{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:Y5626KYRJ5ZSFSZPENU4IK7CYS","short_pith_number":"pith:Y5626KYR","schema_version":"1.0","canonical_sha256":"c77daf2b114f7322cb2f2369c42be2c4a69a49d51f546ec4818bb9ed17c6ad09","source":{"kind":"arxiv","id":"1901.04840","version":1},"attestation_state":"computed","paper":{"title":"Some Implications of the WP-Bailey Tree","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":"2019-01-04T00:47:08Z","abstract_excerpt":"We consider a special case of a WP-Bailey chain of George Andrews, and use it to derive a number of curious transformations of basic hypergeometric series. We also derive two new WP-Bailey pairs, and use them to derive some additional new transformations for basic hypergeometric series. Finally, we briefly consider the implications of WP-Bailey pairs\\\\ $(\\alpha_n(a,k)$, $\\beta_n(a,k))$, in which $\\alpha_n(a,k)$ is independent of $k$, for generalizations of identities of the Rogers-Ramanujan type."},"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":"1901.04840","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-01-04T00:47:08Z","cross_cats_sorted":[],"title_canon_sha256":"aa4da143af80da93a81c93c6e4c5238436178a7166a779619c4c445221053865","abstract_canon_sha256":"033f1453f2e412d0dffb47d7ef92c7e4239e748be323ab6502dc43ccb6d83650"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:21.562804Z","signature_b64":"Kk+WM3FTqcyeJBCyoVuF8UcDO/pYq/+LMrXg3GybwUD7IkIvrLqE0P2s83JJ/MVMbkrL4N6PcSYch4x/XnbLCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c77daf2b114f7322cb2f2369c42be2c4a69a49d51f546ec4818bb9ed17c6ad09","last_reissued_at":"2026-05-17T23:56:21.562226Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:21.562226Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Some Implications of the WP-Bailey Tree","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":"2019-01-04T00:47:08Z","abstract_excerpt":"We consider a special case of a WP-Bailey chain of George Andrews, and use it to derive a number of curious transformations of basic hypergeometric series. We also derive two new WP-Bailey pairs, and use them to derive some additional new transformations for basic hypergeometric series. Finally, we briefly consider the implications of WP-Bailey pairs\\\\ $(\\alpha_n(a,k)$, $\\beta_n(a,k))$, in which $\\alpha_n(a,k)$ is independent of $k$, for generalizations of identities of the Rogers-Ramanujan type."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.04840","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":"1901.04840","created_at":"2026-05-17T23:56:21.562306+00:00"},{"alias_kind":"arxiv_version","alias_value":"1901.04840v1","created_at":"2026-05-17T23:56:21.562306+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.04840","created_at":"2026-05-17T23:56:21.562306+00:00"},{"alias_kind":"pith_short_12","alias_value":"Y5626KYRJ5ZS","created_at":"2026-05-18T12:33:33.725879+00:00"},{"alias_kind":"pith_short_16","alias_value":"Y5626KYRJ5ZSFSZP","created_at":"2026-05-18T12:33:33.725879+00:00"},{"alias_kind":"pith_short_8","alias_value":"Y5626KYR","created_at":"2026-05-18T12:33:33.725879+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/Y5626KYRJ5ZSFSZPENU4IK7CYS","json":"https://pith.science/pith/Y5626KYRJ5ZSFSZPENU4IK7CYS.json","graph_json":"https://pith.science/api/pith-number/Y5626KYRJ5ZSFSZPENU4IK7CYS/graph.json","events_json":"https://pith.science/api/pith-number/Y5626KYRJ5ZSFSZPENU4IK7CYS/events.json","paper":"https://pith.science/paper/Y5626KYR"},"agent_actions":{"view_html":"https://pith.science/pith/Y5626KYRJ5ZSFSZPENU4IK7CYS","download_json":"https://pith.science/pith/Y5626KYRJ5ZSFSZPENU4IK7CYS.json","view_paper":"https://pith.science/paper/Y5626KYR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1901.04840&json=true","fetch_graph":"https://pith.science/api/pith-number/Y5626KYRJ5ZSFSZPENU4IK7CYS/graph.json","fetch_events":"https://pith.science/api/pith-number/Y5626KYRJ5ZSFSZPENU4IK7CYS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Y5626KYRJ5ZSFSZPENU4IK7CYS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Y5626KYRJ5ZSFSZPENU4IK7CYS/action/storage_attestation","attest_author":"https://pith.science/pith/Y5626KYRJ5ZSFSZPENU4IK7CYS/action/author_attestation","sign_citation":"https://pith.science/pith/Y5626KYRJ5ZSFSZPENU4IK7CYS/action/citation_signature","submit_replication":"https://pith.science/pith/Y5626KYRJ5ZSFSZPENU4IK7CYS/action/replication_record"}},"created_at":"2026-05-17T23:56:21.562306+00:00","updated_at":"2026-05-17T23:56:21.562306+00:00"}