{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:LQCKSJHHBORHRDVPAXVL7C3IZJ","short_pith_number":"pith:LQCKSJHH","canonical_record":{"source":{"id":"1707.03703","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-07-12T13:23:44Z","cross_cats_sorted":["math-ph","math.MP","nlin.SI"],"title_canon_sha256":"893b6831f4a7c108b57bb4b964f8221175b5ff1345c9f4a1a799d6247e4d1c76","abstract_canon_sha256":"369d3a145a9643fd7d6e6f77641c4daf54d9fa7e6cf1add29e5990b62936423f"},"schema_version":"1.0"},"canonical_sha256":"5c04a924e70ba2788eaf05eabf8b68ca4fa3605e36144cff70cb88233378e1cb","source":{"kind":"arxiv","id":"1707.03703","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.03703","created_at":"2026-05-18T00:02:45Z"},{"alias_kind":"arxiv_version","alias_value":"1707.03703v1","created_at":"2026-05-18T00:02:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.03703","created_at":"2026-05-18T00:02:45Z"},{"alias_kind":"pith_short_12","alias_value":"LQCKSJHHBORH","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"LQCKSJHHBORHRDVP","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"LQCKSJHH","created_at":"2026-05-18T12:31:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:LQCKSJHHBORHRDVPAXVL7C3IZJ","target":"record","payload":{"canonical_record":{"source":{"id":"1707.03703","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-07-12T13:23:44Z","cross_cats_sorted":["math-ph","math.MP","nlin.SI"],"title_canon_sha256":"893b6831f4a7c108b57bb4b964f8221175b5ff1345c9f4a1a799d6247e4d1c76","abstract_canon_sha256":"369d3a145a9643fd7d6e6f77641c4daf54d9fa7e6cf1add29e5990b62936423f"},"schema_version":"1.0"},"canonical_sha256":"5c04a924e70ba2788eaf05eabf8b68ca4fa3605e36144cff70cb88233378e1cb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:45.664826Z","signature_b64":"Svb72fj/opZRLVmSfeIwxErcUSnqGYJTCoyv16mROQWdNTnXu7PUgI5eZjJfJ9+TqIjRFAF2BB17WeZCMowIAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5c04a924e70ba2788eaf05eabf8b68ca4fa3605e36144cff70cb88233378e1cb","last_reissued_at":"2026-05-18T00:02:45.664329Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:45.664329Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1707.03703","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:02:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hkisXLI5TUswFVjzRuET1siHF26jyuaJsO4LDyR12mobeANerTPaZ4QFqFDro21gDOdWT0KQayf/SdZjOWcqDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T15:12:08.267153Z"},"content_sha256":"0df74532110b8d077e83d420bbb59191bde1afb1245e2395428b6d41c9533fea","schema_version":"1.0","event_id":"sha256:0df74532110b8d077e83d420bbb59191bde1afb1245e2395428b6d41c9533fea"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:LQCKSJHHBORHRDVPAXVL7C3IZJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Normal forms of dispersive scalar Poisson brackets with two independent variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","nlin.SI"],"primary_cat":"math.DG","authors_text":"Guido Carlet, Matteo Casati, Sergey Shadrin","submitted_at":"2017-07-12T13:23:44Z","abstract_excerpt":"We classify the dispersive Poisson brackets with one dependent variable and two independent variables, with leading order of hydrodynamic type, up to Miura transformations. We show that, in contrast to the case of a single independent variable for which a well known triviality result exists, the Miura equivalence classes are parametrised by an infinite number of constants, which we call numerical invariants of the brackets. We obtain explicit formulas for the first few numerical invariants."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.03703","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":""},"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":"2026-05-18T00:02:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ljdTQu5L1CemO88K3Rq6B1RJ07Gq1wpY5ThkqOhfAf+CBVFpC04HIU9t9rGxE6iK1fzX2zZ7wmR+O6WqZxTfCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T15:12:08.267792Z"},"content_sha256":"d010b539fa99308d7bcc91a62bc5e07fcba4c1199f6a1bd0711b92cfee04f198","schema_version":"1.0","event_id":"sha256:d010b539fa99308d7bcc91a62bc5e07fcba4c1199f6a1bd0711b92cfee04f198"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LQCKSJHHBORHRDVPAXVL7C3IZJ/bundle.json","state_url":