{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:VJZW4WS6ADWB5U3LF4D2GKY7AH","short_pith_number":"pith:VJZW4WS6","canonical_record":{"source":{"id":"1710.08175","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-10-23T10:03:51Z","cross_cats_sorted":["math-ph","math.MP","nlin.SI"],"title_canon_sha256":"2d62377c91b73204b55a6abd275353f00c2d2f86ab01b2fe8776b71e54e19267","abstract_canon_sha256":"1945735f6dc0ae16f5d888f8f96c8c51a34d6b747add3c12a2b10632595ff721"},"schema_version":"1.0"},"canonical_sha256":"aa736e5a5e00ec1ed36b2f07a32b1f01cde721f9846ba0f60a84359ba1ea0ce8","source":{"kind":"arxiv","id":"1710.08175","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.08175","created_at":"2026-05-18T00:27:56Z"},{"alias_kind":"arxiv_version","alias_value":"1710.08175v2","created_at":"2026-05-18T00:27:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.08175","created_at":"2026-05-18T00:27:56Z"},{"alias_kind":"pith_short_12","alias_value":"VJZW4WS6ADWB","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"VJZW4WS6ADWB5U3L","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"VJZW4WS6","created_at":"2026-05-18T12:31:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:VJZW4WS6ADWB5U3LF4D2GKY7AH","target":"record","payload":{"canonical_record":{"source":{"id":"1710.08175","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-10-23T10:03:51Z","cross_cats_sorted":["math-ph","math.MP","nlin.SI"],"title_canon_sha256":"2d62377c91b73204b55a6abd275353f00c2d2f86ab01b2fe8776b71e54e19267","abstract_canon_sha256":"1945735f6dc0ae16f5d888f8f96c8c51a34d6b747add3c12a2b10632595ff721"},"schema_version":"1.0"},"canonical_sha256":"aa736e5a5e00ec1ed36b2f07a32b1f01cde721f9846ba0f60a84359ba1ea0ce8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:27:56.869843Z","signature_b64":"JUoaAfVSWHnc4Aidc17BQugNcDE/RH0LfkbCAKfqjs6WvHXVAeNXqGlnDKC5tL0H5SIYPWPgLAhs7o/ihGaOAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aa736e5a5e00ec1ed36b2f07a32b1f01cde721f9846ba0f60a84359ba1ea0ce8","last_reissued_at":"2026-05-18T00:27:56.869224Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:27:56.869224Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.08175","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:27:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MsT4Ld9mvgZGKgL2tpeuP21mEFi71jVc4gGwRmrRizsJpoCzWBPDVRBO23jgfdGZQaExxBg0+j+4wyBMa+jjAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T19:52:29.987362Z"},"content_sha256":"7cfb1a3c613fede2ea2b90147547ac6c2ac3eca85838d80009a5a7a45e277fd1","schema_version":"1.0","event_id":"sha256:7cfb1a3c613fede2ea2b90147547ac6c2ac3eca85838d80009a5a7a45e277fd1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:VJZW4WS6ADWB5U3LF4D2GKY7AH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Higher order dispersive deformations of multidimensional Poisson brackets of hydrodynamic type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","nlin.SI"],"primary_cat":"math.DG","authors_text":"Matteo Casati","submitted_at":"2017-10-23T10:03:51Z","abstract_excerpt":"The theory of multidimensional Poisson vertex algebras (mPVAs) provides a completely algebraic formalism to study the Hamiltonian structure of PDEs, for any number of dependent and independent variables. In this paper, we compute the cohomology of the PVAs associated with two-dimensional, two-components Poisson brackets of hydrodynamic type at the third differential degree. This allows us to obtain their corresponding Poisson-Lichnerowicz cohomology, which is the main building block of the theory of their deformations. Such a cohomology is trivial neither in the second group, corresponding to "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.08175","kind":"arxiv","version":2},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:27:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D03NFeFvSI6KU6NHdUjK93PPY6Jq98Db+hIdp01inn/ckc9Rctz2640jQYa9/kpBDEgkZ+suT1yBq7d0JxHzCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T19:52:29.987711Z"},"content_sha256":"06d366084c80092daf086b4c2e01da5856ef375334ffbc29d0d0ac74660153d6","schema_version":"1.0","event_id":"sha256:06d366084c80092daf086b4c2e01da5856ef375334ffbc29d0d0ac74660153d6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VJZW4WS6ADWB5U3LF4D2GKY7AH/bundle.json","state_url":"https://