{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:MBZNN764PEDEUBMSNFIK56L3QF","short_pith_number":"pith:MBZNN764","schema_version":"1.0","canonical_sha256":"6072d6ffdc79064a05926950aef97b814a8a63d25e0c202e5db291e317657919","source":{"kind":"arxiv","id":"2311.15765","version":2},"attestation_state":"computed","paper":{"title":"Rigorous derivation of the leapfrogging motion for planar Euler equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.flu-dyn"],"primary_cat":"math.AP","authors_text":"Nader Masmoudi, Taoufik Hmidi, Zineb Hassainia","submitted_at":"2023-11-27T12:35:27Z","abstract_excerpt":"The main goal of this paper is to explore the leapfrogging phenomenon in the inviscid planar flows. We show for 2d Euler equations that under suitable constraints, four concentrated vortex patches leapfrog for all time. When observed from a translating frame of reference, the evolution of these vortex patches can be described as a non-rigid time periodic motion. Our proof hinges upon two key components. First, we desingularize the symmetric four point vortex configuration, which leapfrogs in accordance with Love's result \\cite{Love1893}, by concentrated vortex patches. Second, we borrow some t"},"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":"2311.15765","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-11-27T12:35:27Z","cross_cats_sorted":["physics.flu-dyn"],"title_canon_sha256":"64a15eec9b1fd22210ddcc2c2136bd271e44f447128c2e1db8b244c691f7892d","abstract_canon_sha256":"494e958f5e54bb7b3f9ff7e7f324041a1057f4442595a57cfd54037746f7d592"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:20:42.146556Z","signature_b64":"76fb0mKzIr53NQ8ouDvqJYHfZvqh0DvEe1x6weZiNOBkZGlGPp53wQ+MU+UM5Y7K8UAG1bjUSPgRUk8bDO16Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6072d6ffdc79064a05926950aef97b814a8a63d25e0c202e5db291e317657919","last_reissued_at":"2026-07-05T07:20:42.146176Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:20:42.146176Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rigorous derivation of the leapfrogging motion for planar Euler equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.flu-dyn"],"primary_cat":"math.AP","authors_text":"Nader Masmoudi, Taoufik Hmidi, Zineb Hassainia","submitted_at":"2023-11-27T12:35:27Z","abstract_excerpt":"The main goal of this paper is to explore the leapfrogging phenomenon in the inviscid planar flows. We show for 2d Euler equations that under suitable constraints, four concentrated vortex patches leapfrog for all time. When observed from a translating frame of reference, the evolution of these vortex patches can be described as a non-rigid time periodic motion. Our proof hinges upon two key components. First, we desingularize the symmetric four point vortex configuration, which leapfrogs in accordance with Love's result \\cite{Love1893}, by concentrated vortex patches. Second, we borrow some t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.15765","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2311.15765/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2311.15765","created_at":"2026-07-05T07:20:42.146232+00:00"},{"alias_kind":"arxiv_version","alias_value":"2311.15765v2","created_at":"2026-07-05T07:20:42.146232+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.15765","created_at":"2026-07-05T07:20:42.146232+00:00"},{"alias_kind":"pith_short_12","alias_value":"MBZNN764PEDE","created_at":"2026-07-05T07:20:42.146232+00:00"},{"alias_kind":"pith_short_16","alias_value":"MBZNN764PEDEUBMS","created_at":"2026-07-05T07:20:42.146232+00:00"},{"alias_kind":"pith_short_8","alias_value":"MBZNN764","created_at":"2026-07-05T07:20:42.146232+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2506.01477","citing_title":"Long time confinement of multiple concentrated vortices","ref_index":28,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MBZNN764PEDEUBMSNFIK56L3QF","json":"https://pith.science/pith/MBZNN764PEDEUBMSNFIK56L3QF.json","graph_json":"https://pith.science/api/pith-number/MBZNN764PEDEUBMSNFIK56L3QF/graph.json","events_json":"https://pith.science/api/pith-number/MBZNN764PEDEUBMSNFIK56L3QF/events.json","paper":"https://pith.science/paper/MBZNN764"},"agent_actions":{"view_html":"https://pith.science/pith/MBZNN764PEDEUBMSNFIK56L3QF","download_json":"https://pith.science/pith/MBZNN764PEDEUBMSNFIK56L3QF.json","view_paper":"https://pith.science/paper/MBZNN764","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2311.15765&json=true","fetch_graph":"https://pith.science/api/pith-number/MBZNN764PEDEUBMSNFIK56L3QF/graph.json","fetch_events":"https://pith.science/api/pith-number/MBZNN764PEDEUBMSNFIK56L3QF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MBZNN764PEDEUBMSNFIK56L3QF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MBZNN764PEDEUBMSNFIK56L3QF/action/storage_attestation","attest_author":"https://pith.science/pith/MBZNN764PEDEUBMSNFIK56L3QF/action/author_attestation","sign_citation":"https://pith.science/pith/MBZNN764PEDEUBMSNFIK56L3QF/action/citation_signature","submit_replication":"https://pith.science/pith/MBZNN764PEDEUBMSNFIK56L3QF/action/replication_record"}},"created_at":"2026-07-05T07:20:42.146232+00:00","updated_at":"2026-07-05T07:20:42.146232+00:00"}