{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:RXYJPALXV7A6VUB4COIXBK27LN","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":"74c4bfd957282ce6a6124f66262048611de094bfea9821cb9bf65442e92838f6","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2023-09-15T04:07:50Z","title_canon_sha256":"9139d704eb7deddc9ac99e7caad1e394e052016506b17661656c722d935fb92b"},"schema_version":"1.0","source":{"id":"2309.08137","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2309.08137","created_at":"2026-07-05T08:40:38Z"},{"alias_kind":"arxiv_version","alias_value":"2309.08137v2","created_at":"2026-07-05T08:40:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.08137","created_at":"2026-07-05T08:40:38Z"},{"alias_kind":"pith_short_12","alias_value":"RXYJPALXV7A6","created_at":"2026-07-05T08:40:38Z"},{"alias_kind":"pith_short_16","alias_value":"RXYJPALXV7A6VUB4","created_at":"2026-07-05T08:40:38Z"},{"alias_kind":"pith_short_8","alias_value":"RXYJPALX","created_at":"2026-07-05T08:40:38Z"}],"graph_snapshots":[{"event_id":"sha256:7ea57c5b8ecaf1d0df6d0d5a595582113a82b713cd077cbbb0a308c2f14f5af9","target":"graph","created_at":"2026-07-05T08:40:38Z","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/2309.08137/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we study the 2D free boundary incompressible Euler equations with surface tension, where the fluid domain is periodic in $x_1$, and has finite depth. We construct initial data with a flat free boundary and arbitrarily small velocity, such that the gradient of vorticity grows at least double-exponentially for all times during the lifespan of the associated solution. This work generalizes the celebrated result by Kiselev--{\\v{S}}ver{\\'a}k to the free boundary setting. The free boundary introduces some major challenges in the proof due to the deformation of the fluid domain and the","authors_text":"Chenyun Luo, Yao Yao, Zhongtian Hu","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2023-09-15T04:07:50Z","title":"Small scale creation for 2D free boundary Euler equations with surface tension"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.08137","kind":"arxiv","version":2},"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":"sha256:890e700f3c056b395414dbae152a2a196e933809e37665cec0ea40bb064f2dac","target":"record","created_at":"2026-07-05T08:40:38Z","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":"74c4bfd957282ce6a6124f66262048611de094bfea9821cb9bf65442e92838f6","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2023-09-15T04:07:50Z","title_canon_sha256":"9139d704eb7deddc9ac99e7caad1e394e052016506b17661656c722d935fb92b"},"schema_version":"1.0","source":{"id":"2309.08137","kind":"arxiv","version":2}},"canonical_sha256":"8df0978177afc1ead03c139170ab5f5b7f42f60a92191ec7b28fecb3a6574dd9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8df0978177afc1ead03c139170ab5f5b7f42f60a92191ec7b28fecb3a6574dd9","first_computed_at":"2026-07-05T08:40:38.658636Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:40:38.658636Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gIha1h/XtziE7dOF79Rn23fxOhbzcdzDIeDuhycnc4g/SL9fhHgZVftvwta+MNvmKr6ed+R4KtJu1/0z0TONCw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:40:38.659051Z","signed_message":"canonical_sha256_bytes"},"source_id":"2309.08137","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:890e700f3c056b395414dbae152a2a196e933809e37665cec0ea40bb064f2dac","sha256:7ea57c5b8ecaf1d0df6d0d5a595582113a82b713cd077cbbb0a308c2f14f5af9"],"state_sha256":"a4d72f29eccaf8faf8c378dff0398d4b06583218a281de5cce8c2f0c1947ed05"}