{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:YIMIDVQFEF5CGMWFWEDQHBTZIB","short_pith_number":"pith:YIMIDVQF","canonical_record":{"source":{"id":"2406.11379","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-06-17T09:55:36Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"1c60db18c6f1047001a14e9d0a5f7b250cc49bd90fa21ca8fe5ed3f012168262","abstract_canon_sha256":"7f9261d663e35dd220312000c6fac826a9fc00b70a440651502c4c1ac7d2b2fa"},"schema_version":"1.0"},"canonical_sha256":"c21881d605217a2332c5b1070386794061f107cc700cd7d3e4e3275eacb3369f","source":{"kind":"arxiv","id":"2406.11379","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.11379","created_at":"2026-07-05T11:16:02Z"},{"alias_kind":"arxiv_version","alias_value":"2406.11379v3","created_at":"2026-07-05T11:16:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.11379","created_at":"2026-07-05T11:16:02Z"},{"alias_kind":"pith_short_12","alias_value":"YIMIDVQFEF5C","created_at":"2026-07-05T11:16:02Z"},{"alias_kind":"pith_short_16","alias_value":"YIMIDVQFEF5CGMWF","created_at":"2026-07-05T11:16:02Z"},{"alias_kind":"pith_short_8","alias_value":"YIMIDVQF","created_at":"2026-07-05T11:16:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:YIMIDVQFEF5CGMWFWEDQHBTZIB","target":"record","payload":{"canonical_record":{"source":{"id":"2406.11379","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-06-17T09:55:36Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"1c60db18c6f1047001a14e9d0a5f7b250cc49bd90fa21ca8fe5ed3f012168262","abstract_canon_sha256":"7f9261d663e35dd220312000c6fac826a9fc00b70a440651502c4c1ac7d2b2fa"},"schema_version":"1.0"},"canonical_sha256":"c21881d605217a2332c5b1070386794061f107cc700cd7d3e4e3275eacb3369f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:16:02.547455Z","signature_b64":"+IeXJ9t8r3vY5vnKlqxs1kxevVTusI62lHoKw/R3i8+EvyEeSpLkM/KnzZRCxGKQ2dtznvFwMPSrxP2lm5E4Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c21881d605217a2332c5b1070386794061f107cc700cd7d3e4e3275eacb3369f","last_reissued_at":"2026-07-05T11:16:02.546968Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:16:02.546968Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2406.11379","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:16:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eHhKm0k/w4vVqmZmX94biq3ZhMs+D25IbhgFL4m44CzTxR3QFD03Pj2Z6mhxshilJBJCtZ7qAGkuDkUZQylHBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T13:18:26.599989Z"},"content_sha256":"938ea33045927d9c896415b9d6fb1369f4226da7d997eedf0c7130d1f81fb265","schema_version":"1.0","event_id":"sha256:938ea33045927d9c896415b9d6fb1369f4226da7d997eedf0c7130d1f81fb265"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:YIMIDVQFEF5CGMWFWEDQHBTZIB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On existence of Sadovskii vortex patch: A touching pair of symmetric counter-rotating uniform vortex","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"In-Jee Jeong, Kyudong Choi, Young-Jin Sim","submitted_at":"2024-06-17T09:55:36Z","abstract_excerpt":"The Sadovskii vortex patch is a traveling wave for the two-dimensional incompressible Euler equations consisting of an odd symmetric pair of vortex patches touching the symmetry axis. Its existence was first suggested by numerical computations of Sadovskii in [J. Appl. Math. Mech., 1971], and has gained significant interest due to its relevance in inviscid limit of planar flows via Prandtl--Batchelor theory and as the asymptotic state for vortex ring dynamics. In this work, we prove the existence of a Sadovskii vortex patch, by solving the energy maximization problem under the exact impulse co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.11379","kind":"arxiv","version":3},"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/2406.11379/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:16:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jfMMpY1BN3/ngFZW20eLChtNe8XfkwjxeDVxVdRVk/XQr9zmVgfh+I4kegEp3GsythzUP7vJ0EVaGKl0gYMxCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T13:18:26.600879Z"},"content_sha256":"a5ac835e414523311b0a2217958ab6ea2fa8c9ee0e4bc592f4f63bc1c474b2fe","schema_version":"1.0","event_id":"sha256:a5ac835e414523311b0a2217958ab6ea2fa8c9ee0e4bc592f4f63bc1c474b2fe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YIMIDVQFEF5CGMWFWEDQHBTZIB/bundle.json","state_url":"https://pith.science/pith