1702.03611&json=true","fetch_graph":"https://pith.science/api/pith-number/KJFAVBAJADUTRQQSKII5W6C36C/graph.json","fetch_events":"https://pith.science/api/pith-number/KJFAVBAJADUTRQQSKII5W6C36C/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KJFAVBAJADUTRQQSKII5W6C36C/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KJFAVBAJADUTRQQSKII5W6C36C/action/storage_attestation","attest_author":"https://pith.science/pith/KJFAVBAJADUTRQQSKII5W6C36C/action/author_attestation","sign_citation":"https://pith.science/pith/KJFAVBAJADUTRQQSKII5W6C36C/action/citation_signature","submit_replication":"https://pith.science/pith/KJFAVBAJADUTRQQSKII5W6C36C/action/replication_record"}},"created_at":"2026-05-18T00:19:47.692669+00:00","updated_at":"2026-05-18T00:19:47.692669+00:00"}