{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:4EBNXUM6UI5TCS5C7TFZAFEYE7","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"c22fc2e980e320b393c336d1fba00fdc141be2464dcc723f97f96a054e749548","cross_cats_sorted":["math.DG","math.MP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-10-06T11:03:01Z","title_canon_sha256":"46d9196a112249793152c23ec0339e0dc26b509a81d76d8e9ca3923e4c17784d"},"schema_version":"1.0","source":{"id":"1610.01817","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.01817","created_at":"2026-05-18T00:51:57Z"},{"alias_kind":"arxiv_version","alias_value":"1610.01817v1","created_at":"2026-05-18T00:51:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.01817","created_at":"2026-05-18T00:51:57Z"},{"alias_kind":"pith_short_12","alias_value":"4EBNXUM6UI5T","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4EBNXUM6UI5TCS5C","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4EBNXUM6","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:beab43ad8076f9df4e25f0423a3a0b64c4d689c598209173a80de686bd85f396","target":"graph","created_at":"2026-05-18T00:51:57Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"The Lagrangian representation of multi-Hamiltonian PDEs has been introduced by Y. Nutku and one of us (MVP). In this paper we focus on systems which are (at least) bi-Hamiltonian by a pair $A_1$, $A_2$, where $A_1$ is a hydrodynamic-type Hamiltonian operator. We prove that finding the Lagrangian representation is equivalent to finding a generalized vector field $\\tau$ such that $A_2=L_\\tau A_1$. We use this result in order to find the Lagrangian representation when $A_2$ is a homogeneous third-order Hamiltonian operator, although the method that we use can be applied to any other homogeneous H","authors_text":"M.V. Pavlov, R.F. Vitolo","cross_cats":["math.DG","math.MP","nlin.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-10-06T11:03:01Z","title":"Remarks on the Lagrangian representation of bi-Hamiltonian equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.01817","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:5954f855c644a15aacfa6ae0a70517350aa3cf6301540f44421c418786facdda","target":"record","created_at":"2026-05-18T00:51:57Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"c22fc2e980e320b393c336d1fba00fdc141be2464dcc723f97f96a054e749548","cross_cats_sorted":["math.DG","math.MP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-10-06T11:03:01Z","title_canon_sha256":"46d9196a112249793152c23ec0339e0dc26b509a81d76d8e9ca3923e4c17784d"},"schema_version":"1.0","source":{"id":"1610.01817","kind":"arxiv","version":1}},"canonical_sha256":"e102dbd19ea23b314ba2fccb90149827d1f2a2450b0e36cf023ecd37cb8b919f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e102dbd19ea23b314ba2fccb90149827d1f2a2450b0e36cf023ecd37cb8b919f","first_computed_at":"2026-05-18T00:51:57.526284Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:51:57.526284Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5IdwsoONrGyt6sI2tIjupJNQAQAbeJlG0P4vDn1eDI0lWg9zQTYobYcAeAxHcolOEY2dOj8P0ZjO7iCdMMVbAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:51:57.526981Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.01817","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5954f855c644a15aacfa6ae0a70517350aa3cf6301540f44421c418786facdda","sha256:beab43ad8076f9df4e25f0423a3a0b64c4d689c598209173a80de686bd85f396"],"state_sha256":"e95c39f10c1d219634cebf63ed2302a239da6fe677d84fe0d3bcacceab9502c5"}