{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:I747LDETABHWZRVDWMR4AVSKBE","short_pith_number":"pith:I747LDET","schema_version":"1.0","canonical_sha256":"47f9f58c93004f6cc6a3b323c0564a09199e3026a5454febd46f397d7c94a5d7","source":{"kind":"arxiv","id":"2607.07613","version":1},"attestation_state":"computed","paper":{"title":"Time-periodic vortices near translating symmetric dipole patches","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Luca Franzoi, Riccardo Montalto, Taoufik Hmidi","submitted_at":"2026-07-08T16:29:18Z","abstract_excerpt":"We prove the existence of time-periodic solutions of the two-dimensional incompressible Euler equations bifurcating from a translating vortex pair. The reference configuration consists of two symmetric vortex patches of equal strength and opposite sign traveling at constant speed. In a regime of large separation between the vortices, the dynamics may be viewed as a small perturbation of an integrable system. Working in a co-moving frame and using the contour dynamics formulation, we reduce the problem to a nonlinear transport equation for the vortex boundaries. The linearized operator exhibits"},"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":"2607.07613","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-07-08T16:29:18Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"af4a36b5db6abf1f9d868672b2672db37962548b6b918d90fdf885516ef98920","abstract_canon_sha256":"15ba16b08d30c5d5cd9e7841778d89f5424c3d050a6152e94d43aef1ed928b52"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-09T01:20:36.781053Z","signature_b64":"I7t+J2crzEmLjTfZhMKP5mJCMZtAB4wNgf0umLu61EVQgorOzoV+MDgkTC0IxBR6Gvn55t2vzWU8hFQzUU5eDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"47f9f58c93004f6cc6a3b323c0564a09199e3026a5454febd46f397d7c94a5d7","last_reissued_at":"2026-07-09T01:20:36.780545Z","signature_status":"signed_v1","first_computed_at":"2026-07-09T01:20:36.780545Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Time-periodic vortices near translating symmetric dipole patches","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Luca Franzoi, Riccardo Montalto, Taoufik Hmidi","submitted_at":"2026-07-08T16:29:18Z","abstract_excerpt":"We prove the existence of time-periodic solutions of the two-dimensional incompressible Euler equations bifurcating from a translating vortex pair. The reference configuration consists of two symmetric vortex patches of equal strength and opposite sign traveling at constant speed. In a regime of large separation between the vortices, the dynamics may be viewed as a small perturbation of an integrable system. Working in a co-moving frame and using the contour dynamics formulation, we reduce the problem to a nonlinear transport equation for the vortex boundaries. The linearized operator exhibits"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.07613","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.07613/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":"2607.07613","created_at":"2026-07-09T01:20:36.780605+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.07613v1","created_at":"2026-07-09T01:20:36.780605+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.07613","created_at":"2026-07-09T01:20:36.780605+00:00"},{"alias_kind":"pith_short_12","alias_value":"I747LDETABHW","created_at":"2026-07-09T01:20:36.780605+00:00"},{"alias_kind":"pith_short_16","alias_value":"I747LDETABHWZRVD","created_at":"2026-07-09T01:20:36.780605+00:00"},{"alias_kind":"pith_short_8","alias_value":"I747LDET","created_at":"2026-07-09T01:20:36.780605+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/I747LDETABHWZRVDWMR4AVSKBE","json":"https://pith.science/pith/I747LDETABHWZRVDWMR4AVSKBE.json","graph_json":"https://pith.science/api/pith-number/I747LDETABHWZRVDWMR4AVSKBE/graph.json","events_json":"https://pith.science/api/pith-number/I747LDETABHWZRVDWMR4AVSKBE/events.json","paper":"https://pith.science/paper/I747LDET"},"agent_actions":{"view_html":"https://pith.science/pith/I747LDETABHWZRVDWMR4AVSKBE","download_json":"https://pith.science/pith/I747LDETABHWZRVDWMR4AVSKBE.json","view_paper":"https://pith.science/paper/I747LDET","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.07613&json=true","fetch_graph":"https://pith.science/api/pith-number/I747LDETABHWZRVDWMR4AVSKBE/graph.json","fetch_events":"https://pith.science/api/pith-number/I747LDETABHWZRVDWMR4AVSKBE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/I747LDETABHWZRVDWMR4AVSKBE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/I747LDETABHWZRVDWMR4AVSKBE/action/storage_attestation","attest_author":"https://pith.science/pith/I747LDETABHWZRVDWMR4AVSKBE/action/author_attestation","sign_citation":"https://pith.science/pith/I747LDETABHWZRVDWMR4AVSKBE/action/citation_signature","submit_replication":"https://pith.science/pith/I747LDETABHWZRVDWMR4AVSKBE/action/replication_record"}},"created_at":"2026-07-09T01:20:36.780605+00:00","updated_at":"2026-07-09T01:20:36.780605+00:00"}