{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1993:YCRKI3IUG7PIJHRJHTN76QH5PP","short_pith_number":"pith:YCRKI3IU","schema_version":"1.0","canonical_sha256":"c0a2a46d1437de849e293cdbff40fd7be90a9b24283b635bec233bad0a7039e2","source":{"kind":"arxiv","id":"hep-th/9301111","version":1},"attestation_state":"computed","paper":{"title":"On Foundation of the Generalized Nambu Mechanics","license":"","headline":"","cross_cats":["math.SG"],"primary_cat":"hep-th","authors_text":"Leon Takhtajan","submitted_at":"1993-01-26T20:45:26Z","abstract_excerpt":"We outline the basic principles of canonical formalism for the Nambu mechanics---a generalization of Hamiltonian mechanics proposed by Yoichiro Nambu in 1973. It is based on the notion of Nambu bracket which generalizes the Poisson bracket to the multiple operation of higher order $n \\geq 3$ on classical observables and is described by Hambu-Hamilton equations of motion given by $n-1$ Hamiltonians. We introduce the fundamental identity for the Nambu bracket which replaces Jacobi identity as a consistency condition for the dynamics. We show that Nambu structure of given order defines a family o"},"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/9301111","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"1993-01-26T20:45:26Z","cross_cats_sorted":["math.SG"],"title_canon_sha256":"2cd5bebffc770f802ed563ecfe567936d950b234d1a19b568db541b43b5cb475","abstract_canon_sha256":"1a7f628223ee799d6dba89ff5a3a6d0945928f56638d28b571b4dc107aed1999"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:55:55.085035Z","signature_b64":"1S0kHfkYCAq8j4qsAjf+wZjrcJU5M8E79khQV1W/dE4QMSKFixx1g9yCaGGmQpOpK9Fdc0VUNlgcAnQRgtNVDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c0a2a46d1437de849e293cdbff40fd7be90a9b24283b635bec233bad0a7039e2","last_reissued_at":"2026-07-04T15:55:55.084610Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:55:55.084610Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Foundation of the Generalized Nambu Mechanics","license":"","headline":"","cross_cats":["math.SG"],"primary_cat":"hep-th","authors_text":"Leon Takhtajan","submitted_at":"1993-01-26T20:45:26Z","abstract_excerpt":"We outline the basic principles of canonical formalism for the Nambu mechanics---a generalization of Hamiltonian mechanics proposed by Yoichiro Nambu in 1973. It is based on the notion of Nambu bracket which generalizes the Poisson bracket to the multiple operation of higher order $n \\geq 3$ on classical observables and is described by Hambu-Hamilton equations of motion given by $n-1$ Hamiltonians. We introduce the fundamental identity for the Nambu bracket which replaces Jacobi identity as a consistency condition for the dynamics. We show that Nambu structure of given order defines a family o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9301111","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/hep-th/9301111/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":"hep-th/9301111","created_at":"2026-07-04T15:55:55.084679+00:00"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9301111v1","created_at":"2026-07-04T15:55:55.084679+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9301111","created_at":"2026-07-04T15:55:55.084679+00:00"},{"alias_kind":"pith_short_12","alias_value":"YCRKI3IUG7PI","created_at":"2026-07-04T15:55:55.084679+00:00"},{"alias_kind":"pith_short_16","alias_value":"YCRKI3IUG7PIJHRJ","created_at":"2026-07-04T15:55:55.084679+00:00"},{"alias_kind":"pith_short_8","alias_value":"YCRKI3IU","created_at":"2026-07-04T15:55:55.084679+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2606.02421","citing_title":"Dynamics of the Density Cube","ref_index":17,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/YCRKI3IUG7PIJHRJHTN76QH5PP","json":"https://pith.science/pith/YCRKI3IUG7PIJHRJHTN76QH5PP.json","graph_json":"https://pith.science/api/pith-number/YCRKI3IUG7PIJHRJHTN76QH5PP/graph.json","events_json":"https://pith.science/api/pith-number/YCRKI3IUG7PIJHRJHTN76QH5PP/events.json","paper":"https://pith.science/paper/YCRKI3IU"},"agent_actions":{"view_html":"https://pith.science/pith/YCRKI3IUG7PIJHRJHTN76QH5PP","download_json":"https://pith.science/pith/YCRKI3IUG7PIJHRJHTN76QH5PP.json","view_paper":"https://pith.science/paper/YCRKI3IU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=hep-th/9301111&json=true","fetch_graph":"https://pith.science/api/pith-number/YCRKI3IUG7PIJHRJHTN76QH5PP/graph.json","fetch_events":"https://pith.science/api/pith-number/YCRKI3IUG7PIJHRJHTN76QH5PP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YCRKI3IUG7PIJHRJHTN76QH5PP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YCRKI3IUG7PIJHRJHTN76QH5PP/action/storage_attestation","attest_author":"https://pith.science/pith/YCRKI3IUG7PIJHRJHTN76QH5PP/action/author_attestation","sign_citation":"https://pith.science/pith/YCRKI3IUG7PIJHRJHTN76QH5PP/action/citation_signature","submit_replication":"https://pith.science/pith/YCRKI3IUG7PIJHRJHTN76QH5PP/action/replication_record"}},"created_at":"2026-07-04T15:55:55.084679+00:00","updated_at":"2026-07-04T15:55:55.084679+00:00"}