{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:IRDBP5OBMYJMTBWIEMMCI5V6T5","short_pith_number":"pith:IRDBP5OB","schema_version":"1.0","canonical_sha256":"444617f5c16612c986c823182476be9f46875b12bd84efa119e46c79c8c932ab","source":{"kind":"arxiv","id":"1701.00359","version":2},"attestation_state":"computed","paper":{"title":"On moduli space of symmetric orthogonal matrices and exclusive Racah matrix $\\bar S$ for representation $R=[3,1]$ with multiplicities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.GT","math.MP","math.RT"],"primary_cat":"hep-th","authors_text":"A. Morozov","submitted_at":"2017-01-02T10:48:09Z","abstract_excerpt":"Racah matrices and higher $j$-symbols are used in description of braiding properties of conformal blocks and in construction of knot polynomials. However, in complicated cases the logic is actually inverted: they are much better deduced from these applications than from the basic representation theory. Following the recent proposal of arXiv:1612.00422, we obtain the exclusive Racah matrix $\\bar S$ for the currently-front-line case of representation $R=[3,1]$ with non-trivial multiplicities, where it is actually operator valued, i.e. depends on the choice of basises in the intertwiner spaces. E"},"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":"1701.00359","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-01-02T10:48:09Z","cross_cats_sorted":["math-ph","math.GT","math.MP","math.RT"],"title_canon_sha256":"fcbdeb335697bc31fa828c7457012f6c3ffe512f2cce51cabedbbab2f5d0f707","abstract_canon_sha256":"b9a62b2ef1c0da7890e6b6b44c34ea4fe108377e4b74a84a4b02b56b58aae4ba"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:07.909798Z","signature_b64":"3yegStKrk7Uy2QlxOqSlCNTmLoSUiqohMU1ORyRlieIWNFOCRbyXDSHWsexv1LpWSge13h0yiyMfR1XhX9oTAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"444617f5c16612c986c823182476be9f46875b12bd84efa119e46c79c8c932ab","last_reissued_at":"2026-05-18T00:52:07.908772Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:07.908772Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On moduli space of symmetric orthogonal matrices and exclusive Racah matrix $\\bar S$ for representation $R=[3,1]$ with multiplicities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.GT","math.MP","math.RT"],"primary_cat":"hep-th","authors_text":"A. Morozov","submitted_at":"2017-01-02T10:48:09Z","abstract_excerpt":"Racah matrices and higher $j$-symbols are used in description of braiding properties of conformal blocks and in construction of knot polynomials. However, in complicated cases the logic is actually inverted: they are much better deduced from these applications than from the basic representation theory. Following the recent proposal of arXiv:1612.00422, we obtain the exclusive Racah matrix $\\bar S$ for the currently-front-line case of representation $R=[3,1]$ with non-trivial multiplicities, where it is actually operator valued, i.e. depends on the choice of basises in the intertwiner spaces. E"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.00359","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":""},"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":"1701.00359","created_at":"2026-05-18T00:52:07.908892+00:00"},{"alias_kind":"arxiv_version","alias_value":"1701.00359v2","created_at":"2026-05-18T00:52:07.908892+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.00359","created_at":"2026-05-18T00:52:07.908892+00:00"},{"alias_kind":"pith_short_12","alias_value":"IRDBP5OBMYJM","created_at":"2026-05-18T12:31:21.493067+00:00"},{"alias_kind":"pith_short_16","alias_value":"IRDBP5OBMYJMTBWI","created_at":"2026-05-18T12:31:21.493067+00:00"},{"alias_kind":"pith_short_8","alias_value":"IRDBP5OB","created_at":"2026-05-18T12:31:21.493067+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/IRDBP5OBMYJMTBWIEMMCI5V6T5","json":"https://pith.science/pith/IRDBP5OBMYJMTBWIEMMCI5V6T5.json","graph_json":"https://pith.science/api/pith-number/IRDBP5OBMYJMTBWIEMMCI5V6T5/graph.json","events_json":"https://pith.science/api/pith-number/IRDBP5OBMYJMTBWIEMMCI5V6T5/events.json","paper":"https://pith.science/paper/IRDBP5OB"},"agent_actions":{"view_html":"https://pith.science/pith/IRDBP5OBMYJMTBWIEMMCI5V6T5","download_json":"https://pith.science/pith/IRDBP5OBMYJMTBWIEMMCI5V6T5.json","view_paper":"https://pith.science/paper/IRDBP5OB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1701.00359&json=true","fetch_graph":"https://pith.science/api/pith-number/IRDBP5OBMYJMTBWIEMMCI5V6T5/graph.json","fetch_events":"https://pith.science/api/pith-number/IRDBP5OBMYJMTBWIEMMCI5V6T5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IRDBP5OBMYJMTBWIEMMCI5V6T5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IRDBP5OBMYJMTBWIEMMCI5V6T5/action/storage_attestation","attest_author":"https://pith.science/pith/IRDBP5OBMYJMTBWIEMMCI5V6T5/action/author_attestation","sign_citation":"https://pith.science/pith/IRDBP5OBMYJMTBWIEMMCI5V6T5/action/citation_signature","submit_replication":"https://pith.science/pith/IRDBP5OBMYJMTBWIEMMCI5V6T5/action/replication_record"}},"created_at":"2026-05-18T00:52:07.908892+00:00","updated_at":"2026-05-18T00:52:07.908892+00:00"}