/YIMIDVQFEF5CGMWFWEDQHBTZIB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YIMIDVQFEF5CGMWFWEDQHBTZIB/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-13T13:18:26Z","links":{"resolver":"https://pith.science/pith/YIMIDVQFEF5CGMWFWEDQHBTZIB","bundle":"https://pith.science/pith/YIMIDVQFEF5CGMWFWEDQHBTZIB/bundle.json","state":"https://pith.science/pith/YIMIDVQFEF5CGMWFWEDQHBTZIB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YIMIDVQFEF5CGMWFWEDQHBTZIB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:YIMIDVQFEF5CGMWFWEDQHBTZIB","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":"7f9261d663e35dd220312000c6fac826a9fc00b70a440651502c4c1ac7d2b2fa","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-06-17T09:55:36Z","title_canon_sha256":"1c60db18c6f1047001a14e9d0a5f7b250cc49bd90fa21ca8fe5ed3f012168262"},"schema_version":"1.0","source":{"id":"2406.11379","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.11379","created_at":"2026-07-05T11:16:02Z"},{"alias_kind":"arxiv_version","alias_value":"2406.11379v3","created_at":"2026-07-05T11:16:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.11379","created_at":"2026-07-05T11:16:02Z"},{"alias_kind":"pith_short_12","alias_value":"YIMIDVQFEF5C","created_at":"2026-07-05T11:16:02Z"},{"alias_kind":"pith_short_16","alias_value":"YIMIDVQFEF5CGMWF","created_at":"2026-07-05T11:16:02Z"},{"alias_kind":"pith_short_8","alias_value":"YIMIDVQF","created_at":"2026-07-05T11:16:02Z"}],"graph_snapshots":[{"event_id":"sha256:a5ac835e414523311b0a2217958ab6ea2fa8c9ee0e4bc592f4f63bc1c474b2fe","target":"graph","created_at":"2026-07-05T11:16:02Z","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/2406.11379/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Sadovskii vortex patch is a traveling wave for the two-dimensional incompressible Euler equations consisting of an odd symmetric pair of vortex patches touching the symmetry axis. Its existence was first suggested by numerical computations of Sadovskii in [J. Appl. Math. Mech., 1971], and has gained significant interest due to its relevance in inviscid limit of planar flows via Prandtl--Batchelor theory and as the asymptotic state for vortex ring dynamics. In this work, we prove the existence of a Sadovskii vortex patch, by solving the energy maximization problem under the exact impulse co","authors_text":"In-Jee Jeong, Kyudong Choi, Young-Jin Sim","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-06-17T09:55:36Z","title":"On existence of Sadovskii vortex patch: A touching pair of symmetric counter-rotating uniform vortex"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.11379","kind":"arxiv","version":3},"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":"sha256:938ea33045927d9c896415b9d6fb1369f4226da7d997eedf0c7130d1f81fb265","target":"record","created_at":"2026-07-05T11:16:02Z","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":"7f9261d663e35dd220312000c6fac826a9fc00b70a440651502c4c1ac7d2b2fa","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-06-17T09:55:36Z","title_canon_sha256":"1c60db18c6f1047001a14e9d0a5f7b250cc49bd90fa21ca8fe5ed3f012168262"},"schema_version":"1.0","source":{"id":"2406.11379","kind":"arxiv","version":3}},"canonical_sha256":"c21881d605217a2332c5b1070386794061f107cc700cd7d3e4e3275eacb3369f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c21881d605217a2332c5b1070386794061f107cc700cd7d3e4e3275eacb3369f","first_computed_at":"2026-07-05T11:16:02.546968Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:16:02.546968Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+IeXJ9t8r3vY5vnKlqxs1kxevVTusI62lHoKw/R3i8+EvyEeSpLkM/KnzZRCxGKQ2dtznvFwMPSrxP2lm5E4Cw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:16:02.547455Z","signed_message":"canonical_sha256_bytes"},"source_id":"2406.11379","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:938ea33045927d9c896415b9d6fb1369f4226da7d997eedf0c7130d1f81fb265","sha256:a5ac835e414523311b0a2217958ab6ea2fa8c9ee0e4bc592f4f63bc1c474b2fe"],"state_sha256":"d7684c20c46adb5b67e36b04ecf4b7dbe61f2073c3900b0154d1ed2f17569fea"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sLW9QvHtWOm232f6f9HDo2crg6Uv+Hh4hJIHjuAP2AoFNOAtqtuLuzb4RKBd++1FPCwr/FyTgccuDiSc97uhCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T13:18:26.612554Z","bundle_sha256":"481c92ebed943bb46d3d397be595488b8e9f6efc3a5889fa92881fdbaced7f58"}}