{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:X5UJZEZDVZLFKWZNKHBG6WKNGA","short_pith_number":"pith:X5UJZEZD","canonical_record":{"source":{"id":"1901.04404","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-01-14T17:05:45Z","cross_cats_sorted":["math.DG","math.DS","math.MP"],"title_canon_sha256":"6deb0c5433c52d495c37c096f794d43ff5795f23961937940e04f72a979ad849","abstract_canon_sha256":"c02d2a510fad70d6307a1471413859c29e121b4040b1c53823eb7ee5ffc82451"},"schema_version":"1.0"},"canonical_sha256":"bf689c9323ae56555b2d51c26f594d3028a598b7cd46eca23ec467a3c549fe01","source":{"kind":"arxiv","id":"1901.04404","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.04404","created_at":"2026-05-17T23:56:25Z"},{"alias_kind":"arxiv_version","alias_value":"1901.04404v1","created_at":"2026-05-17T23:56:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.04404","created_at":"2026-05-17T23:56:25Z"},{"alias_kind":"pith_short_12","alias_value":"X5UJZEZDVZLF","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"X5UJZEZDVZLFKWZN","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"X5UJZEZD","created_at":"2026-05-18T12:33:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:X5UJZEZDVZLFKWZNKHBG6WKNGA","target":"record","payload":{"canonical_record":{"source":{"id":"1901.04404","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-01-14T17:05:45Z","cross_cats_sorted":["math.DG","math.DS","math.MP"],"title_canon_sha256":"6deb0c5433c52d495c37c096f794d43ff5795f23961937940e04f72a979ad849","abstract_canon_sha256":"c02d2a510fad70d6307a1471413859c29e121b4040b1c53823eb7ee5ffc82451"},"schema_version":"1.0"},"canonical_sha256":"bf689c9323ae56555b2d51c26f594d3028a598b7cd46eca23ec467a3c549fe01","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:25.647943Z","signature_b64":"/2rD9kGpJJ8U+6aslgbXUos/OEAWqpd5y+Xebcx1NZX8tALBzaIyd9VqIpNHkuzk2XSRpPMCeRU4ymytIBOVDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bf689c9323ae56555b2d51c26f594d3028a598b7cd46eca23ec467a3c549fe01","last_reissued_at":"2026-05-17T23:56:25.647439Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:25.647439Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1901.04404","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":"2026-05-17T23:56:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eyNZc1c7Z88FgPUa3yGjTbinF1O0mUp0Z3+Fmv7mmFmfoqtPCqqye4KsVHXfEyCqkhenVBg8SlWFRKkAVXN4Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T15:48:02.548821Z"},"content_sha256":"82c882bceb5a98c04f750e863d41a048bda3920c7d7cb282155a774f46c5a112","schema_version":"1.0","event_id":"sha256:82c882bceb5a98c04f750e863d41a048bda3920c7d7cb282155a774f46c5a112"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:X5UJZEZDVZLFKWZNKHBG6WKNGA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A basis of Casimirs in 3D magnetohydrodynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.DS","math.MP"],"primary_cat":"math-ph","authors_text":"Boris Khesin, Cheng Yang, Daniel Peralta-Salas","submitted_at":"2019-01-14T17:05:45Z","abstract_excerpt":"We prove that any regular Casimir in 3D magnetohydrodynamics is a function of the magnetic helicity and cross-helicity. In other words, these two helicities are the only independent regular integral invariants of the coadjoint action of the MHD group $\\text{SDiff}(M)\\ltimes\\mathfrak X^*(M)$, which is the semidirect product of the group of volume-preserving diffeomorphisms and the dual space of its Lie algebra."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.04404","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":"2026-05-17T23:56:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7UCaeLYM/DYnBHC62c1NVq6re8YjCnWEZ6E2y2d9ne9GHm1y00M7n0Osni9lXEYlI+NroRqa5I5P58UygPX6Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T15:48:02.549522Z"},"content_sha256":"73961c7f06da09d72bd0536af47a8ed2b9667b9bef05f9922bf2fe620f11a5dd","schema_version":"1.0","event_id":"sha256:73961c7f06da09d72bd0536af47a8ed2b9667b9bef05f9922bf2fe620f11a5dd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/X5UJZEZDVZLFKWZNKHBG6WKNGA/bundle.json","state_url":"https://pith.science/