{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:JKDUAOMLT52POQK3LYTT2DWKYB","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":"965576325151d3edf22b840eaf30ae69edb30357bbe790cdec0519583d00e26a","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math-ph","submitted_at":"2014-04-03T12:25:48Z","title_canon_sha256":"23a7a32962bab1bfb586a0051cf09a9d399b363e17e3298969108ad3911811a1"},"schema_version":"1.0","source":{"id":"1404.0876","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.0876","created_at":"2026-05-18T02:32:06Z"},{"alias_kind":"arxiv_version","alias_value":"1404.0876v4","created_at":"2026-05-18T02:32:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.0876","created_at":"2026-05-18T02:32:06Z"},{"alias_kind":"pith_short_12","alias_value":"JKDUAOMLT52P","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"JKDUAOMLT52POQK3","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"JKDUAOML","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:4fdf49c4e081d62966d16cad27e6dc4e4c6ec8b98c8a486c6afc40ed7430385b","target":"graph","created_at":"2026-05-18T02:32:06Z","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 $9j$ symbols of $\\mathfrak{su}(1,1)$ are studied within the framework of the generic superintegrable system on the 3-sphere. The canonical bases corresponding to the binary coupling schemes of four $\\mathfrak{su}(1,1)$ representations are constructed explicitly in terms of Jacobi polynomials and are seen to correspond to the separation of variables in different cylindrical coordinate systems. A triple integral expression for the $9j$ coefficients exhibiting their symmetries is derived. A double integral formula is obtained by extending the model to the complex three-sphere and taking the c","authors_text":"Luc Vinet, Vincent X. Genest","cross_cats":["math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math-ph","submitted_at":"2014-04-03T12:25:48Z","title":"The Generic Superintegrable System on the 3-Sphere and the $9j$ Symbols of $\\mathfrak{su}(1,1)$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.0876","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":"sha256:0f4560df9b1b8a719c0e9eb528bbfc6d112962d56542bef2570ff92f40a3216a","target":"record","created_at":"2026-05-18T02:32:06Z","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":"965576325151d3edf22b840eaf30ae69edb30357bbe790cdec0519583d00e26a","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math-ph","submitted_at":"2014-04-03T12:25:48Z","title_canon_sha256":"23a7a32962bab1bfb586a0051cf09a9d399b363e17e3298969108ad3911811a1"},"schema_version":"1.0","source":{"id":"1404.0876","kind":"arxiv","version":4}},"canonical_sha256":"4a8740398b9f74f7415b5e273d0ecac04d53fc668bf4fa6c79f734e49cb0125c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4a8740398b9f74f7415b5e273d0ecac04d53fc668bf4fa6c79f734e49cb0125c","first_computed_at":"2026-05-18T02:32:06.205025Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:32:06.205025Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sxS9+mCanjVSHSlKqd8dCetPBnen2qw7Kxv9ciOmT6MxfqzRNU5GD1WmeBbtGLziAJf3m2UC0ScVGCaq82anDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:32:06.205432Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.0876","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0f4560df9b1b8a719c0e9eb528bbfc6d112962d56542bef2570ff92f40a3216a","sha256:4fdf49c4e081d62966d16cad27e6dc4e4c6ec8b98c8a486c6afc40ed7430385b"],"state_sha256":"39ffe00fd7e2537a3eb93ded9c70fc06e5266bc7754ff33f7e341b8a3e2d1914"}