{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:KW6HXDF5QUVBM6XGLJZZ2CU7MP","short_pith_number":"pith:KW6HXDF5","schema_version":"1.0","canonical_sha256":"55bc7b8cbd852a167ae65a739d0a9f63e30ac7450f68da8ef16ec67121fcf4f6","source":{"kind":"arxiv","id":"1901.02872","version":1},"attestation_state":"computed","paper":{"title":"A Reciprocity Relation for WP-Bailey Pairs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"James Mc Laughlin, Peter Zimmer","submitted_at":"2019-01-06T16:30:51Z","abstract_excerpt":"We derive a new general transformation for WP-Bailey pairs by considering the a certain limiting case of a WP-Bailey chain previously found by the authors, and examine several consequences of this new transformation. These consequences include new summation formulae involving WP-Bailey pairs. Other consequences include new proofs of some classical identities due to Jacobi, Ramanujan and others, and indeed extend these identities to identities involving particular specializations of arbitrary WP-Bailey pairs."},"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":"1901.02872","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-01-06T16:30:51Z","cross_cats_sorted":[],"title_canon_sha256":"16dccfd5ddba2f4ec3f4dfad96895fe8f68268bb6b15a75ba5dc748974325066","abstract_canon_sha256":"0d94e7ae01f23a452ef376cc9f6f5347dc5f3b9260ec2a8bbd1ffdc13befede8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:39.309711Z","signature_b64":"2ECFJWz4to6hm01HJAwHG4lFOZP2sKORokKzHN3/VqDDV7DGAdocDAZVh/7kNf6CsKw87jBWiYioGMUpaECUBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"55bc7b8cbd852a167ae65a739d0a9f63e30ac7450f68da8ef16ec67121fcf4f6","last_reissued_at":"2026-05-17T23:56:39.309096Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:39.309096Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Reciprocity Relation for WP-Bailey Pairs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"James Mc Laughlin, Peter Zimmer","submitted_at":"2019-01-06T16:30:51Z","abstract_excerpt":"We derive a new general transformation for WP-Bailey pairs by considering the a certain limiting case of a WP-Bailey chain previously found by the authors, and examine several consequences of this new transformation. These consequences include new summation formulae involving WP-Bailey pairs. Other consequences include new proofs of some classical identities due to Jacobi, Ramanujan and others, and indeed extend these identities to identities involving particular specializations of arbitrary WP-Bailey pairs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.02872","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":"1901.02872","created_at":"2026-05-17T23:56:39.309183+00:00"},{"alias_kind":"arxiv_version","alias_value":"1901.02872v1","created_at":"2026-05-17T23:56:39.309183+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.02872","created_at":"2026-05-17T23:56:39.309183+00:00"},{"alias_kind":"pith_short_12","alias_value":"KW6HXDF5QUVB","created_at":"2026-05-18T12:33:21.387695+00:00"},{"alias_kind":"pith_short_16","alias_value":"KW6HXDF5QUVBM6XG","created_at":"2026-05-18T12:33:21.387695+00:00"},{"alias_kind":"pith_short_8","alias_value":"KW6HXDF5","created_at":"2026-05-18T12:33:21.387695+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/KW6HXDF5QUVBM6XGLJZZ2CU7MP","json":"https://pith.science/pith/KW6HXDF5QUVBM6XGLJZZ2CU7MP.json","graph_json":"https://pith.science/api/pith-number/KW6HXDF5QUVBM6XGLJZZ2CU7MP/graph.json","events_json":"https://pith.science/api/pith-number/KW6HXDF5QUVBM6XGLJZZ2CU7MP/events.json","paper":"https://pith.science/paper/KW6HXDF5"},"agent_actions":{"view_html":"https://pith.science/pith/KW6HXDF5QUVBM6XGLJZZ2CU7MP","download_json":"https://pith.science/pith/KW6HXDF5QUVBM6XGLJZZ2CU7MP.json","view_paper":"https://pith.science/paper/KW6HXDF5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1901.02872&json=true","fetch_graph":"https://pith.science/api/pith-number/KW6HXDF5QUVBM6XGLJZZ2CU7MP/graph.json","fetch_events":"https://pith.science/api/pith-number/KW6HXDF5QUVBM6XGLJZZ2CU7MP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KW6HXDF5QUVBM6XGLJZZ2CU7MP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KW6HXDF5QUVBM6XGLJZZ2CU7MP/action/storage_attestation","attest_author":"https://pith.science/pith/KW6HXDF5QUVBM6XGLJZZ2CU7MP/action/author_attestation","sign_citation":"https://pith.science/pith/KW6HXDF5QUVBM6XGLJZZ2CU7MP/action/citation_signature","submit_replication":"https://pith.science/pith/KW6HXDF5QUVBM6XGLJZZ2CU7MP/action/replication_record"}},"created_at":"2026-05-17T23:56:39.309183+00:00","updated_at":"2026-05-17T23:56:39.309183+00:00"}