{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:R5JX5QN6RSU74LFBMPLCI7WNPL","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":"c2af6000f24ca4f7127c1d21b05957349ed71b75595b577fe7f90eb51f7846c6","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2012-11-25T10:59:00Z","title_canon_sha256":"cda4d2497633475d3a32881ff8dec2fc50c7fa3afe11eae607126c8bfc0e9fbd"},"schema_version":"1.0","source":{"id":"1211.5756","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.5756","created_at":"2026-05-18T01:52:55Z"},{"alias_kind":"arxiv_version","alias_value":"1211.5756v4","created_at":"2026-05-18T01:52:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.5756","created_at":"2026-05-18T01:52:55Z"},{"alias_kind":"pith_short_12","alias_value":"R5JX5QN6RSU7","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"R5JX5QN6RSU74LFB","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"R5JX5QN6","created_at":"2026-05-18T12:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:4779f10d6256e68f5e5760a2a6a37d2327f809ae023a16e2fa7d81ae9f38328e","target":"graph","created_at":"2026-05-18T01:52:55Z","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":"In this paper we consider the averaging of local field-theoretic Poisson brackets in the multi-dimensional case. As a result, we construct a local Poisson bracket for the regular Whitham system in the multidimensional situation. The procedure is based on the procedure of averaging of local conservation laws and follows the Dubrovin - Novikov scheme of the bracket averaging suggested in one-dimensional case. However, the features of the phase space of modulated parameters in higher dimensions lead to a different natural class of the averaged brackets in comparison with the one-dimensional situa","authors_text":"Andrei Maltsev","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2012-11-25T10:59:00Z","title":"The multi-dimensional Hamiltonian Structures in the Whitham method"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.5756","kind":"arxiv","version":4},"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":"sha256:0c83715fe8ddd3f1cf36de0a127a6fa03a0e2d55debea322f8d5bcc0f0904c7e","target":"record","created_at":"2026-05-18T01:52:55Z","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":"c2af6000f24ca4f7127c1d21b05957349ed71b75595b577fe7f90eb51f7846c6","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2012-11-25T10:59:00Z","title_canon_sha256":"cda4d2497633475d3a32881ff8dec2fc50c7fa3afe11eae607126c8bfc0e9fbd"},"schema_version":"1.0","source":{"id":"1211.5756","kind":"arxiv","version":4}},"canonical_sha256":"8f537ec1be8ca9fe2ca163d6247ecd7ae2bfbbcc588e01c4c179991125d10afa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8f537ec1be8ca9fe2ca163d6247ecd7ae2bfbbcc588e01c4c179991125d10afa","first_computed_at":"2026-05-18T01:52:55.406557Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:52:55.406557Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YVM+QEwjPhRsGzi2nvJEJKXpwXG3T872SbHHN0SRv0FBDCnVnsJCaAMpWiaDWndc2K0Cuwj2/qzNZoI/msfeCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:52:55.407123Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.5756","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0c83715fe8ddd3f1cf36de0a127a6fa03a0e2d55debea322f8d5bcc0f0904c7e","sha256:4779f10d6256e68f5e5760a2a6a37d2327f809ae023a16e2fa7d81ae9f38328e"],"state_sha256":"8a116e7ba5d6766cd3ff47bbe77148ec50ce394e45fbfc8f3593d16ad60b1c09"}