{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:TI3JEGSTGTNIT3TT4UETSPC6Q3","short_pith_number":"pith:TI3JEGST","schema_version":"1.0","canonical_sha256":"9a36921a5334da89ee73e509393c5e86cc10b615ed11ac1bf2f50b260e61eada","source":{"kind":"arxiv","id":"1901.07908","version":1},"attestation_state":"computed","paper":{"title":"Factors of some truncated basic hypergeometric series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Victor J. W. Guo","submitted_at":"2019-01-22T03:40:32Z","abstract_excerpt":"We prove that certain basic hypergeometric series truncated at $k=n-1$ have the factor $\\Phi_n(q)^2$, where $\\Phi_n(q)$ is the $n$-th cyclotomic polynomial. This confirms two recent conjectures of the author and Zudilin. We also put forward some conjectures on $q$-congruences modulo $\\Phi_n(q)^2$."},"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":"1901.07908","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-01-22T03:40:32Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"f2104f461f946fc88f8b09f7eef553dabed308627cb84699acf284ae69a5c789","abstract_canon_sha256":"9cc36896f132774fc5d742e544a230d7d743ba4cffd4692b0e7c58f543ae2a01"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:55:39.486256Z","signature_b64":"uyOOIfY9gKfeil8e0S6/tGHp7Xu+458q0aO9LrRrjQO8kH79n2EHGrpK4jgpn5pQWkFlV6/HssswrydTDVgWBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9a36921a5334da89ee73e509393c5e86cc10b615ed11ac1bf2f50b260e61eada","last_reissued_at":"2026-05-17T23:55:39.485895Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:55:39.485895Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Factors of some truncated basic hypergeometric series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Victor J. W. Guo","submitted_at":"2019-01-22T03:40:32Z","abstract_excerpt":"We prove that certain basic hypergeometric series truncated at $k=n-1$ have the factor $\\Phi_n(q)^2$, where $\\Phi_n(q)$ is the $n$-th cyclotomic polynomial. This confirms two recent conjectures of the author and Zudilin. We also put forward some conjectures on $q$-congruences modulo $\\Phi_n(q)^2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.07908","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":"1901.07908","created_at":"2026-05-17T23:55:39.485948+00:00"},{"alias_kind":"arxiv_version","alias_value":"1901.07908v1","created_at":"2026-05-17T23:55:39.485948+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.07908","created_at":"2026-05-17T23:55:39.485948+00:00"},{"alias_kind":"pith_short_12","alias_value":"TI3JEGSTGTNI","created_at":"2026-05-18T12:33:27.125529+00:00"},{"alias_kind":"pith_short_16","alias_value":"TI3JEGSTGTNIT3TT","created_at":"2026-05-18T12:33:27.125529+00:00"},{"alias_kind":"pith_short_8","alias_value":"TI3JEGST","created_at":"2026-05-18T12:33:27.125529+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/TI3JEGSTGTNIT3TT4UETSPC6Q3","json":"https://pith.science/pith/TI3JEGSTGTNIT3TT4UETSPC6Q3.json","graph_json":"https://pith.science/api/pith-number/TI3JEGSTGTNIT3TT4UETSPC6Q3/graph.json","events_json":"https://pith.science/api/pith-number/TI3JEGSTGTNIT3TT4UETSPC6Q3/events.json","paper":"https://pith.science/paper/TI3JEGST"},"agent_actions":{"view_html":"https://pith.science/pith/TI3JEGSTGTNIT3TT4UETSPC6Q3","download_json":"https://pith.science/pith/TI3JEGSTGTNIT3TT4UETSPC6Q3.json","view_paper":"https://pith.science/paper/TI3JEGST","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1901.07908&json=true","fetch_graph":"https://pith.science/api/pith-number/TI3JEGSTGTNIT3TT4UETSPC6Q3/graph.json","fetch_events":"https://pith.science/api/pith-number/TI3JEGSTGTNIT3TT4UETSPC6Q3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TI3JEGSTGTNIT3TT4UETSPC6Q3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TI3JEGSTGTNIT3TT4UETSPC6Q3/action/storage_attestation","attest_author":"https://pith.science/pith/TI3JEGSTGTNIT3TT4UETSPC6Q3/action/author_attestation","sign_citation":"https://pith.science/pith/TI3JEGSTGTNIT3TT4UETSPC6Q3/action/citation_signature","submit_replication":"https://pith.science/pith/TI3JEGSTGTNIT3TT4UETSPC6Q3/action/replication_record"}},"created_at":"2026-05-17T23:55:39.485948+00:00","updated_at":"2026-05-17T23:55:39.485948+00:00"}