{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:TI3JEGSTGTNIT3TT4UETSPC6Q3","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"9cc36896f132774fc5d742e544a230d7d743ba4cffd4692b0e7c58f543ae2a01","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-01-22T03:40:32Z","title_canon_sha256":"f2104f461f946fc88f8b09f7eef553dabed308627cb84699acf284ae69a5c789"},"schema_version":"1.0","source":{"id":"1901.07908","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.07908","created_at":"2026-05-17T23:55:39Z"},{"alias_kind":"arxiv_version","alias_value":"1901.07908v1","created_at":"2026-05-17T23:55:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.07908","created_at":"2026-05-17T23:55:39Z"},{"alias_kind":"pith_short_12","alias_value":"TI3JEGSTGTNI","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"TI3JEGSTGTNIT3TT","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"TI3JEGST","created_at":"2026-05-18T12:33:27Z"}],"graph_snapshots":[{"event_id":"sha256:3aa788c09784ee53aecfc078f146e2431b5d1865b309b32116485cb21fb8e4c4","target":"graph","created_at":"2026-05-17T23:55:39Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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 $\\Phi_n(q)^2$.","authors_text":"Victor J. W. Guo","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-01-22T03:40:32Z","title":"Factors of some truncated basic hypergeometric series"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.07908","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:b03b17cef003bce83a763fcb7a0124b05ccebd3532ae9407b96bc1d1ca1d4fe2","target":"record","created_at":"2026-05-17T23:55:39Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"9cc36896f132774fc5d742e544a230d7d743ba4cffd4692b0e7c58f543ae2a01","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-01-22T03:40:32Z","title_canon_sha256":"f2104f461f946fc88f8b09f7eef553dabed308627cb84699acf284ae69a5c789"},"schema_version":"1.0","source":{"id":"1901.07908","kind":"arxiv","version":1}},"canonical_sha256":"9a36921a5334da89ee73e509393c5e86cc10b615ed11ac1bf2f50b260e61eada","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9a36921a5334da89ee73e509393c5e86cc10b615ed11ac1bf2f50b260e61eada","first_computed_at":"2026-05-17T23:55:39.485895Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:55:39.485895Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uyOOIfY9gKfeil8e0S6/tGHp7Xu+458q0aO9LrRrjQO8kH79n2EHGrpK4jgpn5pQWkFlV6/HssswrydTDVgWBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:55:39.486256Z","signed_message":"canonical_sha256_bytes"},"source_id":"1901.07908","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b03b17cef003bce83a763fcb7a0124b05ccebd3532ae9407b96bc1d1ca1d4fe2","sha256:3aa788c09784ee53aecfc078f146e2431b5d1865b309b32116485cb21fb8e4c4"],"state_sha256":"46b4fd89166bb776f0ed28f417755e09dc49eea2ee99e1b007a470d2aa03041e"}