{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:ZEPHH5WUDKFJK5GC5NDMEQKYCK","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":"7a464aa18d5dab73499322f024003d9416f77d11e19a95b45a40491d9ca33ff2","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2020-12-08T16:41:46Z","title_canon_sha256":"26f9594fe3a11c3d0fbe101da6c8b04698f9de24624aa2f761f1d959b112d41d"},"schema_version":"1.0","source":{"id":"2012.04548","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2012.04548","created_at":"2026-07-05T03:00:47Z"},{"alias_kind":"arxiv_version","alias_value":"2012.04548v1","created_at":"2026-07-05T03:00:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2012.04548","created_at":"2026-07-05T03:00:47Z"},{"alias_kind":"pith_short_12","alias_value":"ZEPHH5WUDKFJ","created_at":"2026-07-05T03:00:47Z"},{"alias_kind":"pith_short_16","alias_value":"ZEPHH5WUDKFJK5GC","created_at":"2026-07-05T03:00:47Z"},{"alias_kind":"pith_short_8","alias_value":"ZEPHH5WU","created_at":"2026-07-05T03:00:47Z"}],"graph_snapshots":[{"event_id":"sha256:a6306a17b3308fe3127e93a797b7f6ee6eb6a3cbc8237b19702f24a7848a4bd9","target":"graph","created_at":"2026-07-05T03:00:47Z","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/2012.04548/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we show that the only solution of the vortex sheet equation, either stationary or uniformly rotating with negative angular velocity $\\Omega$, such that it has positive vorticity and is concentrated in a finite disjoint union of smooth curves with finite length is the trivial one: constant vorticity amplitude supported on a union of nested, concentric circles. The proof follows a desingularization argument and a calculus of variations flavor.","authors_text":"Jaemin Park, Javier G\\'omez-Serrano, Jia Shi, Yao Yao","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2020-12-08T16:41:46Z","title":"Remarks on stationary and uniformly-rotating vortex sheets: Rigidity results"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2012.04548","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:ad379ef0071e17b701d1df240cbef28fd17e464a45d7cab69fe89634c0f91bd9","target":"record","created_at":"2026-07-05T03:00:47Z","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":"7a464aa18d5dab73499322f024003d9416f77d11e19a95b45a40491d9ca33ff2","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2020-12-08T16:41:46Z","title_canon_sha256":"26f9594fe3a11c3d0fbe101da6c8b04698f9de24624aa2f761f1d959b112d41d"},"schema_version":"1.0","source":{"id":"2012.04548","kind":"arxiv","version":1}},"canonical_sha256":"c91e73f6d41a8a9574c2eb46c2415812ae94f0e42720aa16f99fed307c7184cd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c91e73f6d41a8a9574c2eb46c2415812ae94f0e42720aa16f99fed307c7184cd","first_computed_at":"2026-07-05T03:00:47.231386Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:00:47.231386Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iFFk8EdobTpXnCur/eLHnev1XUKOTV1lyQuCl4mRHdfdBEeM4BwgsmmPzTee0J9WwCGRD/dLpvpXxMHN6HGWDw==","signature_status":"signed_v1","signed_at":"2026-07-05T03:00:47.231918Z","signed_message":"canonical_sha256_bytes"},"source_id":"2012.04548","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ad379ef0071e17b701d1df240cbef28fd17e464a45d7cab69fe89634c0f91bd9","sha256:a6306a17b3308fe3127e93a797b7f6ee6eb6a3cbc8237b19702f24a7848a4bd9"],"state_sha256":"87a8bb82ae39afe2a44c1ee246f1291d3dd19b76443b5daaa7add04c3f261557"}