{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:S5434ZNV7IY3HP3SEM62Y6WEUL","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":"47ccedcd71601c13acee8965e1f5b58fd4e7de8ca610204ce49a2bd77fa83b5e","cross_cats_sorted":["math.MP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-02-19T19:44:58Z","title_canon_sha256":"3853e8e11418e41140d805e5b7b1705bc8ca2716e50e2b25ef64b8c64d12c8e5"},"schema_version":"1.0","source":{"id":"1502.05677","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.05677","created_at":"2026-05-18T02:07:26Z"},{"alias_kind":"arxiv_version","alias_value":"1502.05677v2","created_at":"2026-05-18T02:07:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.05677","created_at":"2026-05-18T02:07:26Z"},{"alias_kind":"pith_short_12","alias_value":"S5434ZNV7IY3","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"S5434ZNV7IY3HP3S","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"S5434ZNV","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:a07b4ac9f4fe3de3336f7fa30a9c1fa555435aa376d2bb794c4470b76a3a6dbe","target":"graph","created_at":"2026-05-18T02:07:26Z","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":"First-order Hamiltonian operators of hydrodynamic type were introduced by Drubrovin and Novikov in 1983. In 2D, they are generated by a pair of contravariant metrics $g$, $\\tilde{g}$ and a pair of differential-geometric objects $b$, $\\tilde{b}$. If the determinant of the pencil $g+\\lambda \\tilde{g}$ vanishes for all $\\lambda$, the operator is called degenerate. In this paper we provide a complete classification of degenerate two- and three-component Hamiltonian operators. Moreover, we study the integrability, by the method of hydrodynamic reductions, of 2+1 Hamiltonian systems arising from the","authors_text":"Andrea Savoldi","cross_cats":["math.MP","nlin.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-02-19T19:44:58Z","title":"Degenerate first-order Hamiltonian operators of hydrodynamic type in 2D"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.05677","kind":"arxiv","version":2},"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":"sha256:226e5adf21299e2154ae1d816cd0608cf08863b23ad96abb6477b59cf8ad3a3e","target":"record","created_at":"2026-05-18T02:07:26Z","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":"47ccedcd71601c13acee8965e1f5b58fd4e7de8ca610204ce49a2bd77fa83b5e","cross_cats_sorted":["math.MP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-02-19T19:44:58Z","title_canon_sha256":"3853e8e11418e41140d805e5b7b1705bc8ca2716e50e2b25ef64b8c64d12c8e5"},"schema_version":"1.0","source":{"id":"1502.05677","kind":"arxiv","version":2}},"canonical_sha256":"9779be65b5fa31b3bf72233dac7ac4a2dfbbb846a94d16f49e9148fa94aa6efd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9779be65b5fa31b3bf72233dac7ac4a2dfbbb846a94d16f49e9148fa94aa6efd","first_computed_at":"2026-05-18T02:07:26.443888Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:07:26.443888Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"idSGX93SKCWsRM3XROFTnhCmbkFXO7zcIrDNWFLVRWbrFofG+hhGJOrGXJEzSk65Wj6YeP00KxcRisZVi+XvDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:07:26.444436Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.05677","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:226e5adf21299e2154ae1d816cd0608cf08863b23ad96abb6477b59cf8ad3a3e","sha256:a07b4ac9f4fe3de3336f7fa30a9c1fa555435aa376d2bb794c4470b76a3a6dbe"],"state_sha256":"f479cd40195902280fa4983ae2452606cc9a24e42e950a9197df1de2c19ab93c"}