{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:QAWF4O5LQ7FKPSSZ6L3RUDTYK5","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":"defad99ed6e2fd867c00cab461d7b1bad2249e237ae1d566e908f648599279c1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-09-29T20:17:51Z","title_canon_sha256":"90afc44fe7388ff2fb9a5ab0c851b607ebe766e444a52619b845dc38dbf4fb81"},"schema_version":"1.0","source":{"id":"1309.7656","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.7656","created_at":"2026-05-18T03:00:12Z"},{"alias_kind":"arxiv_version","alias_value":"1309.7656v2","created_at":"2026-05-18T03:00:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.7656","created_at":"2026-05-18T03:00:12Z"},{"alias_kind":"pith_short_12","alias_value":"QAWF4O5LQ7FK","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QAWF4O5LQ7FKPSSZ","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QAWF4O5L","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:2f688d02158df5b83ddaade0c0f699c9f785c8f6c9667906f906d17d1a287c36","target":"graph","created_at":"2026-05-18T03:00:12Z","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":"Just as with the Gauss hypergeometric function, particular cases of the local Heun function can be Liouvillian (that is, \"elementary\") functions. One way to obtain these functions is by pull-back transformations of Gauss hypergeometric equations with Liouvillian solutions. This paper presents the Liouvillian solutions of Heun's equations that are pull-backs of the parametric hypergeometric equations with cyclic or dihedral monodromy groups.","authors_text":"Raimundas Vidunas","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-09-29T20:17:51Z","title":"Degenerate and dihedral Heun functions with parameters"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.7656","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":"sha256:01ab62ca000d1faacda263a9574356d60dd206d27795a78b7b6d47448d584edf","target":"record","created_at":"2026-05-18T03:00:12Z","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":"defad99ed6e2fd867c00cab461d7b1bad2249e237ae1d566e908f648599279c1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-09-29T20:17:51Z","title_canon_sha256":"90afc44fe7388ff2fb9a5ab0c851b607ebe766e444a52619b845dc38dbf4fb81"},"schema_version":"1.0","source":{"id":"1309.7656","kind":"arxiv","version":2}},"canonical_sha256":"802c5e3bab87caa7ca59f2f71a0e78576efb487a8e9348b3ac0a73dbcd2c5c42","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"802c5e3bab87caa7ca59f2f71a0e78576efb487a8e9348b3ac0a73dbcd2c5c42","first_computed_at":"2026-05-18T03:00:12.450210Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:00:12.450210Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FQAmUk6xgQttPTqtwQLXGJfoQvLiQTTQya6qvXFv1Am8Rnl8Mvx5I1MitLl4qbDR4KsGuV+o0/VOHEXYbTEuDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:00:12.450769Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.7656","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:01ab62ca000d1faacda263a9574356d60dd206d27795a78b7b6d47448d584edf","sha256:2f688d02158df5b83ddaade0c0f699c9f785c8f6c9667906f906d17d1a287c36"],"state_sha256":"a974dd3ef4d38723190e09c211d63c099419c7f13c406d48dc7cdc86a367a248"}