{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:XLIFQLIKBMPKS2SDSXILKQZHNB","short_pith_number":"pith:XLIFQLIK","schema_version":"1.0","canonical_sha256":"bad0582d0a0b1ea96a4395d0b54327686c436d4c45105c3fb51a3fb756cc8315","source":{"kind":"arxiv","id":"1501.02305","version":1},"attestation_state":"computed","paper":{"title":"Distinct parts partitions without sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Karl Mahlburg, Karthik Nataraj, Kathrin Bringmann","submitted_at":"2015-01-10T03:09:15Z","abstract_excerpt":"Partitions without sequences of consecutive integers as parts have been studied recently by many authors, including Andrews, Holroyd, Liggett, and Romik, among others. Their results include a description of combinatorial properties, hypergeometric representations for the generating functions, and asymptotic formulas for the enumeration functions. We complete a similar investigation of partitions into distinct parts without sequences, which are of particular interest due to their relationship with the Rogers-Ramanujan identities. Our main results include a double series representation for the g"},"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":"1501.02305","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-01-10T03:09:15Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"89e9b4c014198d435a00f6280d045c017db5c22f8536875954a7cf3c89069261","abstract_canon_sha256":"f516a99e640c88e1a73f6ff8b83bac7fb41793d012f18cfcdc0630b79f5e9e9a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:38.291378Z","signature_b64":"i0wOVuNCHuJFgNgc4q8aphtQBK1k26/nd67HcMynkd1bYgjggxSRJw55M/hh2oqBO5eSl7kbMTQORNdUmQsTCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bad0582d0a0b1ea96a4395d0b54327686c436d4c45105c3fb51a3fb756cc8315","last_reissued_at":"2026-05-18T02:29:38.290918Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:38.290918Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Distinct parts partitions without sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Karl Mahlburg, Karthik Nataraj, Kathrin Bringmann","submitted_at":"2015-01-10T03:09:15Z","abstract_excerpt":"Partitions without sequences of consecutive integers as parts have been studied recently by many authors, including Andrews, Holroyd, Liggett, and Romik, among others. Their results include a description of combinatorial properties, hypergeometric representations for the generating functions, and asymptotic formulas for the enumeration functions. We complete a similar investigation of partitions into distinct parts without sequences, which are of particular interest due to their relationship with the Rogers-Ramanujan identities. Our main results include a double series representation for the g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.02305","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":"1501.02305","created_at":"2026-05-18T02:29:38.290976+00:00"},{"alias_kind":"arxiv_version","alias_value":"1501.02305v1","created_at":"2026-05-18T02:29:38.290976+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.02305","created_at":"2026-05-18T02:29:38.290976+00:00"},{"alias_kind":"pith_short_12","alias_value":"XLIFQLIKBMPK","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_16","alias_value":"XLIFQLIKBMPKS2SD","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_8","alias_value":"XLIFQLIK","created_at":"2026-05-18T12:29:50.041715+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/XLIFQLIKBMPKS2SDSXILKQZHNB","json":"https://pith.science/pith/XLIFQLIKBMPKS2SDSXILKQZHNB.json","graph_json":"https://pith.science/api/pith-number/XLIFQLIKBMPKS2SDSXILKQZHNB/graph.json","events_json":"https://pith.science/api/pith-number/XLIFQLIKBMPKS2SDSXILKQZHNB/events.json","paper":"https://pith.science/paper/XLIFQLIK"},"agent_actions":{"view_html":"https://pith.science/pith/XLIFQLIKBMPKS2SDSXILKQZHNB","download_json":"https://pith.science/pith/XLIFQLIKBMPKS2SDSXILKQZHNB.json","view_paper":"https://pith.science/paper/XLIFQLIK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1501.02305&json=true","fetch_graph":"https://pith.science/api/pith-number/XLIFQLIKBMPKS2SDSXILKQZHNB/graph.json","fetch_events":"https://pith.science/api/pith-number/XLIFQLIKBMPKS2SDSXILKQZHNB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XLIFQLIKBMPKS2SDSXILKQZHNB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XLIFQLIKBMPKS2SDSXILKQZHNB/action/storage_attestation","attest_author":"https://pith.science/pith/XLIFQLIKBMPKS2SDSXILKQZHNB/action/author_attestation","sign_citation":"https://pith.science/pith/XLIFQLIKBMPKS2SDSXILKQZHNB/action/citation_signature","submit_replication":"https://pith.science/pith/XLIFQLIKBMPKS2SDSXILKQZHNB/action/replication_record"}},"created_at":"2026-05-18T02:29:38.290976+00:00","updated_at":"2026-05-18T02:29:38.290976+00:00"}