{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2003:NQ6TXZXAE5UZUTTN6XYBNE5I3O","short_pith_number":"pith:NQ6TXZXA","schema_version":"1.0","canonical_sha256":"6c3d3be6e027699a4e6df5f01693a8dbb489f1f06d5bb34cd22f0b96f575e09a","source":{"kind":"arxiv","id":"hep-th/0306084","version":1},"attestation_state":"computed","paper":{"title":"Generalized Toda mechanics associated with classical Lie algebras and their reductions","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Liu Zhao, Wangyun Liu, Zhanying Yang","submitted_at":"2003-06-10T13:05:11Z","abstract_excerpt":"For any classical Lie algebra $g$, we construct a family of integrable generalizations of Toda mechanics labeled a pair of ordered integers $(m,n)$. The universal form of the Lax pair, equations of motion, Hamiltonian as well as Poisson brackets are provided, and explicit examples for $\\mathfrak{g}=B_{r},C_{r},D_{r}$ with $m,n\\leq3$ are also given. For all $m,n$, it is shown that the dynamics of the $(m,n-1)$- and the $(m-1,n)$-Toda chains are natural reductions of that of the $(m,n)$-chain, and for $m=n$, there is also a family of symmetrically reduced Toda systems, the $(m,m)_{\\mathrm{Sym}}$"},"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":"hep-th/0306084","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"2003-06-10T13:05:11Z","cross_cats_sorted":[],"title_canon_sha256":"0d272b4dd24aa554b800acf25c3be1f865d2126149ad36b6436de4f0d28aea8e","abstract_canon_sha256":"2d7896992767adc71746de033355b559ffda4cdeca89974272a9e2b47d335b78"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:25:46.180347Z","signature_b64":"b3VW8hqS8eEWeNZ0sNvDoA6rAqJB3l7P+qtUIkP1HXf/dd9ZxDEL3wCNCLa8uhd5PXethP66Ek/E2jj40xL5AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6c3d3be6e027699a4e6df5f01693a8dbb489f1f06d5bb34cd22f0b96f575e09a","last_reissued_at":"2026-05-18T00:25:46.179674Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:25:46.179674Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Generalized Toda mechanics associated with classical Lie algebras and their reductions","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Liu Zhao, Wangyun Liu, Zhanying Yang","submitted_at":"2003-06-10T13:05:11Z","abstract_excerpt":"For any classical Lie algebra $g$, we construct a family of integrable generalizations of Toda mechanics labeled a pair of ordered integers $(m,n)$. The universal form of the Lax pair, equations of motion, Hamiltonian as well as Poisson brackets are provided, and explicit examples for $\\mathfrak{g}=B_{r},C_{r},D_{r}$ with $m,n\\leq3$ are also given. For all $m,n$, it is shown that the dynamics of the $(m,n-1)$- and the $(m-1,n)$-Toda chains are natural reductions of that of the $(m,n)$-chain, and for $m=n$, there is also a family of symmetrically reduced Toda systems, the $(m,m)_{\\mathrm{Sym}}$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0306084","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":"hep-th/0306084","created_at":"2026-05-18T00:25:46.179778+00:00"},{"alias_kind":"arxiv_version","alias_value":"hep-th/0306084v1","created_at":"2026-05-18T00:25:46.179778+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/0306084","created_at":"2026-05-18T00:25:46.179778+00:00"},{"alias_kind":"pith_short_12","alias_value":"NQ6TXZXAE5UZ","created_at":"2026-05-18T12:25:52.051335+00:00"},{"alias_kind":"pith_short_16","alias_value":"NQ6TXZXAE5UZUTTN","created_at":"2026-05-18T12:25:52.051335+00:00"},{"alias_kind":"pith_short_8","alias_value":"NQ6TXZXA","created_at":"2026-05-18T12:25:52.051335+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/NQ6TXZXAE5UZUTTN6XYBNE5I3O","json":"https://pith.science/pith/NQ6TXZXAE5UZUTTN6XYBNE5I3O.json","graph_json":"https://pith.science/api/pith-number/NQ6TXZXAE5UZUTTN6XYBNE5I3O/graph.json","events_json":"https://pith.science/api/pith-number/NQ6TXZXAE5UZUTTN6XYBNE5I3O/events.json","paper":"https://pith.science/paper/NQ6TXZXA"},"agent_actions":{"view_html":"https://pith.science/pith/NQ6TXZXAE5UZUTTN6XYBNE5I3O","download_json":"https://pith.science/pith/NQ6TXZXAE5UZUTTN6XYBNE5I3O.json","view_paper":"https://pith.science/paper/NQ6TXZXA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=hep-th/0306084&json=true","fetch_graph":"https://pith.science/api/pith-number/NQ6TXZXAE5UZUTTN6XYBNE5I3O/graph.json","fetch_events":"https://pith.science/api/pith-number/NQ6TXZXAE5UZUTTN6XYBNE5I3O/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NQ6TXZXAE5UZUTTN6XYBNE5I3O/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NQ6TXZXAE5UZUTTN6XYBNE5I3O/action/storage_attestation","attest_author":"https://pith.science/pith/NQ6TXZXAE5UZUTTN6XYBNE5I3O/action/author_attestation","sign_citation":"https://pith.science/pith/NQ6TXZXAE5UZUTTN6XYBNE5I3O/action/citation_signature","submit_replication":"https://pith.science/pith/NQ6TXZXAE5UZUTTN6XYBNE5I3O/action/replication_record"}},"created_at":"2026-05-18T00:25:46.179778+00:00","updated_at":"2026-05-18T00:25:46.179778+00:00"}