{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:LN6ZV4VXSDU62LHBMSRXS24JGL","short_pith_number":"pith:LN6ZV4VX","schema_version":"1.0","canonical_sha256":"5b7d9af2b790e9ed2ce164a3796b8932e2f638238fb4fe22c797efaacbe030b2","source":{"kind":"arxiv","id":"1312.4555","version":1},"attestation_state":"computed","paper":{"title":"Semi-invariants and Integrals of the Full Symmetric sl(n) Toda Lattice","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"nlin.SI","authors_text":"A.S. Sorin, Yu.B. Chernyakov","submitted_at":"2013-12-16T21:04:34Z","abstract_excerpt":"We consider the full symmetric version of the Lax operator of the Toda lattice which is known as the full symmetric Toda lattice. The phase space of this system is the generic orbit of the coadjoint action of the Borel subgroup B^+(n) of SL(n,R). This system is integrable. We propose a new method of constructing semi-invariants and integrals of the full symmetric Toda lattice. Using only the Toda equations for the Lax eigenvector matrix we prove the existence of the semi-invariants which are Plucker coordinates in the corresponding projective spaces. Then we use these semi-invariants to constr"},"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":"1312.4555","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2013-12-16T21:04:34Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"47e7dfd6b34a2fc3ebe4e48b605eb3603d7cadae7526a7244d0c15a23f962211","abstract_canon_sha256":"77a3e281b8420a1a3697ac84b136a9af760218e45f0401d8d1672b781df6b5e9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:04:16.739206Z","signature_b64":"i7IMr35QuN3C7mrwrZ7CaUGLEndd9Y/EIO/p73JrgHIjsVCKKkOr7L8EWzf2gVZXAhG7otE9zWsFZbAQwNfKDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5b7d9af2b790e9ed2ce164a3796b8932e2f638238fb4fe22c797efaacbe030b2","last_reissued_at":"2026-05-18T03:04:16.738800Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:04:16.738800Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Semi-invariants and Integrals of the Full Symmetric sl(n) Toda Lattice","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"nlin.SI","authors_text":"A.S. Sorin, Yu.B. Chernyakov","submitted_at":"2013-12-16T21:04:34Z","abstract_excerpt":"We consider the full symmetric version of the Lax operator of the Toda lattice which is known as the full symmetric Toda lattice. The phase space of this system is the generic orbit of the coadjoint action of the Borel subgroup B^+(n) of SL(n,R). This system is integrable. We propose a new method of constructing semi-invariants and integrals of the full symmetric Toda lattice. Using only the Toda equations for the Lax eigenvector matrix we prove the existence of the semi-invariants which are Plucker coordinates in the corresponding projective spaces. Then we use these semi-invariants to constr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.4555","kind":"arxiv","version":1},"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":"1312.4555","created_at":"2026-05-18T03:04:16.738858+00:00"},{"alias_kind":"arxiv_version","alias_value":"1312.4555v1","created_at":"2026-05-18T03:04:16.738858+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.4555","created_at":"2026-05-18T03:04:16.738858+00:00"},{"alias_kind":"pith_short_12","alias_value":"LN6ZV4VXSDU6","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_16","alias_value":"LN6ZV4VXSDU62LHB","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_8","alias_value":"LN6ZV4VX","created_at":"2026-05-18T12:27:51.066281+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/LN6ZV4VXSDU62LHBMSRXS24JGL","json":"https://pith.science/pith/LN6ZV4VXSDU62LHBMSRXS24JGL.json","graph_json":"https://pith.science/api/pith-number/LN6ZV4VXSDU62LHBMSRXS24JGL/graph.json","events_json":"https://pith.science/api/pith-number/LN6ZV4VXSDU62LHBMSRXS24JGL/events.json","paper":"https://pith.science/paper/LN6ZV4VX"},"agent_actions":{"view_html":"https://pith.science/pith/LN6ZV4VXSDU62LHBMSRXS24JGL","download_json":"https://pith.science/pith/LN6ZV4VXSDU62LHBMSRXS24JGL.json","view_paper":"https://pith.science/paper/LN6ZV4VX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1312.4555&json=true","fetch_graph":"https://pith.science/api/pith-number/LN6ZV4VXSDU62LHBMSRXS24JGL/graph.json","fetch_events":"https://pith.science/api/pith-number/LN6ZV4VXSDU62LHBMSRXS24JGL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LN6ZV4VXSDU62LHBMSRXS24JGL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LN6ZV4VXSDU62LHBMSRXS24JGL/action/storage_attestation","attest_author":"https://pith.science/pith/LN6ZV4VXSDU62LHBMSRXS24JGL/action/author_attestation","sign_citation":"https://pith.science/pith/LN6ZV4VXSDU62LHBMSRXS24JGL/action/citation_signature","submit_replication":"https://pith.science/pith/LN6ZV4VXSDU62LHBMSRXS24JGL/action/replication_record"}},"created_at":"2026-05-18T03:04:16.738858+00:00","updated_at":"2026-05-18T03:04:16.738858+00:00"}