{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:DCG3UGARGMU4IADJZJVDP5NST5","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":"5e6e0bba771d8a96232180aafd32e23489a981d4b06cb09b881fd74124311a44","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.NT","submitted_at":"2017-11-15T23:10:06Z","title_canon_sha256":"4b39d1adb6bd444cef3b41744676450495132d043e014a098d79a19a324057b1"},"schema_version":"1.0","source":{"id":"1711.05842","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.05842","created_at":"2026-05-18T00:15:37Z"},{"alias_kind":"arxiv_version","alias_value":"1711.05842v2","created_at":"2026-05-18T00:15:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.05842","created_at":"2026-05-18T00:15:37Z"},{"alias_kind":"pith_short_12","alias_value":"DCG3UGARGMU4","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"DCG3UGARGMU4IADJ","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"DCG3UGAR","created_at":"2026-05-18T12:31:10Z"}],"graph_snapshots":[{"event_id":"sha256:5006c1e4c4c5513d21aca4f3355bb5bf593c13c3bd570af1165e1460ea724d79","target":"graph","created_at":"2026-05-18T00:15:37Z","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":"For an odd prime $p$, let $\\phi$ denote the quadratic character of the multiplicative group ${\\mathbb F}_p^\\times$, where ${\\mathbb F}_p$ is the finite field of $p$ elements. In this paper, we will obtain evaluations of the hypergeometric functions $ {}_2F_1\\left(\\begin{matrix} \\phi\\psi & \\psi\\\\ & \\phi \\end{matrix};x\\right)$, $x\\in {\\mathbb F}_p$, $x\\neq 0, 1$, over ${\\mathbb F}_p$ in terms of Hecke character attached to CM elliptic curves for characters $\\psi$ of ${\\mathbb F}_p^\\times$ of order $3$, $4$, $6$, $8$, and $12$.","authors_text":"Fang-Ting Tu, Yifan Yang","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.NT","submitted_at":"2017-11-15T23:10:06Z","title":"Evaluation of Certain Hypergeometric Functions over Finite Fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.05842","kind":"arxiv","version":2},"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":"sha256:9455241c950951c0fa3e958c1b9f4ad4e7c83f693b749249117f5e2265dffa35","target":"record","created_at":"2026-05-18T00:15:37Z","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":"5e6e0bba771d8a96232180aafd32e23489a981d4b06cb09b881fd74124311a44","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.NT","submitted_at":"2017-11-15T23:10:06Z","title_canon_sha256":"4b39d1adb6bd444cef3b41744676450495132d043e014a098d79a19a324057b1"},"schema_version":"1.0","source":{"id":"1711.05842","kind":"arxiv","version":2}},"canonical_sha256":"188dba18113329c40069ca6a37f5b29f7ce28efc49f44df7c5e7f02e2747ff55","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"188dba18113329c40069ca6a37f5b29f7ce28efc49f44df7c5e7f02e2747ff55","first_computed_at":"2026-05-18T00:15:37.022766Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:15:37.022766Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nralmGVN4VMF8WB7UqltpWdJD3ee2JIKoVYwsSR88i9lWYB8r+S1QxMtcFn5buIamIDkMdb/xEv7S7EhYZwIDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:15:37.023325Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.05842","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9455241c950951c0fa3e958c1b9f4ad4e7c83f693b749249117f5e2265dffa35","sha256:5006c1e4c4c5513d21aca4f3355bb5bf593c13c3bd570af1165e1460ea724d79"],"state_sha256":"87f4b009863cf6807c05d03f55ffa081817cab279987b04ddaa0dbe34a3cdf70"}