{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:N6T3THT6G5ITT3KDX6OOADIW4L","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":"9578b0c0231544dc25972c95da691a7fdc4932cd16412549f7698a9f9f1f3bb6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-04-12T14:02:42Z","title_canon_sha256":"352905d0f1b03979fa00dcddb4a06e458a2801a72f0fa31cc7a081597b836827"},"schema_version":"1.0","source":{"id":"1204.2730","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.2730","created_at":"2026-05-18T03:58:03Z"},{"alias_kind":"arxiv_version","alias_value":"1204.2730v1","created_at":"2026-05-18T03:58:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.2730","created_at":"2026-05-18T03:58:03Z"},{"alias_kind":"pith_short_12","alias_value":"N6T3THT6G5IT","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"N6T3THT6G5ITT3KD","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"N6T3THT6","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:0fcc9a343743c3da715c8328eeb7d007e414ca16ba7e251c970f9e16ba495497","target":"graph","created_at":"2026-05-18T03:58:03Z","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":"Pull-back transformations between Heun and Gauss hypergeometric equations give useful expressions of Heun functions in terms of better understood hypergeometric functions. This article classifies, up to Mobius automorphisms, the coverings P1-to-P1 that yield pull-back transformations from hypergeometric to Heun equations with at least one free parameter (excluding the cases when the involved hypergeometric equation has cyclic or dihedral monodromy). In all, 61 parametric hypergeometric-to-Heun transformations are found, of maximal degree 12. Among them, 28 pull-backs are compositions of smalle","authors_text":"Galina Filipuk, Raimundas Vidunas","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-04-12T14:02:42Z","title":"A classification of coverings yielding Heun-to-hypergeometric reductions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.2730","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":"sha256:4a7d5e97de27e1402d32aee0b6cf1055d39d05e7939f6e6951f5c0e1f3212b5d","target":"record","created_at":"2026-05-18T03:58:03Z","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":"9578b0c0231544dc25972c95da691a7fdc4932cd16412549f7698a9f9f1f3bb6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-04-12T14:02:42Z","title_canon_sha256":"352905d0f1b03979fa00dcddb4a06e458a2801a72f0fa31cc7a081597b836827"},"schema_version":"1.0","source":{"id":"1204.2730","kind":"arxiv","version":1}},"canonical_sha256":"6fa7b99e7e375139ed43bf9ce00d16e2fcdea6373d484b0266d84f7549f14504","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6fa7b99e7e375139ed43bf9ce00d16e2fcdea6373d484b0266d84f7549f14504","first_computed_at":"2026-05-18T03:58:03.641437Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:58:03.641437Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kXx8oKqXtGzdmR/52F+OvKwoHkzvc1PUgBTK0fVag4eAGq4KMDOEKeR+8LVbFy4Kq89XegHmOAYnzP6rd2xuAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:58:03.642103Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.2730","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4a7d5e97de27e1402d32aee0b6cf1055d39d05e7939f6e6951f5c0e1f3212b5d","sha256:0fcc9a343743c3da715c8328eeb7d007e414ca16ba7e251c970f9e16ba495497"],"state_sha256":"1a42766b402d12bdcdd71b2ae2308cc3e0f8a12a5f6a95943f33fd95f2397386"}