"https://pith.science/pith/LQCKSJHHBORHRDVPAXVL7C3IZJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LQCKSJHHBORHRDVPAXVL7C3IZJ/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":"2026-05-29T15:12:08Z","links":{"resolver":"https://pith.science/pith/LQCKSJHHBORHRDVPAXVL7C3IZJ","bundle":"https://pith.science/pith/LQCKSJHHBORHRDVPAXVL7C3IZJ/bundle.json","state":"https://pith.science/pith/LQCKSJHHBORHRDVPAXVL7C3IZJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LQCKSJHHBORHRDVPAXVL7C3IZJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:LQCKSJHHBORHRDVPAXVL7C3IZJ","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":"369d3a145a9643fd7d6e6f77641c4daf54d9fa7e6cf1add29e5990b62936423f","cross_cats_sorted":["math-ph","math.MP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-07-12T13:23:44Z","title_canon_sha256":"893b6831f4a7c108b57bb4b964f8221175b5ff1345c9f4a1a799d6247e4d1c76"},"schema_version":"1.0","source":{"id":"1707.03703","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.03703","created_at":"2026-05-18T00:02:45Z"},{"alias_kind":"arxiv_version","alias_value":"1707.03703v1","created_at":"2026-05-18T00:02:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.03703","created_at":"2026-05-18T00:02:45Z"},{"alias_kind":"pith_short_12","alias_value":"LQCKSJHHBORH","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"LQCKSJHHBORHRDVP","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"LQCKSJHH","created_at":"2026-05-18T12:31:28Z"}],"graph_snapshots":[{"event_id":"sha256:d010b539fa99308d7bcc91a62bc5e07fcba4c1199f6a1bd0711b92cfee04f198","target":"graph","created_at":"2026-05-18T00:02:45Z","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":"We classify the dispersive Poisson brackets with one dependent variable and two independent variables, with leading order of hydrodynamic type, up to Miura transformations. We show that, in contrast to the case of a single independent variable for which a well known triviality result exists, the Miura equivalence classes are parametrised by an infinite number of constants, which we call numerical invariants of the brackets. We obtain explicit formulas for the first few numerical invariants.","authors_text":"Guido Carlet, Matteo Casati, Sergey Shadrin","cross_cats":["math-ph","math.MP","nlin.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-07-12T13:23:44Z","title":"Normal forms of dispersive scalar Poisson brackets with two independent variables"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.03703","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":"sha256:0df74532110b8d077e83d420bbb59191bde1afb1245e2395428b6d41c9533fea","target":"record","created_at":"2026-05-18T00:02:45Z","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":"369d3a145a9643fd7d6e6f77641c4daf54d9fa7e6cf1add29e5990b62936423f","cross_cats_sorted":["math-ph","math.MP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-07-12T13:23:44Z","title_canon_sha256":"893b6831f4a7c108b57bb4b964f8221175b5ff1345c9f4a1a799d6247e4d1c76"},"schema_version":"1.0","source":{"id":"1707.03703","kind":"arxiv","version":1}},"canonical_sha256":"5c04a924e70ba2788eaf05eabf8b68ca4fa3605e36144cff70cb88233378e1cb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5c04a924e70ba2788eaf05eabf8b68ca4fa3605e36144cff70cb88233378e1cb","first_computed_at":"2026-05-18T00:02:45.664329Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:45.664329Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Svb72fj/opZRLVmSfeIwxErcUSnqGYJTCoyv16mROQWdNTnXu7PUgI5eZjJfJ9+TqIjRFAF2BB17WeZCMowIAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:45.664826Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.03703","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0df74532110b8d077e83d420bbb59191bde1afb1245e2395428b6d41c9533fea","sha256:d010b539fa99308d7bcc91a62bc5e07fcba4c1199f6a1bd0711b92cfee04f198"],"state_sha256":"669c98601329f60c1d266c00d6302dd593cc157d6b9758f7c3af22d018f420ef"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"esgtqg9jJKJPYRRcVe+i3v+yFsgB/4+Q1B9z95sQM+plIT67QLiKmgy8LTmXAnlvyDDVSOcF0ugJdMpT5V7BCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T15:12:08.271361Z","bundle_sha256":"f10ab6e6180f2a695aadc7dbd3cbdc2cf933241e44c97bb39d871b644c90300b"}}