{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:F2ZL7IEAPBIVQ3SHYLFT2AHMLF","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":"219a9488846d249bbd3e75b7d9809efcb94bde34592dabdc3982432592ebf6fd","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2010-12-16T13:40:14Z","title_canon_sha256":"c3d8fb70ace9d712de26a46890751864b2edc81c01049d0bf5f286e57a80645e"},"schema_version":"1.0","source":{"id":"1012.3597","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.3597","created_at":"2026-05-18T04:33:06Z"},{"alias_kind":"arxiv_version","alias_value":"1012.3597v1","created_at":"2026-05-18T04:33:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.3597","created_at":"2026-05-18T04:33:06Z"},{"alias_kind":"pith_short_12","alias_value":"F2ZL7IEAPBIV","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"F2ZL7IEAPBIVQ3SH","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"F2ZL7IEA","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:f2347150ec0d167a7b9f7c547e0940ad4dbccd57463e62f12ab44138260c35d3","target":"graph","created_at":"2026-05-18T04:33:06Z","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":"Two possible diagnostics of stretching and folding (S&F) in fluid flows are discussed, based on the dynamics of the gradient of potential vorticity ($q = \\bom\\cdot\\nabla\\theta$) associated with solutions of the three-dimensional Euler and Navier-Stokes equations. The vector $\\bdB = \\nabla q \\times \\nabla\\theta$ satisfies the same type of stretching and folding equation as that for the vorticity field $\\bom $ in the incompressible Euler equations (Gibbon & Holm, 2010). The quantity $\\theta$ may be chosen as the potential temperature for the stratified, rotating Euler/Navier-Stokes equations, or","authors_text":"D. D. Holm, J. D. Gibbon","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2010-12-16T13:40:14Z","title":"Stretching and folding diagnostics in solutions of the three-dimensional Euler and Navier-Stokes equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.3597","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:cfcb7513778f08672315cf711fa8a3c8139060725f2b8e405b82920ae6b0b4a4","target":"record","created_at":"2026-05-18T04:33:06Z","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":"219a9488846d249bbd3e75b7d9809efcb94bde34592dabdc3982432592ebf6fd","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2010-12-16T13:40:14Z","title_canon_sha256":"c3d8fb70ace9d712de26a46890751864b2edc81c01049d0bf5f286e57a80645e"},"schema_version":"1.0","source":{"id":"1012.3597","kind":"arxiv","version":1}},"canonical_sha256":"2eb2bfa0807851586e47c2cb3d00ec596503b591e7a694e1aba9117d6d41f28b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2eb2bfa0807851586e47c2cb3d00ec596503b591e7a694e1aba9117d6d41f28b","first_computed_at":"2026-05-18T04:33:06.156756Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:33:06.156756Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"y06b+zAh5Kwoe/SJwjcP6J2F4QtotN7uBxphuTgrR6cn/iJ8JAHzEbfRSKVRYO6RsggXEdRBaLmPV8BBm94pCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:33:06.157495Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.3597","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cfcb7513778f08672315cf711fa8a3c8139060725f2b8e405b82920ae6b0b4a4","sha256:f2347150ec0d167a7b9f7c547e0940ad4dbccd57463e62f12ab44138260c35d3"],"state_sha256":"04e8229aa2f79276a0333a0d78a85b6f79abc3cfbd7044687338fbdfecafa0ec"}