{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:WQHBQGGDBXRD7ITV3PNNXTFPEI","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":"d9da1deb20dbde525f8a6093d99ecba2719efc3a17b34495651b3266b59ff613","cross_cats_sorted":[],"license":"","primary_cat":"math.CA","submitted_at":"2007-12-28T01:10:02Z","title_canon_sha256":"1e543d73da39377c370649a2e39e2ff44071ecab04f39a23c49e912b8c022702"},"schema_version":"1.0","source":{"id":"0712.4299","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0712.4299","created_at":"2026-05-18T00:12:46Z"},{"alias_kind":"arxiv_version","alias_value":"0712.4299v2","created_at":"2026-05-18T00:12:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0712.4299","created_at":"2026-05-18T00:12:46Z"},{"alias_kind":"pith_short_12","alias_value":"WQHBQGGDBXRD","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"WQHBQGGDBXRD7ITV","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"WQHBQGGD","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:f76d8ff3769a58e938a2be4ffd9be8b14eab2f66f5e484789388e9ea020d1344","target":"graph","created_at":"2026-05-18T00:12:46Z","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 usefulness of Riemann P-symbols in deriving identities involving the parametrized special function Hl is explored. Hl is the analytic local solution of the Heun equation, the canonical second-order differential equation on the Riemann sphere with four regular singular points. The identities discussed include ones coming from Moebius automorphisms and F-homotopies, and also quadratic and biquadratic transformations. The case when Hl is identical to a generalized hypergeometric function of 3F2 type is examined, and Pfaff and Euler transformations of 3F2(a1,a2,e+1;b1,e;x) are derived. They ex","authors_text":"Robert S. Maier","cross_cats":[],"headline":"","license":"","primary_cat":"math.CA","submitted_at":"2007-12-28T01:10:02Z","title":"P-symbols, Heun Identities, and 3F2 Identities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0712.4299","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":"sha256:483b0a93d3e7a975d4e4c27350b0bf8fadc63a1d8dccfca049308c5b0a7ba135","target":"record","created_at":"2026-05-18T00:12:46Z","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":"d9da1deb20dbde525f8a6093d99ecba2719efc3a17b34495651b3266b59ff613","cross_cats_sorted":[],"license":"","primary_cat":"math.CA","submitted_at":"2007-12-28T01:10:02Z","title_canon_sha256":"1e543d73da39377c370649a2e39e2ff44071ecab04f39a23c49e912b8c022702"},"schema_version":"1.0","source":{"id":"0712.4299","kind":"arxiv","version":2}},"canonical_sha256":"b40e1818c30de23fa275dbdadbccaf221d656be397f7729f94ba3d3e13a52350","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b40e1818c30de23fa275dbdadbccaf221d656be397f7729f94ba3d3e13a52350","first_computed_at":"2026-05-18T00:12:46.383393Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:46.383393Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fQ6j7TNSIa40tUr5CpZkBohhxKPFwcY5Pi8mukJrQPa0bseiXtmJebbrdlZhEJYoDjTfrJeuNN++hhaAZgWnDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:46.383870Z","signed_message":"canonical_sha256_bytes"},"source_id":"0712.4299","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:483b0a93d3e7a975d4e4c27350b0bf8fadc63a1d8dccfca049308c5b0a7ba135","sha256:f76d8ff3769a58e938a2be4ffd9be8b14eab2f66f5e484789388e9ea020d1344"],"state_sha256":"eed388a6a29f5673ca160866c264f3f2f6c0c04c9054bbd843c35efbb2681869"}