{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:MTS4OCDLAJ6AWARBTA6DXNUU6W","short_pith_number":"pith:MTS4OCDL","schema_version":"1.0","canonical_sha256":"64e5c7086b027c0b0221983c3bb694f5bbadb29cca0c73ff00585cc7c7bbb386","source":{"kind":"arxiv","id":"1510.05864","version":1},"attestation_state":"computed","paper":{"title":"Asymptotic behavior of 2D incompressible ideal flow around small disks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"C. Lacave, H. J. Nussenzveig Lopes, M. C. Lopes Filho","submitted_at":"2015-10-20T12:32:54Z","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1510.05864","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-10-20T12:32:54Z","cross_cats_sorted":[],"title_canon_sha256":"112a55d77e82651d689d56083d34291ff132db46e77d3bdca10cc245dd5a01a3","abstract_canon_sha256":"a730b61d6626c3196833e7d3397bf488e1e51f6de78225fa400a0551db4962c8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:29:39.508082Z","signature_b64":"xvW1j9s+RnuAz+NbYPb8ccA0+ec1QKOhtS6//5+UMJgGnvbrr2u9D2QE9RfGdbEJ7sxgoZ46KoILyNAVbGgzBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"64e5c7086b027c0b0221983c3bb694f5bbadb29cca0c73ff00585cc7c7bbb386","last_reissued_at":"2026-05-18T01:29:39.507410Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:29:39.507410Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Asymptotic behavior of 2D incompressible ideal flow around small disks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"C. Lacave, H. J. Nussenzveig Lopes, M. C. Lopes Filho","submitted_at":"2015-10-20T12:32:54Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.05864","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1510.05864","created_at":"2026-05-18T01:29:39.507512+00:00"},{"alias_kind":"arxiv_version","alias_value":"1510.05864v1","created_at":"2026-05-18T01:29:39.507512+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.05864","created_at":"2026-05-18T01:29:39.507512+00:00"},{"alias_kind":"pith_short_12","alias_value":"MTS4OCDLAJ6A","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_16","alias_value":"MTS4OCDLAJ6AWARB","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_8","alias_value":"MTS4OCDL","created_at":"2026-05-18T12:29:32.376354+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MTS4OCDLAJ6AWARBTA6DXNUU6W","json":"https://pith.science/pith/MTS4OCDLAJ6AWARBTA6DXNUU6W.json","graph_json":"https://pith.science/api/pith-number/MTS4OCDLAJ6AWARBTA6DXNUU6W/graph.json","events_json":"https://pith.science/api/pith-number/MTS4OCDLAJ6AWARBTA6DXNUU6W/events.json","paper":"https://pith.science/paper/MTS4OCDL"},"agent_actions":{"view_html":"https://pith.science/pith/MTS4OCDLAJ6AWARBTA6DXNUU6W","download_json":"https://pith.science/pith/MTS4OCDLAJ6AWARBTA6DXNUU6W.json","view_paper":"https://pith.science/paper/MTS4OCDL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1510.05864&json=true","fetch_graph":"https://pith.science/api/pith-number/MTS4OCDLAJ6AWARBTA6DXNUU6W/graph.json","fetch_events":"https://pith.science/api/pith-number/MTS4OCDLAJ6AWARBTA6DXNUU6W/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MTS4OCDLAJ6AWARBTA6DXNUU6W/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MTS4OCDLAJ6AWARBTA6DXNUU6W/action/storage_attestation","attest_author":"https://pith.science/pith/MTS4OCDLAJ6AWARBTA6DXNUU6W/action/author_attestation","sign_citation":"https://pith.science/pith/MTS4OCDLAJ6AWARBTA6DXNUU6W/action/citation_signature","submit_replication":"https://pith.science/pith/MTS4OCDLAJ6AWARBTA6DXNUU6W/action/replication_record"}},"created_at":"2026-05-18T01:29:39.507512+00:00","updated_at":"2026-05-18T01:29:39.507512+00:00"}