{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:SSGB3JQHBZ3E6NOXL762HHASF6","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":"5492dc0e40151586237e8212d5f59e905637aa8dc2bffe04cfd984c239ba63f7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-06-05T13:40:36Z","title_canon_sha256":"0f7cf85f2444400e39ddf53dfbdb7a2eaab70148f2b02309b11b879532bb3427"},"schema_version":"1.0","source":{"id":"2506.05034","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.05034","created_at":"2026-07-05T11:16:41Z"},{"alias_kind":"arxiv_version","alias_value":"2506.05034v1","created_at":"2026-07-05T11:16:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.05034","created_at":"2026-07-05T11:16:41Z"},{"alias_kind":"pith_short_12","alias_value":"SSGB3JQHBZ3E","created_at":"2026-07-05T11:16:41Z"},{"alias_kind":"pith_short_16","alias_value":"SSGB3JQHBZ3E6NOX","created_at":"2026-07-05T11:16:41Z"},{"alias_kind":"pith_short_8","alias_value":"SSGB3JQH","created_at":"2026-07-05T11:16:41Z"}],"graph_snapshots":[{"event_id":"sha256:3311c1354cc004b87cc3cca0cc9ab3c8532085ba516b28baa39b08997de80ec0","target":"graph","created_at":"2026-07-05T11:16:41Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2506.05034/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that any uniformly rotating solution of the 2D incompressible Euler equation with compactly supported vorticity $\\omega$ must be radially symmetric whenever its angular velocity satisfies $\\Omega \\in (-\\infty,\\inf \\omega / 2] \\cup \\, [ \\sup \\omega / 2, +\\infty )$, in both the patch and smooth settings. This result extends the rigidity theorems established in \\cite{Gom2021MR4312192} (\\textit{Duke Math. J.},170(13):2957-3038, 2021), which were confined to the case of non-positive angular velocities and non-negative vorticity. Moreover, our results do not impose any regularity conditions","authors_text":"Boquan Fan, Weicheng Zhan, Yuchen Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-06-05T13:40:36Z","title":"Remarks on radial symmetry of stationary and uniformly-rotating solutions for the 2D Euler equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.05034","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":"sha256:2e9a5494b6fa835738d5c7ae3e431c6f6b56bd3bb2b520668b434830aaae4a27","target":"record","created_at":"2026-07-05T11:16:41Z","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":"5492dc0e40151586237e8212d5f59e905637aa8dc2bffe04cfd984c239ba63f7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-06-05T13:40:36Z","title_canon_sha256":"0f7cf85f2444400e39ddf53dfbdb7a2eaab70148f2b02309b11b879532bb3427"},"schema_version":"1.0","source":{"id":"2506.05034","kind":"arxiv","version":1}},"canonical_sha256":"948c1da6070e764f35d75ffda39c122f92ab35ce224ded35904d78cdd761c01a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"948c1da6070e764f35d75ffda39c122f92ab35ce224ded35904d78cdd761c01a","first_computed_at":"2026-07-05T11:16:41.354804Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:16:41.354804Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IK38mIxjPLtebxtCvElhcN5hlCwPpL5mE/bpWXhegU+wtkYpvQ22DYsoZiI5IzY94EaF3Z+6aEHD5dXjMK9NAw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:16:41.355376Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.05034","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2e9a5494b6fa835738d5c7ae3e431c6f6b56bd3bb2b520668b434830aaae4a27","sha256:3311c1354cc004b87cc3cca0cc9ab3c8532085ba516b28baa39b08997de80ec0"],"state_sha256":"cf11192443daa4e35f722713abb68be076097c7ffac52a76b8464d10ea3d5379"}