{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:7I3IHVXKTA246EIMM73SC4JL6D","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":"64f7bb00e75fa85fe91dd00447d70784a7db39babfd8f7ea8c348a252d4200f6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2005-04-13T19:55:46Z","title_canon_sha256":"7eca74886a67c6ddf1a4165cff0fe72618286cdd907fba64d8f9b5b17cdb682a"},"schema_version":"1.0","source":{"id":"math/0504264","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0504264","created_at":"2026-05-18T03:46:04Z"},{"alias_kind":"arxiv_version","alias_value":"math/0504264v2","created_at":"2026-05-18T03:46:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0504264","created_at":"2026-05-18T03:46:04Z"},{"alias_kind":"pith_short_12","alias_value":"7I3IHVXKTA24","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"7I3IHVXKTA246EIM","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"7I3IHVXK","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:f3788949a3c857b0254bf9991224ce2329b432dd32e34f6402896713d5f8f0f0","target":"graph","created_at":"2026-05-18T03:46:04Z","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":"This paper presents explicit expressions for algebraic Gauss hypergeometric functions. We consider solutions of hypergeometric equations with the tetrahedral, octahedral and icosahedral monodromy groups. Conceptually, we pull-back such a hypergeometric equation onto its Darboux curve so that the pull-backed equation has a cyclic monodromy group. Minimal degree of the pull-back coverings is 4, 6 or 12 (for the three monodromy groups, respectively). In explicit terms, we replace the independent variable by a rational function of degree 4, 6 or 12, and transform hypergeometric functions to radica","authors_text":"Raimundas Vidunas","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2005-04-13T19:55:46Z","title":"Darboux evaluations of algebraic Gauss hypergeometric functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0504264","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":"sha256:95f190ed2c6189858832a34c6da0082188675d29c349bbb2c4b3a1d62229d7bd","target":"record","created_at":"2026-05-18T03:46:04Z","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":"64f7bb00e75fa85fe91dd00447d70784a7db39babfd8f7ea8c348a252d4200f6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2005-04-13T19:55:46Z","title_canon_sha256":"7eca74886a67c6ddf1a4165cff0fe72618286cdd907fba64d8f9b5b17cdb682a"},"schema_version":"1.0","source":{"id":"math/0504264","kind":"arxiv","version":2}},"canonical_sha256":"fa3683d6ea9835cf110c67f721712bf0e2c8fbfc8846d0afec6746ae0ea6e8b5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fa3683d6ea9835cf110c67f721712bf0e2c8fbfc8846d0afec6746ae0ea6e8b5","first_computed_at":"2026-05-18T03:46:04.324231Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:46:04.324231Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"265/0S2Krv9HTUfuDBMnpuPxuNB6BtLlZVw2/nWaDj7p78MaHzXw94g3DOXbyPK9ncvQDLCUkR/qSBM++ko7BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:46:04.325112Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0504264","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:95f190ed2c6189858832a34c6da0082188675d29c349bbb2c4b3a1d62229d7bd","sha256:f3788949a3c857b0254bf9991224ce2329b432dd32e34f6402896713d5f8f0f0"],"state_sha256":"f1582db1c1f2c82f4107ee57975c8baeedd6e18db190bae1f073b5281fd65f6b"}