{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:MX6OR3Z7MFBVW5V7GCL5DWJRSP","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":"06c1b7fb4305f2e46cf9fc729586c4aad0575c9f75546d6d367c0f57cdb05a97","cross_cats_sorted":["math.AG","math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2009-06-18T17:41:57Z","title_canon_sha256":"810fc43eaf6003e686443f792d7c7bea60da440f7c89c4644e88601400dd9f7c"},"schema_version":"1.0","source":{"id":"0906.3485","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0906.3485","created_at":"2026-05-18T02:57:07Z"},{"alias_kind":"arxiv_version","alias_value":"0906.3485v4","created_at":"2026-05-18T02:57:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0906.3485","created_at":"2026-05-18T02:57:07Z"},{"alias_kind":"pith_short_12","alias_value":"MX6OR3Z7MFBV","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"MX6OR3Z7MFBVW5V7","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"MX6OR3Z7","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:d1c1d16f55e5076fa3080019cbf55d015ccb65c9ca1c62b3e8af981321180a01","target":"graph","created_at":"2026-05-18T02:57:07Z","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":"The hypergeometric functions ${}_nF_{n-1}$ are higher transcendental functions, but for certain parameter values they become algebraic, because the monodromy of the defining hypergeometric differential equation becomes finite. It is shown that many algebraic ${}_nF_{n-1}$'s, for which the finite monodromy is irreducible but imprimitive, can be represented as combinations of certain explicitly algebraic functions of a single variable; namely, the roots of trinomials. This generalizes a result of Birkeland, and is derived as a corollary of a family of binomial coefficient identities that is of i","authors_text":"Robert S. Maier","cross_cats":["math.AG","math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2009-06-18T17:41:57Z","title":"The Uniformization of Certain Algebraic Hypergeometric Functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.3485","kind":"arxiv","version":4},"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:fa6b4b64e622bb0215b2b29db3de9b62f798c97f44afe55c10052428175f5690","target":"record","created_at":"2026-05-18T02:57:07Z","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":"06c1b7fb4305f2e46cf9fc729586c4aad0575c9f75546d6d367c0f57cdb05a97","cross_cats_sorted":["math.AG","math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2009-06-18T17:41:57Z","title_canon_sha256":"810fc43eaf6003e686443f792d7c7bea60da440f7c89c4644e88601400dd9f7c"},"schema_version":"1.0","source":{"id":"0906.3485","kind":"arxiv","version":4}},"canonical_sha256":"65fce8ef3f61435b76bf3097d1d93193f786a880f226c25f9d23ea2c3a3bd2f5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"65fce8ef3f61435b76bf3097d1d93193f786a880f226c25f9d23ea2c3a3bd2f5","first_computed_at":"2026-05-18T02:57:07.132198Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:57:07.132198Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vGap5OrOPtDIjBKrRm/39Ow2KFcDxg0/8K+SDx6fj1r6FMcJvkhksW57iURGSGaZF72mVW3ZKiSTT7QbNPSNDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:57:07.132795Z","signed_message":"canonical_sha256_bytes"},"source_id":"0906.3485","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fa6b4b64e622bb0215b2b29db3de9b62f798c97f44afe55c10052428175f5690","sha256:d1c1d16f55e5076fa3080019cbf55d015ccb65c9ca1c62b3e8af981321180a01"],"state_sha256":"678c5c08e90b9c8fd20325011e7819f5bd2783a0e1148dbd9f428646d7774b13"}