{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2000:FYOMEKKD5DMGJGZIQZ35E4WTKF","short_pith_number":"pith:FYOMEKKD","schema_version":"1.0","canonical_sha256":"2e1cc22943e8d8649b288677d272d3515d9ff4fbbd337ed95d16e8a0c2af868d","source":{"kind":"arxiv","id":"math/0007097","version":2},"attestation_state":"computed","paper":{"title":"Clebsch-Gordan and Racah-Wigner coefficients for a continuous series of representations of U_q(sl(2,R))","license":"","headline":"","cross_cats":["hep-th"],"primary_cat":"math.QA","authors_text":"B. Ponsot, J. Teschner","submitted_at":"2000-07-15T13:39:42Z","abstract_excerpt":"The decomposition of tensor products of representations into irreducibles is studied for a continuous family of integrable operator representations of $U_q(sl(2,R)$. It is described by an explicit integral transformation involving a distributional kernel that can be seen as an analogue of the Clebsch-Gordan coefficients. Moreover, we also study the relation between two canonical decompositions of triple tensor products into irreducibles. It can be represented by an integral transformation with a kernel that generalizes the Racah-Wigner coefficients. This kernel is explicitly calculated."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"math/0007097","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.QA","submitted_at":"2000-07-15T13:39:42Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"514846f26560b9f00d82a18b3d396e47c72541cde5ca37f5552ecc820c42c859","abstract_canon_sha256":"90a416b653fd0de42552c3e627575da43ffb0da22468b23bfb84f6c6b908396c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T16:21:13.450392Z","signature_b64":"igNvPQiiIqxRYYUP6foUfqOaKXwQvYxkCx022mbDISgDk+VyK5RlpoP1lsWP4b3jTKgA1+OB7zeDCBamB+mnDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2e1cc22943e8d8649b288677d272d3515d9ff4fbbd337ed95d16e8a0c2af868d","last_reissued_at":"2026-07-04T16:21:13.449964Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T16:21:13.449964Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Clebsch-Gordan and Racah-Wigner coefficients for a continuous series of representations of U_q(sl(2,R))","license":"","headline":"","cross_cats":["hep-th"],"primary_cat":"math.QA","authors_text":"B. Ponsot, J. Teschner","submitted_at":"2000-07-15T13:39:42Z","abstract_excerpt":"The decomposition of tensor products of representations into irreducibles is studied for a continuous family of integrable operator representations of $U_q(sl(2,R)$. It is described by an explicit integral transformation involving a distributional kernel that can be seen as an analogue of the Clebsch-Gordan coefficients. Moreover, we also study the relation between two canonical decompositions of triple tensor products into irreducibles. It can be represented by an integral transformation with a kernel that generalizes the Racah-Wigner coefficients. This kernel is explicitly calculated."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0007097","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0007097/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"math/0007097","created_at":"2026-07-04T16:21:13.450021+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0007097v2","created_at":"2026-07-04T16:21:13.450021+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0007097","created_at":"2026-07-04T16:21:13.450021+00:00"},{"alias_kind":"pith_short_12","alias_value":"FYOMEKKD5DMG","created_at":"2026-07-04T16:21:13.450021+00:00"},{"alias_kind":"pith_short_16","alias_value":"FYOMEKKD5DMGJGZI","created_at":"2026-07-04T16:21:13.450021+00:00"},{"alias_kind":"pith_short_8","alias_value":"FYOMEKKD","created_at":"2026-07-04T16:21:13.450021+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":5,"internal_anchor_count":2,"sample":[{"citing_arxiv_id":"2505.00501","citing_title":"Minimal Factorization of Chern-Simons Theory -- Gravitational Anyonic Edge Modes","ref_index":115,"is_internal_anchor":true},{"citing_arxiv_id":"2506.04151","citing_title":"Surgery and statistics in 3d gravity","ref_index":57,"is_internal_anchor":true},{"citing_arxiv_id":"2604.26038","citing_title":"The Super Virasoro Minimal String from 3d Supergravity","ref_index":62,"is_internal_anchor":false},{"citing_arxiv_id":"2604.09396","citing_title":"The many facets of a hyperbolic tetrahedron: open and closed triangulations of 3d gravity","ref_index":63,"is_internal_anchor":false},{"citing_arxiv_id":"2604.04471","citing_title":"From hyperbolic to complex Euler integrals","ref_index":15,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FYOMEKKD5DMGJGZIQZ35E4WTKF","json":"https://pith.science/pith/FYOMEKKD5DMGJGZIQZ35E4WTKF.json","graph_json":"https://pith.science/api/pith-number/FYOMEKKD5DMGJGZIQZ35E4WTKF/graph.json","events_json":"https://pith.science/api/pith-number/FYOMEKKD5DMGJGZIQZ35E4WTKF/events.json","paper":"https://pith.science/paper/FYOMEKKD"},"agent_actions":{"view_html":"https://pith.science/pith/FYOMEKKD5DMGJGZIQZ35E4WTKF","download_json":"https://pith.science/pith/FYOMEKKD5DMGJGZIQZ35E4WTKF.json","view_paper":"https://pith.science/paper/FYOMEKKD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0007097&json=true","fetch_graph":"https://pith.science/api/pith-number/FYOMEKKD5DMGJGZIQZ35E4WTKF/graph.json","fetch_events":"https://pith.science/api/pith-number/FYOMEKKD5DMGJGZIQZ35E4WTKF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FYOMEKKD5DMGJGZIQZ35E4WTKF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FYOMEKKD5DMGJGZIQZ35E4WTKF/action/storage_attestation","attest_author":"https://pith.science/pith/FYOMEKKD5DMGJGZIQZ35E4WTKF/action/author_attestation","sign_citation":"https://pith.science/pith/FYOMEKKD5DMGJGZIQZ35E4WTKF/action/citation_signature","submit_replication":"https://pith.science/pith/FYOMEKKD5DMGJGZIQZ35E4WTKF/action/replication_record"}},"created_at":"2026-07-04T16:21:13.450021+00:00","updated_at":"2026-07-04T16:21:13.450021+00:00"}