pith/X5UJZEZDVZLFKWZNKHBG6WKNGA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/X5UJZEZDVZLFKWZNKHBG6WKNGA/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":"2026-06-07T15:48:02Z","links":{"resolver":"https://pith.science/pith/X5UJZEZDVZLFKWZNKHBG6WKNGA","bundle":"https://pith.science/pith/X5UJZEZDVZLFKWZNKHBG6WKNGA/bundle.json","state":"https://pith.science/pith/X5UJZEZDVZLFKWZNKHBG6WKNGA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/X5UJZEZDVZLFKWZNKHBG6WKNGA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:X5UJZEZDVZLFKWZNKHBG6WKNGA","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":"c02d2a510fad70d6307a1471413859c29e121b4040b1c53823eb7ee5ffc82451","cross_cats_sorted":["math.DG","math.DS","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-01-14T17:05:45Z","title_canon_sha256":"6deb0c5433c52d495c37c096f794d43ff5795f23961937940e04f72a979ad849"},"schema_version":"1.0","source":{"id":"1901.04404","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.04404","created_at":"2026-05-17T23:56:25Z"},{"alias_kind":"arxiv_version","alias_value":"1901.04404v1","created_at":"2026-05-17T23:56:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.04404","created_at":"2026-05-17T23:56:25Z"},{"alias_kind":"pith_short_12","alias_value":"X5UJZEZDVZLF","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"X5UJZEZDVZLFKWZN","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"X5UJZEZD","created_at":"2026-05-18T12:33:33Z"}],"graph_snapshots":[{"event_id":"sha256:73961c7f06da09d72bd0536af47a8ed2b9667b9bef05f9922bf2fe620f11a5dd","target":"graph","created_at":"2026-05-17T23:56:25Z","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 prove that any regular Casimir in 3D magnetohydrodynamics is a function of the magnetic helicity and cross-helicity. In other words, these two helicities are the only independent regular integral invariants of the coadjoint action of the MHD group $\\text{SDiff}(M)\\ltimes\\mathfrak X^*(M)$, which is the semidirect product of the group of volume-preserving diffeomorphisms and the dual space of its Lie algebra.","authors_text":"Boris Khesin, Cheng Yang, Daniel Peralta-Salas","cross_cats":["math.DG","math.DS","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-01-14T17:05:45Z","title":"A basis of Casimirs in 3D magnetohydrodynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.04404","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":"sha256:82c882bceb5a98c04f750e863d41a048bda3920c7d7cb282155a774f46c5a112","target":"record","created_at":"2026-05-17T23:56:25Z","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":"c02d2a510fad70d6307a1471413859c29e121b4040b1c53823eb7ee5ffc82451","cross_cats_sorted":["math.DG","math.DS","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-01-14T17:05:45Z","title_canon_sha256":"6deb0c5433c52d495c37c096f794d43ff5795f23961937940e04f72a979ad849"},"schema_version":"1.0","source":{"id":"1901.04404","kind":"arxiv","version":1}},"canonical_sha256":"bf689c9323ae56555b2d51c26f594d3028a598b7cd46eca23ec467a3c549fe01","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bf689c9323ae56555b2d51c26f594d3028a598b7cd46eca23ec467a3c549fe01","first_computed_at":"2026-05-17T23:56:25.647439Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:25.647439Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/2rD9kGpJJ8U+6aslgbXUos/OEAWqpd5y+Xebcx1NZX8tALBzaIyd9VqIpNHkuzk2XSRpPMCeRU4ymytIBOVDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:25.647943Z","signed_message":"canonical_sha256_bytes"},"source_id":"1901.04404","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:82c882bceb5a98c04f750e863d41a048bda3920c7d7cb282155a774f46c5a112","sha256:73961c7f06da09d72bd0536af47a8ed2b9667b9bef05f9922bf2fe620f11a5dd"],"state_sha256":"56f6bdfbf498e54926944223c3668d007534e4a4ee2fbd0cfd6a67aad369c61a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WhSIqI02dlESjNIxidK5yX/F9LW8EvwuzCC0qRsqgqM+j9Okfw+8/Baeqpsq60p59qUZtCphnWvgTc8CPgvVAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T15:48:02.553176Z","bundle_sha256":"b452637bc6339fe6c1913650446bcb1909a62cb3f54136027af3ceae574270b0"}}