{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:PX4SOEKWWD6PN3ZV6GRQBL4LQ3","short_pith_number":"pith:PX4SOEKW","schema_version":"1.0","canonical_sha256":"7df9271156b0fcf6ef35f1a300af8b86eb62baa4f7ec7ccea5a993613a7f9cbf","source":{"kind":"arxiv","id":"1501.06843","version":2},"attestation_state":"computed","paper":{"title":"Exotic Bailey-Slater SPT-Functions II: Hecke-Rogers-Type Double Sums and Bailey Pairs From Groups A, C, E","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Chris Jennings-Shaffer, Frank Garvan","submitted_at":"2015-01-27T17:52:26Z","abstract_excerpt":"We investigate spt-crank-type functions arising from Bailey pairs. We recall four spt-type functions corresponding to the Bailey pairs $A1$, $A3$, $A5$, and $A7$ of Slater and given four new spt-type functions corresponding to Bailey pairs $C1$, $C5$, $E2$, and $E4$. Each of these functions can be thought of as a count on the number of appearances of the smallest part in certain integer partitions. We prove simple Ramanujan type congruences for these functions that are explained by a spt-crank-type function. The spt-crank-type functions are two variable $q$-series determined by a Bailey pair, "},"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":"1501.06843","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-01-27T17:52:26Z","cross_cats_sorted":[],"title_canon_sha256":"2c4feb2bc07612a1c5cdbb75568cc0c48c060a84dd68a62cc853edea44f1b5b1","abstract_canon_sha256":"857ab5f6f741dc570c3740b464d5f35f4459aa07c8ce76a039b5d183d3da3e97"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:25.425679Z","signature_b64":"sNLgsp3Nqtvwsz1fnBAo2yucxJpsNN2fnQg+IPz5e1049/WDNOyPe4DOxEx+atBEy2jETh6xw84jrLUTE4g7Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7df9271156b0fcf6ef35f1a300af8b86eb62baa4f7ec7ccea5a993613a7f9cbf","last_reissued_at":"2026-05-18T01:11:25.425111Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:25.425111Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Exotic Bailey-Slater SPT-Functions II: Hecke-Rogers-Type Double Sums and Bailey Pairs From Groups A, C, E","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Chris Jennings-Shaffer, Frank Garvan","submitted_at":"2015-01-27T17:52:26Z","abstract_excerpt":"We investigate spt-crank-type functions arising from Bailey pairs. We recall four spt-type functions corresponding to the Bailey pairs $A1$, $A3$, $A5$, and $A7$ of Slater and given four new spt-type functions corresponding to Bailey pairs $C1$, $C5$, $E2$, and $E4$. Each of these functions can be thought of as a count on the number of appearances of the smallest part in certain integer partitions. We prove simple Ramanujan type congruences for these functions that are explained by a spt-crank-type function. The spt-crank-type functions are two variable $q$-series determined by a Bailey pair, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.06843","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":"1501.06843","created_at":"2026-05-18T01:11:25.425196+00:00"},{"alias_kind":"arxiv_version","alias_value":"1501.06843v2","created_at":"2026-05-18T01:11:25.425196+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.06843","created_at":"2026-05-18T01:11:25.425196+00:00"},{"alias_kind":"pith_short_12","alias_value":"PX4SOEKWWD6P","created_at":"2026-05-18T12:29:37.295048+00:00"},{"alias_kind":"pith_short_16","alias_value":"PX4SOEKWWD6PN3ZV","created_at":"2026-05-18T12:29:37.295048+00:00"},{"alias_kind":"pith_short_8","alias_value":"PX4SOEKW","created_at":"2026-05-18T12:29:37.295048+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/PX4SOEKWWD6PN3ZV6GRQBL4LQ3","json":"https://pith.science/pith/PX4SOEKWWD6PN3ZV6GRQBL4LQ3.json","graph_json":"https://pith.science/api/pith-number/PX4SOEKWWD6PN3ZV6GRQBL4LQ3/graph.json","events_json":"https://pith.science/api/pith-number/PX4SOEKWWD6PN3ZV6GRQBL4LQ3/events.json","paper":"https://pith.science/paper/PX4SOEKW"},"agent_actions":{"view_html":"https://pith.science/pith/PX4SOEKWWD6PN3ZV6GRQBL4LQ3","download_json":"https://pith.science/pith/PX4SOEKWWD6PN3ZV6GRQBL4LQ3.json","view_paper":"https://pith.science/paper/PX4SOEKW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1501.06843&json=true","fetch_graph":"https://pith.science/api/pith-number/PX4SOEKWWD6PN3ZV6GRQBL4LQ3/graph.json","fetch_events":"https://pith.science/api/pith-number/PX4SOEKWWD6PN3ZV6GRQBL4LQ3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PX4SOEKWWD6PN3ZV6GRQBL4LQ3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PX4SOEKWWD6PN3ZV6GRQBL4LQ3/action/storage_attestation","attest_author":"https://pith.science/pith/PX4SOEKWWD6PN3ZV6GRQBL4LQ3/action/author_attestation","sign_citation":"https://pith.science/pith/PX4SOEKWWD6PN3ZV6GRQBL4LQ3/action/citation_signature","submit_replication":"https://pith.science/pith/PX4SOEKWWD6PN3ZV6GRQBL4LQ3/action/replication_record"}},"created_at":"2026-05-18T01:11:25.425196+00:00","updated_at":"2026-05-18T01:11:25.425196+00:00"}