{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:O3J4IGGOOSUTM2QT533OEKQXTY","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":"b59fad4175de385413e0cf68dcd95efef2b0fb199e2a8a0d235e4fc968f4d797","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-12-13T17:33:33Z","title_canon_sha256":"eca0fa559a9c4176481fb60e26dff631ea10c9610473d17ff640edf31ec6913b"},"schema_version":"1.0","source":{"id":"1612.04297","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.04297","created_at":"2026-05-18T00:55:04Z"},{"alias_kind":"arxiv_version","alias_value":"1612.04297v1","created_at":"2026-05-18T00:55:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.04297","created_at":"2026-05-18T00:55:04Z"},{"alias_kind":"pith_short_12","alias_value":"O3J4IGGOOSUT","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"O3J4IGGOOSUTM2QT","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"O3J4IGGO","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:8e37b2bdb62b5d4759bacb5e7ea6359a1b85ff44c5a3bef66b8493dcbeda015d","target":"graph","created_at":"2026-05-18T00:55:04Z","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 study a general class of Euler equations driven by a forcing with a \\emph{commutator structure} of the form $[\\mathcal{L},\\mathbf{u}](\\rho)=\\mathcal{L}(\\rho \\mathbf{u})- \\mathcal{L}(\\rho)\\mathbf{u}$, where $\\mathbf{u}$ is the velocity field and $\\mathcal{L}$ is the \"action\" which belongs to a rather general class of translation invariant operators. Such systems arise, for example, as the hydrodynamic description of velocity alignment, where action involves convolutions with bounded, positive influence kernels, $\\mathcal{L}_\\phi(f)=\\phi*f$. Our interest lies with a much larger class of $\\mat","authors_text":"Eitan Tadmor, Roman Shvydkoy","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-12-13T17:33:33Z","title":"Eulerian dynamics with a commutator forcing"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.04297","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:c821de6db2f66918d57bb5318965aa95f77bbd06a00e346d7d3e6343482b20f3","target":"record","created_at":"2026-05-18T00:55:04Z","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":"b59fad4175de385413e0cf68dcd95efef2b0fb199e2a8a0d235e4fc968f4d797","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-12-13T17:33:33Z","title_canon_sha256":"eca0fa559a9c4176481fb60e26dff631ea10c9610473d17ff640edf31ec6913b"},"schema_version":"1.0","source":{"id":"1612.04297","kind":"arxiv","version":1}},"canonical_sha256":"76d3c418ce74a9366a13eef6e22a179e10ab7d3f2c23229b428162470249a4f4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"76d3c418ce74a9366a13eef6e22a179e10ab7d3f2c23229b428162470249a4f4","first_computed_at":"2026-05-18T00:55:04.892058Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:55:04.892058Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zLsZC6rVHv+r6E5A/DX7XQF/0yJNL20Kj0Xwaw5IvcToPN0NhQ+NThcTHHAf0/LTA2ntPty/JsYGOlTo9lx3DA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:55:04.892793Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.04297","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c821de6db2f66918d57bb5318965aa95f77bbd06a00e346d7d3e6343482b20f3","sha256:8e37b2bdb62b5d4759bacb5e7ea6359a1b85ff44c5a3bef66b8493dcbeda015d"],"state_sha256":"826d0e0d4f2bf1f13b39402cd202d7bab6424a882ee07dc6783a760702d6f97b"}