{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:6GDNEXUB6THXELH7ANZR2OM2YE","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":"0e5f589052f40e09d457cff4d5c50ac1ad4b459de1ecd3eb68df251edb4a2560","cross_cats_sorted":[],"license":"","primary_cat":"math.AP","submitted_at":"2006-08-22T12:09:40Z","title_canon_sha256":"0703ebabcbe8820acc555b7708e5dd7cf392f94d5d44b703042d4de36a144ee6"},"schema_version":"1.0","source":{"id":"math/0608541","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0608541","created_at":"2026-05-18T04:08:53Z"},{"alias_kind":"arxiv_version","alias_value":"math/0608541v1","created_at":"2026-05-18T04:08:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0608541","created_at":"2026-05-18T04:08:53Z"},{"alias_kind":"pith_short_12","alias_value":"6GDNEXUB6THX","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"6GDNEXUB6THXELH7","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"6GDNEXUB","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:19473c6a6ff6badf28279cf1ab743e2dc063513a1702e9e64be9656fdad8c7bc","target":"graph","created_at":"2026-05-18T04:08:53Z","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":"In [Math. Meth. Appl. Sci. 19 (1996) 53-62], C. Marchioro examined the problem of vorticity confinement in the exterior of a smooth bounded domain. The main result in Marchioro's paper is that solutions of the incompressible 2D Euler equations with compactly supported nonnegative initial vorticity in the exterior of a connected bounded region have vorticity support with diameter growing at most like $\\mathcal{O}(t^{(1/2)+\\vare})$, for any $\\vare>0$. In addition, if the domain is the exterior of a disk, then the vorticity support is contained in a disk of radius $\\mathcal{O}(t^{1/3})$. The purp","authors_text":"D. Iftimie, H. J. Nussenzveig Lopes, M. C. Lopes Filho","cross_cats":[],"headline":"","license":"","primary_cat":"math.AP","submitted_at":"2006-08-22T12:09:40Z","title":"Confinement of vorticity in two dimensional ideal incompressible exterior flow"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0608541","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":"sha256:37e5c7c1ea9f3d50e69f0b07df14048cbf1be7341d34764953a0d569c1757112","target":"record","created_at":"2026-05-18T04:08:53Z","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":"0e5f589052f40e09d457cff4d5c50ac1ad4b459de1ecd3eb68df251edb4a2560","cross_cats_sorted":[],"license":"","primary_cat":"math.AP","submitted_at":"2006-08-22T12:09:40Z","title_canon_sha256":"0703ebabcbe8820acc555b7708e5dd7cf392f94d5d44b703042d4de36a144ee6"},"schema_version":"1.0","source":{"id":"math/0608541","kind":"arxiv","version":1}},"canonical_sha256":"f186d25e81f4cf722cff03731d399ac101f72076b242951a3bc08b7b9a64c075","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f186d25e81f4cf722cff03731d399ac101f72076b242951a3bc08b7b9a64c075","first_computed_at":"2026-05-18T04:08:53.299910Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:08:53.299910Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lriL9hi3Z4XWaL69zCxnlkmyWGpbycLka4JmVuVVqRNtlQbeDfsxk0kC7wlVWtMJo1IcohkVIWNFsDdHHxXtCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:08:53.300645Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0608541","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:37e5c7c1ea9f3d50e69f0b07df14048cbf1be7341d34764953a0d569c1757112","sha256:19473c6a6ff6badf28279cf1ab743e2dc063513a1702e9e64be9656fdad8c7bc"],"state_sha256":"5a89c488aeadd5c3b8b53e68e50b9cf86d91c0eb552a9487a5411580944a7ec7"}