{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:MPMC3SMDCXR2DB5TUCZFAC3BYX","short_pith_number":"pith:MPMC3SMD","schema_version":"1.0","canonical_sha256":"63d82dc98315e3a187b3a0b2500b61c5f920e4cd3bb1dc0f3f9902528f6353db","source":{"kind":"arxiv","id":"1312.1975","version":2},"attestation_state":"computed","paper":{"title":"Orbit Approach to Separation of Variables in sl(3)-Related Integrable Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"nlin.SI","authors_text":"Julia Bernatska, Petro Holod","submitted_at":"2013-12-06T19:34:48Z","abstract_excerpt":"Using the orbit method we attempt to reveal geometric and algebraic meaning of separation of variables for the integrable systems on coadjoint orbits in an $\\mathfrak{sl}(3)$ loop algebra. We consider two types of generic orbits embedded into a common manifold, endowed with two nonsingular Lie-Poisson brackets. We prove that separation of variables on orbits of both types is realized by the same variables of separation. We also construct the integrable systems on these orbits: a coupled 3-component nonlinear Schr\\\"{o}dinger equation and an isotropic SU(3) Landau-Lifshitz equation."},"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":"1312.1975","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2013-12-06T19:34:48Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"dacf5858cea71c3eba92072b9623829f43909898c784bc0aba578bd8e6a0af83","abstract_canon_sha256":"15b25fc4946b281c0b774ac2de886c92a093dd8203f94b3e65cd137775975524"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:00:40.873257Z","signature_b64":"RnDMY7b1893IKm2fKDbklhIzO5/c0sUCULIjvauKOx0CxjFwuvxjtplR7eAOsOipP8+HSuDk35jA8+I9q4bKAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"63d82dc98315e3a187b3a0b2500b61c5f920e4cd3bb1dc0f3f9902528f6353db","last_reissued_at":"2026-05-18T01:00:40.872689Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:00:40.872689Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Orbit Approach to Separation of Variables in sl(3)-Related Integrable Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"nlin.SI","authors_text":"Julia Bernatska, Petro Holod","submitted_at":"2013-12-06T19:34:48Z","abstract_excerpt":"Using the orbit method we attempt to reveal geometric and algebraic meaning of separation of variables for the integrable systems on coadjoint orbits in an $\\mathfrak{sl}(3)$ loop algebra. We consider two types of generic orbits embedded into a common manifold, endowed with two nonsingular Lie-Poisson brackets. We prove that separation of variables on orbits of both types is realized by the same variables of separation. We also construct the integrable systems on these orbits: a coupled 3-component nonlinear Schr\\\"{o}dinger equation and an isotropic SU(3) Landau-Lifshitz equation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1975","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":"1312.1975","created_at":"2026-05-18T01:00:40.872782+00:00"},{"alias_kind":"arxiv_version","alias_value":"1312.1975v2","created_at":"2026-05-18T01:00:40.872782+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.1975","created_at":"2026-05-18T01:00:40.872782+00:00"},{"alias_kind":"pith_short_12","alias_value":"MPMC3SMDCXR2","created_at":"2026-05-18T12:27:52.871228+00:00"},{"alias_kind":"pith_short_16","alias_value":"MPMC3SMDCXR2DB5T","created_at":"2026-05-18T12:27:52.871228+00:00"},{"alias_kind":"pith_short_8","alias_value":"MPMC3SMD","created_at":"2026-05-18T12:27:52.871228+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/MPMC3SMDCXR2DB5TUCZFAC3BYX","json":"https://pith.science/pith/MPMC3SMDCXR2DB5TUCZFAC3BYX.json","graph_json":"https://pith.science/api/pith-number/MPMC3SMDCXR2DB5TUCZFAC3BYX/graph.json","events_json":"https://pith.science/api/pith-number/MPMC3SMDCXR2DB5TUCZFAC3BYX/events.json","paper":"https://pith.science/paper/MPMC3SMD"},"agent_actions":{"view_html":"https://pith.science/pith/MPMC3SMDCXR2DB5TUCZFAC3BYX","download_json":"https://pith.science/pith/MPMC3SMDCXR2DB5TUCZFAC3BYX.json","view_paper":"https://pith.science/paper/MPMC3SMD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1312.1975&json=true","fetch_graph":"https://pith.science/api/pith-number/MPMC3SMDCXR2DB5TUCZFAC3BYX/graph.json","fetch_events":"https://pith.science/api/pith-number/MPMC3SMDCXR2DB5TUCZFAC3BYX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MPMC3SMDCXR2DB5TUCZFAC3BYX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MPMC3SMDCXR2DB5TUCZFAC3BYX/action/storage_attestation","attest_author":"https://pith.science/pith/MPMC3SMDCXR2DB5TUCZFAC3BYX/action/author_attestation","sign_citation":"https://pith.science/pith/MPMC3SMDCXR2DB5TUCZFAC3BYX/action/citation_signature","submit_replication":"https://pith.science/pith/MPMC3SMDCXR2DB5TUCZFAC3BYX/action/replication_record"}},"created_at":"2026-05-18T01:00:40.872782+00:00","updated_at":"2026-05-18T01:00:40.872782+00:00"}