{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:NY26TMLHNMB44REUB7VFKTLBF6","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":"c2fa1a40189b595d530d2f64417c2e76c01ee13333834623f7deb425eda13f74","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-30T19:47:12Z","title_canon_sha256":"ce5adcf1c78a6932cd61443ecf2bab284419974205869a641b4dcab478a4cf24"},"schema_version":"1.0","source":{"id":"1610.09701","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.09701","created_at":"2026-05-18T00:06:43Z"},{"alias_kind":"arxiv_version","alias_value":"1610.09701v3","created_at":"2026-05-18T00:06:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.09701","created_at":"2026-05-18T00:06:43Z"},{"alias_kind":"pith_short_12","alias_value":"NY26TMLHNMB4","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"NY26TMLHNMB44REU","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"NY26TMLH","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:129319ac46fa6c2ba82d29e99ef4f8e84dc613989ed90de99dfed70b87faebb5","target":"graph","created_at":"2026-05-18T00:06:43Z","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 show that given an initial vorticity which is bounded and $m$-fold rotationally symmetric for $m \\ge 3$, there is a unique global solution to the 2D Euler equation on the whole plane. That is, in the well-known $L^1 \\cap L^\\infty$ theory of Yudovich, the $L^1$ assumption can be dropped upon having an appropriate symmetry condition. This contains a class of radially homogeneous solutions to the 2D Euler equation, which gives rise to a new 1D fluid model. We discuss several interesting properties of this 1D system. Using this framework, we construct time quasi-periodic solutions to the 2D Eul","authors_text":"In-Jee Jeong, Tarek M. Elgindi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-30T19:47:12Z","title":"Symmetries and Critical Phenomena in Fluids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.09701","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":"sha256:151c26df90c3a9378be1d3f0df23c2f25a0f95805863cc06ace16e3e82adc097","target":"record","created_at":"2026-05-18T00:06:43Z","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":"c2fa1a40189b595d530d2f64417c2e76c01ee13333834623f7deb425eda13f74","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-30T19:47:12Z","title_canon_sha256":"ce5adcf1c78a6932cd61443ecf2bab284419974205869a641b4dcab478a4cf24"},"schema_version":"1.0","source":{"id":"1610.09701","kind":"arxiv","version":3}},"canonical_sha256":"6e35e9b1676b03ce44940fea554d612fad464864c30476ab29bdffc314d616db","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6e35e9b1676b03ce44940fea554d612fad464864c30476ab29bdffc314d616db","first_computed_at":"2026-05-18T00:06:43.782998Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:43.782998Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jPx4civ3JC33dof85ePNZpjRkr9gG9tq2Ajvd5/BwUKp+WI5OE6hxqoQsSzWbSoYbnAduDSLPkFuQnwBFtafAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:43.783510Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.09701","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:151c26df90c3a9378be1d3f0df23c2f25a0f95805863cc06ace16e3e82adc097","sha256:129319ac46fa6c2ba82d29e99ef4f8e84dc613989ed90de99dfed70b87faebb5"],"state_sha256":"ff1aa9312c38e0f880117f1dc445b70212686b8e7bdaa9e319709f7ac9f4f651"}