{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:N4BJL7BNWHFWWGIO46BBYI5JFL","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":"6484ba2c01b85bac530de2286e16feae14c783aaf7e5b5637c6d1c9cc1387df2","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2019-02-07T01:28:48Z","title_canon_sha256":"da317d2843f7f7854a15e47e87cdb33bc04fe10b7527cd12c5c54659f901dfb8"},"schema_version":"1.0","source":{"id":"1902.02442","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.02442","created_at":"2026-05-17T23:47:53Z"},{"alias_kind":"arxiv_version","alias_value":"1902.02442v3","created_at":"2026-05-17T23:47:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.02442","created_at":"2026-05-17T23:47:53Z"},{"alias_kind":"pith_short_12","alias_value":"N4BJL7BNWHFW","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"N4BJL7BNWHFWWGIO","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"N4BJL7BN","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:b7895d0a0dbf9c19fb113738312872539192fcbe2cc3075efbd0e29496670684","target":"graph","created_at":"2026-05-17T23:47:53Z","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":"For the free probability analogue of Euclidean space endowed with the Gaussian measure we apply the approach of Arnold to derive Euler equations for a Lie algebra of non-commutative vector fields which preserve a certain trace. We extend the equations to vector fields satisfying non-commutative smoothness requirements. We introduce a cyclic vorticity and show that it satisfies a vorticity equation and that it produces a family of conserved quantities.","authors_text":"Dan-Virgil Voiculescu","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2019-02-07T01:28:48Z","title":"A Hydrodynamic Exercise in Free Probability: Setting up Free Euler Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.02442","kind":"arxiv","version":3},"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":"sha256:2a21b17b0f7a0d72f97b3fa644bb540c42124cd6205fffda78e51a01e8278e0a","target":"record","created_at":"2026-05-17T23:47:53Z","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":"6484ba2c01b85bac530de2286e16feae14c783aaf7e5b5637c6d1c9cc1387df2","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2019-02-07T01:28:48Z","title_canon_sha256":"da317d2843f7f7854a15e47e87cdb33bc04fe10b7527cd12c5c54659f901dfb8"},"schema_version":"1.0","source":{"id":"1902.02442","kind":"arxiv","version":3}},"canonical_sha256":"6f0295fc2db1cb6b190ee7821c23a92ad36222aad31ac2e0566beac322b64f15","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6f0295fc2db1cb6b190ee7821c23a92ad36222aad31ac2e0566beac322b64f15","first_computed_at":"2026-05-17T23:47:53.748083Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:53.748083Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EomE44JsnwU7vcjopIU1tJHanG5R8MPgdl0hBGhwljpgJK4wch6F5+eqWTEsO9czqkxYU5On0WJKYlIceQSSCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:53.748597Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.02442","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2a21b17b0f7a0d72f97b3fa644bb540c42124cd6205fffda78e51a01e8278e0a","sha256:b7895d0a0dbf9c19fb113738312872539192fcbe2cc3075efbd0e29496670684"],"state_sha256":"1c21d58d3c61ff2cb48717f21c8debe0c835ec63fd1bc2e0f31b78dfb8d0f3ad"}