{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:HXVJKFA3EVA3T4XUBABEDOWEOK","short_pith_number":"pith:HXVJKFA3","schema_version":"1.0","canonical_sha256":"3dea95141b2541b9f2f4080241bac472a6b324547b0e96c5f120ef978a54872e","source":{"kind":"arxiv","id":"2408.16720","version":3},"attestation_state":"computed","paper":{"title":"Orthosymplectic $R$-matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.QA","nlin.SI"],"primary_cat":"math.RT","authors_text":"Alexander Tsymbaliuk, Kyungtak Hong","submitted_at":"2024-08-29T17:11:48Z","abstract_excerpt":"We present a formula for trigonometric orthosymplectic $R$-matrices associated with any parity sequence, and establish their factorization into the ordered product of $q$-exponents parametrized by positive roots in the corresponding reduced root systems. The latter is crucially based on the construction of orthogonal bases of the positive subalgebra through $q$-bracketings and combinatorics of dominant Lyndon words, as developed in [Clark, Hill, Wang, \"Quantum shuffles and quantum supergroups of basic type\", Quantum Topol. 7 (2016), no.3, 553-638]. We further evaluate the affine orthosymplecti"},"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":"2408.16720","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2024-08-29T17:11:48Z","cross_cats_sorted":["hep-th","math.QA","nlin.SI"],"title_canon_sha256":"b18438657c385651a13a8919b564eb5b89b72e0c0e9e75f0593be06363e7f243","abstract_canon_sha256":"cfb3803892d88f057cae6b8a99310687d7f57bb71b78790bca87047d6b5411d7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:01:32.470624Z","signature_b64":"FmvTNtDaXBeVwMOQNaQNsdCm6HVROOd9tGljVfIttLdVS7uRuZdVc9FmeXJEVoskAqSjmBDxa8qO1j7A9S14AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3dea95141b2541b9f2f4080241bac472a6b324547b0e96c5f120ef978a54872e","last_reissued_at":"2026-05-20T00:01:32.469867Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:01:32.469867Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Orthosymplectic $R$-matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.QA","nlin.SI"],"primary_cat":"math.RT","authors_text":"Alexander Tsymbaliuk, Kyungtak Hong","submitted_at":"2024-08-29T17:11:48Z","abstract_excerpt":"We present a formula for trigonometric orthosymplectic $R$-matrices associated with any parity sequence, and establish their factorization into the ordered product of $q$-exponents parametrized by positive roots in the corresponding reduced root systems. The latter is crucially based on the construction of orthogonal bases of the positive subalgebra through $q$-bracketings and combinatorics of dominant Lyndon words, as developed in [Clark, Hill, Wang, \"Quantum shuffles and quantum supergroups of basic type\", Quantum Topol. 7 (2016), no.3, 553-638]. We further evaluate the affine orthosymplecti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.16720","kind":"arxiv","version":3},"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/2408.16720/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":"2408.16720","created_at":"2026-05-20T00:01:32.469987+00:00"},{"alias_kind":"arxiv_version","alias_value":"2408.16720v3","created_at":"2026-05-20T00:01:32.469987+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.16720","created_at":"2026-05-20T00:01:32.469987+00:00"},{"alias_kind":"pith_short_12","alias_value":"HXVJKFA3EVA3","created_at":"2026-05-20T00:01:32.469987+00:00"},{"alias_kind":"pith_short_16","alias_value":"HXVJKFA3EVA3T4XU","created_at":"2026-05-20T00:01:32.469987+00:00"},{"alias_kind":"pith_short_8","alias_value":"HXVJKFA3","created_at":"2026-05-20T00:01:32.469987+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/HXVJKFA3EVA3T4XUBABEDOWEOK","json":"https://pith.science/pith/HXVJKFA3EVA3T4XUBABEDOWEOK.json","graph_json":"https://pith.science/api/pith-number/HXVJKFA3EVA3T4XUBABEDOWEOK/graph.json","events_json":"https://pith.science/api/pith-number/HXVJKFA3EVA3T4XUBABEDOWEOK/events.json","paper":"https://pith.science/paper/HXVJKFA3"},"agent_actions":{"view_html":"https://pith.science/pith/HXVJKFA3EVA3T4XUBABEDOWEOK","download_json":"https://pith.science/pith/HXVJKFA3EVA3T4XUBABEDOWEOK.json","view_paper":"https://pith.science/paper/HXVJKFA3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2408.16720&json=true","fetch_graph":"https://pith.science/api/pith-number/HXVJKFA3EVA3T4XUBABEDOWEOK/graph.json","fetch_events":"https://pith.science/api/pith-number/HXVJKFA3EVA3T4XUBABEDOWEOK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HXVJKFA3EVA3T4XUBABEDOWEOK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HXVJKFA3EVA3T4XUBABEDOWEOK/action/storage_attestation","attest_author":"https://pith.science/pith/HXVJKFA3EVA3T4XUBABEDOWEOK/action/author_attestation","sign_citation":"https://pith.science/pith/HXVJKFA3EVA3T4XUBABEDOWEOK/action/citation_signature","submit_replication":"https://pith.science/pith/HXVJKFA3EVA3T4XUBABEDOWEOK/action/replication_record"}},"created_at":"2026-05-20T00:01:32.469987+00:00","updated_at":"2026-05-20T00:01:32.469987+00:00"}