{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:KZVHOA5VVZLBQZII5SFYQ56456","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":"c719bbdb8d8766d741f6c8ef741d4454b8085b927ff347de8cc05686b76a83ac","cross_cats_sorted":["math.DS","math.PR","nlin.CD","physics.flu-dyn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-09-18T00:20:15Z","title_canon_sha256":"799dda82dacb6e895e2e5b78eca134fe44f43472f3dfc9632dd1a37fc196d699"},"schema_version":"1.0","source":{"id":"1809.06484","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.06484","created_at":"2026-05-18T00:05:27Z"},{"alias_kind":"arxiv_version","alias_value":"1809.06484v1","created_at":"2026-05-18T00:05:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.06484","created_at":"2026-05-18T00:05:27Z"},{"alias_kind":"pith_short_12","alias_value":"KZVHOA5VVZLB","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"KZVHOA5VVZLBQZII","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"KZVHOA5V","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:a357e84f3ac8ecaac4b4be14e83d50452dd1a3ad90ecb27f7abd13c76ed97e43","target":"graph","created_at":"2026-05-18T00:05:27Z","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 the Lagrangian flow associated to velocity fields arising from various models of fluid mechanics subject to white-in-time, $H^s$-in-space stochastic forcing in a periodic box. We prove that in many circumstances, these flows are chaotic, that is, the top Lyapunov exponent is strictly positive. Our main results are for the Navier-Stokes equations on $\\mathbb T^2$ and the hyper-viscous regularized Navier-Stokes equations on $\\mathbb T^3$ (at arbitrary Reynolds number and hyper-viscosity parameters), subject to forcing which is non-degenerate at high frequencies. As an application, we st","authors_text":"Alex Blumenthal, Jacob Bedrossian, Samuel Punshon-Smith","cross_cats":["math.DS","math.PR","nlin.CD","physics.flu-dyn"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-09-18T00:20:15Z","title":"Lagrangian chaos and scalar advection in stochastic fluid mechanics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.06484","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":"sha256:264957b79ffaab4cc7350732433aff51c52c946a31973a8b51861957d7d422be","target":"record","created_at":"2026-05-18T00:05:27Z","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":"c719bbdb8d8766d741f6c8ef741d4454b8085b927ff347de8cc05686b76a83ac","cross_cats_sorted":["math.DS","math.PR","nlin.CD","physics.flu-dyn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-09-18T00:20:15Z","title_canon_sha256":"799dda82dacb6e895e2e5b78eca134fe44f43472f3dfc9632dd1a37fc196d699"},"schema_version":"1.0","source":{"id":"1809.06484","kind":"arxiv","version":1}},"canonical_sha256":"566a7703b5ae56186508ec8b8877dcefa1f23de3a8fb9030434b888aa39ff1c6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"566a7703b5ae56186508ec8b8877dcefa1f23de3a8fb9030434b888aa39ff1c6","first_computed_at":"2026-05-18T00:05:27.034498Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:27.034498Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Jj2xEogvS01en1ClLLPYW1z173WDHLJkfT0FUJCUYCNYxUED1eGku7swED155by5U1O3U3mm6aEJz3NJJhbPCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:27.035173Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.06484","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:264957b79ffaab4cc7350732433aff51c52c946a31973a8b51861957d7d422be","sha256:a357e84f3ac8ecaac4b4be14e83d50452dd1a3ad90ecb27f7abd13c76ed97e43"],"state_sha256":"d6bccf290f91dbc15b9d801762181a598d5877ef37a445bcde2d4a11e4b3ca54"}