{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:MTS4OCDLAJ6AWARBTA6DXNUU6W","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":"a730b61d6626c3196833e7d3397bf488e1e51f6de78225fa400a0551db4962c8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-10-20T12:32:54Z","title_canon_sha256":"112a55d77e82651d689d56083d34291ff132db46e77d3bdca10cc245dd5a01a3"},"schema_version":"1.0","source":{"id":"1510.05864","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.05864","created_at":"2026-05-18T01:29:39Z"},{"alias_kind":"arxiv_version","alias_value":"1510.05864v1","created_at":"2026-05-18T01:29:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.05864","created_at":"2026-05-18T01:29:39Z"},{"alias_kind":"pith_short_12","alias_value":"MTS4OCDLAJ6A","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MTS4OCDLAJ6AWARB","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MTS4OCDL","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:88f7062d5b85a02e341afc40bd0c40874262ee5a09b84e6071cdd562cfe9ba91","target":"graph","created_at":"2026-05-18T01:29:39Z","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 this article, we study the homogenization limit of a family of solutions to the incompressible 2D Euler equations in the exterior of a family of $n_k$ disjoint disks with centers $\\{z^k_i\\}$ and radii $\\varepsilon_k$. We assume that the initial velocities $u_0^k$ are smooth, divergence-free, tangent to the boundary and that they vanish at infinity. We allow, but we do not require, $n_k \\to \\infty$, and we assume $\\varepsilon_k \\to 0$ as $k\\to \\infty$.\n  Let $\\gamma^k_i$ be the circulation of $u_0^k$ around the circle $\\{|x-z^k_i|=\\varepsilon_k\\}$. We prove that the homogenization limit reta","authors_text":"C. Lacave, H. J. Nussenzveig Lopes, M. C. Lopes Filho","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-10-20T12:32:54Z","title":"Asymptotic behavior of 2D incompressible ideal flow around small disks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.05864","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":"sha256:89826ee57a20c55faf2aa19c9d96e657fbfde60ac4fb5475c879379d366ed9ff","target":"record","created_at":"2026-05-18T01:29:39Z","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":"a730b61d6626c3196833e7d3397bf488e1e51f6de78225fa400a0551db4962c8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-10-20T12:32:54Z","title_canon_sha256":"112a55d77e82651d689d56083d34291ff132db46e77d3bdca10cc245dd5a01a3"},"schema_version":"1.0","source":{"id":"1510.05864","kind":"arxiv","version":1}},"canonical_sha256":"64e5c7086b027c0b0221983c3bb694f5bbadb29cca0c73ff00585cc7c7bbb386","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"64e5c7086b027c0b0221983c3bb694f5bbadb29cca0c73ff00585cc7c7bbb386","first_computed_at":"2026-05-18T01:29:39.507410Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:29:39.507410Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xvW1j9s+RnuAz+NbYPb8ccA0+ec1QKOhtS6//5+UMJgGnvbrr2u9D2QE9RfGdbEJ7sxgoZ46KoILyNAVbGgzBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:29:39.508082Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.05864","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:89826ee57a20c55faf2aa19c9d96e657fbfde60ac4fb5475c879379d366ed9ff","sha256:88f7062d5b85a02e341afc40bd0c40874262ee5a09b84e6071cdd562cfe9ba91"],"state_sha256":"3c136ea2a2848de5beac9d323340a3d9f4dbf07d396cf178127daa9af0a1a4e6"}