{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:7WUMOSXIEXYKF2TBBAHOC67L2I","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":"c704eb2654d2f938f90c08f56e092d306b989a4e67554f57e80d6102700bc9cf","cross_cats_sorted":["math.MP","math.QA","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-11-09T09:33:15Z","title_canon_sha256":"7ec5eae4ae716ccf2b8657806044224f47bd758d2beb1dd3e62d69ea20e2bada"},"schema_version":"1.0","source":{"id":"1411.2213","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.2213","created_at":"2026-05-18T00:51:52Z"},{"alias_kind":"arxiv_version","alias_value":"1411.2213v1","created_at":"2026-05-18T00:51:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.2213","created_at":"2026-05-18T00:51:52Z"},{"alias_kind":"pith_short_12","alias_value":"7WUMOSXIEXYK","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"7WUMOSXIEXYKF2TB","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"7WUMOSXI","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:2f5c3797c96bf47bc1ef387669f0f493a9be72cc3821e931b6c08750d77f9a6b","target":"graph","created_at":"2026-05-18T00:51:52Z","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":"We review and supplement the recent result by the authors on the reduction of the three dimensional $R$ (3d $R$) satisfying the tetrahedron equation to the quantum $R$ matrices for the $q$-oscillator representations of $U_q(D^{(2)}_{n+1})$, $U_q(A^{(2)}_{2n})$ and $U_q(C^{(1)}_{n})$. A new formula for the 3d $R$ and a quantum $R$ matrix for $n=1$ are presented and a proof of the irreducibility of the tensor product of the $q$-oscillator representations is detailed.","authors_text":"Atsuo Kuniba, Masato Okado","cross_cats":["math.MP","math.QA","nlin.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-11-09T09:33:15Z","title":"Tetrahedron equation and quantum $R$ matrices for $q$-oscillator representations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.2213","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":"sha256:7536200ee3eae71128e093040457d0d0c3b5700ba1d288365dbf2e954cf9975a","target":"record","created_at":"2026-05-18T00:51:52Z","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":"c704eb2654d2f938f90c08f56e092d306b989a4e67554f57e80d6102700bc9cf","cross_cats_sorted":["math.MP","math.QA","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-11-09T09:33:15Z","title_canon_sha256":"7ec5eae4ae716ccf2b8657806044224f47bd758d2beb1dd3e62d69ea20e2bada"},"schema_version":"1.0","source":{"id":"1411.2213","kind":"arxiv","version":1}},"canonical_sha256":"fda8c74ae825f0a2ea61080ee17bebd23b432a61d08ce5c776970fabe2f17ba1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fda8c74ae825f0a2ea61080ee17bebd23b432a61d08ce5c776970fabe2f17ba1","first_computed_at":"2026-05-18T00:51:52.465384Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:51:52.465384Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EwkbIKTPC0G4hOJEgSI09pTjGc2+nzr3ecssCCzxkqtej+/Hf4nNI+4ExJ97+rkvfyMj3xZuPs5CwMlkktqgAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:51:52.466025Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.2213","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7536200ee3eae71128e093040457d0d0c3b5700ba1d288365dbf2e954cf9975a","sha256:2f5c3797c96bf47bc1ef387669f0f493a9be72cc3821e931b6c08750d77f9a6b"],"state_sha256":"ce6e2f011ef270ac9ddb3af06a77a2ecf04c9bcb5f32aed7dbaa5813ba4d396c"}