pith.science/pith/VJZW4WS6ADWB5U3LF4D2GKY7AH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VJZW4WS6ADWB5U3LF4D2GKY7AH/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-07-02T19:52:29Z","links":{"resolver":"https://pith.science/pith/VJZW4WS6ADWB5U3LF4D2GKY7AH","bundle":"https://pith.science/pith/VJZW4WS6ADWB5U3LF4D2GKY7AH/bundle.json","state":"https://pith.science/pith/VJZW4WS6ADWB5U3LF4D2GKY7AH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VJZW4WS6ADWB5U3LF4D2GKY7AH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:VJZW4WS6ADWB5U3LF4D2GKY7AH","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":"1945735f6dc0ae16f5d888f8f96c8c51a34d6b747add3c12a2b10632595ff721","cross_cats_sorted":["math-ph","math.MP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-10-23T10:03:51Z","title_canon_sha256":"2d62377c91b73204b55a6abd275353f00c2d2f86ab01b2fe8776b71e54e19267"},"schema_version":"1.0","source":{"id":"1710.08175","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.08175","created_at":"2026-05-18T00:27:56Z"},{"alias_kind":"arxiv_version","alias_value":"1710.08175v2","created_at":"2026-05-18T00:27:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.08175","created_at":"2026-05-18T00:27:56Z"},{"alias_kind":"pith_short_12","alias_value":"VJZW4WS6ADWB","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"VJZW4WS6ADWB5U3L","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"VJZW4WS6","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:06d366084c80092daf086b4c2e01da5856ef375334ffbc29d0d0ac74660153d6","target":"graph","created_at":"2026-05-18T00:27:56Z","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 theory of multidimensional Poisson vertex algebras (mPVAs) provides a completely algebraic formalism to study the Hamiltonian structure of PDEs, for any number of dependent and independent variables. In this paper, we compute the cohomology of the PVAs associated with two-dimensional, two-components Poisson brackets of hydrodynamic type at the third differential degree. This allows us to obtain their corresponding Poisson-Lichnerowicz cohomology, which is the main building block of the theory of their deformations. Such a cohomology is trivial neither in the second group, corresponding to ","authors_text":"Matteo Casati","cross_cats":["math-ph","math.MP","nlin.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-10-23T10:03:51Z","title":"Higher order dispersive deformations of multidimensional Poisson brackets of hydrodynamic type"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.08175","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":"sha256:7cfb1a3c613fede2ea2b90147547ac6c2ac3eca85838d80009a5a7a45e277fd1","target":"record","created_at":"2026-05-18T00:27:56Z","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":"1945735f6dc0ae16f5d888f8f96c8c51a34d6b747add3c12a2b10632595ff721","cross_cats_sorted":["math-ph","math.MP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-10-23T10:03:51Z","title_canon_sha256":"2d62377c91b73204b55a6abd275353f00c2d2f86ab01b2fe8776b71e54e19267"},"schema_version":"1.0","source":{"id":"1710.08175","kind":"arxiv","version":2}},"canonical_sha256":"aa736e5a5e00ec1ed36b2f07a32b1f01cde721f9846ba0f60a84359ba1ea0ce8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aa736e5a5e00ec1ed36b2f07a32b1f01cde721f9846ba0f60a84359ba1ea0ce8","first_computed_at":"2026-05-18T00:27:56.869224Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:27:56.869224Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JUoaAfVSWHnc4Aidc17BQugNcDE/RH0LfkbCAKfqjs6WvHXVAeNXqGlnDKC5tL0H5SIYPWPgLAhs7o/ihGaOAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:27:56.869843Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.08175","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7cfb1a3c613fede2ea2b90147547ac6c2ac3eca85838d80009a5a7a45e277fd1","sha256:06d366084c80092daf086b4c2e01da5856ef375334ffbc29d0d0ac74660153d6"],"state_sha256":"267011368c7a644c2fc85f9a67cc0ff61ef66b40c6f5e2712f831d81fc52e166"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l3ZiI6QpRlwZuUAnC/R3jFb/UyNy58yqNuQrLswOWTA8D3h1tNglZ/umeY30rVq7A+Jx70OIjxlLNe/YNntPCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T19:52:29.989972Z","bundle_sha256":"4f92fe67736ceadedb026ca5d2834612ec8f30d9107c7c62fc62af3c7cda8ca3"}}