{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:FNSB4E6TZVP7M2M63RUARL4R3A","short_pith_number":"pith:FNSB4E6T","schema_version":"1.0","canonical_sha256":"2b641e13d3cd5ff6699edc6808af91d80e1c203601d2a82b244f48aedf48b408","source":{"kind":"arxiv","id":"1507.07977","version":1},"attestation_state":"computed","paper":{"title":"Asymptotics for the partial fractions of the restricted partition generating function II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Cormac O'Sullivan","submitted_at":"2015-07-28T22:40:51Z","abstract_excerpt":"The generating function for $p_N(n)$, the number of partitions of $n$ into at most $N$ parts, may be written as a product of $N$ factors. In part I, we studied the behavior of coefficients in the partial fraction decomposition of this product as $N \\to \\infty$ by applying the saddle-point method to get the asymptotics of the main terms. In this second part we bound the error terms. This involves estimating products of sines and further saddle-point arguments. The saddle-points needed are associated to zeros of the analytically continued 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":"1507.07977","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-07-28T22:40:51Z","cross_cats_sorted":[],"title_canon_sha256":"103d9f97640f32b5ab49ffbb1c06ebc88ac6fc9837fdf26764b9847ba756903c","abstract_canon_sha256":"633a9957b933156859edeb7fc6753fc0bd85e1d55757f0856f2ab54f8fec61e1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:08.766781Z","signature_b64":"Aq6j9jrvACf/SCsYP60NJs20NpBOenTHOMB3fEywrNdYmacW0THt/nrPMWjqgG1YuKvmaqIBtiHd/SDt76k8AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2b641e13d3cd5ff6699edc6808af91d80e1c203601d2a82b244f48aedf48b408","last_reissued_at":"2026-05-18T01:36:08.766202Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:08.766202Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Asymptotics for the partial fractions of the restricted partition generating function II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Cormac O'Sullivan","submitted_at":"2015-07-28T22:40:51Z","abstract_excerpt":"The generating function for $p_N(n)$, the number of partitions of $n$ into at most $N$ parts, may be written as a product of $N$ factors. In part I, we studied the behavior of coefficients in the partial fraction decomposition of this product as $N \\to \\infty$ by applying the saddle-point method to get the asymptotics of the main terms. In this second part we bound the error terms. This involves estimating products of sines and further saddle-point arguments. The saddle-points needed are associated to zeros of the analytically continued dilogarithm."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.07977","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":"1507.07977","created_at":"2026-05-18T01:36:08.766290+00:00"},{"alias_kind":"arxiv_version","alias_value":"1507.07977v1","created_at":"2026-05-18T01:36:08.766290+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.07977","created_at":"2026-05-18T01:36:08.766290+00:00"},{"alias_kind":"pith_short_12","alias_value":"FNSB4E6TZVP7","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_16","alias_value":"FNSB4E6TZVP7M2M6","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_8","alias_value":"FNSB4E6T","created_at":"2026-05-18T12:29:19.899920+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/FNSB4E6TZVP7M2M63RUARL4R3A","json":"https://pith.science/pith/FNSB4E6TZVP7M2M63RUARL4R3A.json","graph_json":"https://pith.science/api/pith-number/FNSB4E6TZVP7M2M63RUARL4R3A/graph.json","events_json":"https://pith.science/api/pith-number/FNSB4E6TZVP7M2M63RUARL4R3A/events.json","paper":"https://pith.science/paper/FNSB4E6T"},"agent_actions":{"view_html":"https://pith.science/pith/FNSB4E6TZVP7M2M63RUARL4R3A","download_json":"https://pith.science/pith/FNSB4E6TZVP7M2M63RUARL4R3A.json","view_paper":"https://pith.science/paper/FNSB4E6T","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1507.07977&json=true","fetch_graph":"https://pith.science/api/pith-number/FNSB4E6TZVP7M2M63RUARL4R3A/graph.json","fetch_events":"https://pith.science/api/pith-number/FNSB4E6TZVP7M2M63RUARL4R3A/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FNSB4E6TZVP7M2M63RUARL4R3A/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FNSB4E6TZVP7M2M63RUARL4R3A/action/storage_attestation","attest_author":"https://pith.science/pith/FNSB4E6TZVP7M2M63RUARL4R3A/action/author_attestation","sign_citation":"https://pith.science/pith/FNSB4E6TZVP7M2M63RUARL4R3A/action/citation_signature","submit_replication":"https://pith.science/pith/FNSB4E6TZVP7M2M63RUARL4R3A/action/replication_record"}},"created_at":"2026-05-18T01:36:08.766290+00:00","updated_at":"2026-05-18T01:36:08.766290+00:00"}