{"as_of":"2026-08-09T07:43:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:7c7e9f4012adf32cb103ca2dbd75f668315bec9e56784a23e9cb2f288cc94b9f","coverage":[{"denominator":67,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":67,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T14:05:46.554013Z","state":"measured"},{"denominator":67,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":67,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-09T06:31:02.800959+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2507.19935/citation-record","integrity":"/paper/2507.19935/integrity","json":"/paper/2507.19935/citation-record.json","paper":"/paper/2507.19935"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:05:47.283756Z","title":"Stability of Lamb dipoles","venue":null,"work_id":"22681978-fc7c-4835-8e69-c34b6f5f0592","year":2022},"citing_paper":{"arxiv_id":"2507.19935","last_updated":"2025-07-29T06:02:32Z","snapshot_observed_at":"2026-08-07T21:46:16.772241Z","submitted_at":"2025-07-26T12:42:53Z","title":"Stability of oppositely-propagating pair of Hill's spherical vortices","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-06T14:05:44.264266Z"},"links":{"citing_paper":"/paper/2507.19935"},"observation_digest":"sha256:8e9678dc516fdac7826f3cf0e8ecb9af3191f5e9f08120bb4bb76d66bb2e9712","observation_id":"509d4b1a-b8a1-4107-bbee-d87e97577ecb","resolution":{"observed_at":"2026-08-06T14:05:47.286752Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2507.16474","last_updated":"2026-07-07T06:13:32Z","snapshot_observed_at":"2026-08-07T14:50:50.224083Z","submitted_at":"2025-07-22T11:23:16Z","title":"Stability for multiple Lamb dipoles","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2507.16474","snapshot_observed_at":"2026-08-06T14:05:44.328436Z","title":"Stability for multiple Lamb dipoles","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.19935","last_updated":"2025-07-29T06:02:32Z","snapshot_observed_at":"2026-08-07T21:46:16.772241Z","submitted_at":"2025-07-26T12:42:53Z","title":"Stability of oppositely-propagating pair of Hill's spherical vortices","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-06T14:05:44.328436Z"},"links":{"cited_paper":"/paper/2507.16474","citing_paper":"/paper/2507.19935"},"observation_digest":"sha256:235fbd257058d5729b8fbfeb056145e318929b05291c54aaa3d05fd33ba17f9d","observation_id":"ca64be12-a768-42aa-b056-1db9520781bb","resolution":{"observed_at":"2026-08-06T14:05:44.328436Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:05:47.274632Z","title":null,"venue":null,"work_id":"61641536-654c-4ab5-81b7-da14f112eec4","year":2000},"citing_paper":{"arxiv_id":"2507.19935","last_updated":"2025-07-29T06:02:32Z","snapshot_observed_at":"2026-08-07T21:46:16.772241Z","submitted_at":"2025-07-26T12:42:53Z","title":"Stability of oppositely-propagating pair of Hill's spherical vortices","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-06T14:05:44.428713Z"},"links":{"citing_paper":"/paper/2507.19935"},"observation_digest":"sha256:c4ff042838a5013da351df92f02b4dd443c3241a7c32d8522e880d6ad6899029","observation_id":"e4f7268d-84b3-4321-bc3d-8cc73330647f","resolution":{"observed_at":"2026-08-06T14:05:47.277512Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:05:47.265276Z","title":"On the existence of leapfrogging pair of circular vortex filaments","venue":null,"work_id":"d01ad7ef-3be6-4483-94ef-4d3a836979a3","year":2019},"citing_paper":{"arxiv_id":"2507.19935","last_updated":"2025-07-29T06:02:32Z","snapshot_observed_at":"2026-08-07T21:46:16.772241Z","submitted_at":"2025-07-26T12:42:53Z","title":"Stability of oppositely-propagating pair of Hill's spherical vortices","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-06T14:05:44.524604Z"},"links":{"citing_paper":"/paper/2507.19935"},"observation_digest":"sha256:74e6734249252d673839687f7bb6e5f3a2f48f2b55b5af25bfb64ba6b5e7ba7a","observation_id":"eb28c7e1-d757-4a31-a354-0c425f1e03b5","resolution":{"observed_at":"2026-08-06T14:05:47.268510Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:05:47.256347Z","title":"Amick and L","venue":null,"work_id":"fc6e30dd-e736-4372-8980-662c76ec0425","year":1986},"citing_paper":{"arxiv_id":"2507.19935","last_updated":"2025-07-29T06:02:32Z","snapshot_observed_at":"2026-08-07T21:46:16.772241Z","submitted_at":"2025-07-26T12:42:53Z","title":"Stability of oppositely-propagating pair of Hill's spherical vortices","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-06T14:05:44.594984Z"},"links":{"citing_paper":"/paper/2507.19935"},"observation_digest":"sha256:ac75f853f76f16f5154d59bf7cbe4a0e5a990695c76ff9fc16012c8f35eb6546","observation_id":"813e1431-74cd-4b7d-bc83-1e29bb0e2bca","resolution":{"observed_at":"2026-08-06T14:05:47.259162Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:05:47.248152Z","title":"Motion of three vortices","venue":null,"work_id":"37f679bf-5163-4f16-abae-07e75d438182","year":1979},"citing_paper":{"arxiv_id":"2507.19935","last_updated":"2025-07-29T06:02:32Z","snapshot_observed_at":"2026-08-07T21:46:16.772241Z","submitted_at":"2025-07-26T12:42:53Z","title":"Stability of oppositely-propagating pair of Hill's spherical vortices","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-06T14:05:44.682148Z"},"links":{"citing_paper":"/paper/2507.19935"},"observation_digest":"sha256:6225d7740c057b5d73d9ef87c9a6eeda09c1e99fd0108ef3b0a11f6ad88aab65","observation_id":"a436acf5-7972-4dd6-a5fa-5b47b974e908","resolution":{"observed_at":"2026-08-06T14:05:47.251095Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:05:47.238803Z","title":"Point vortex dynamics: A classical mathematics playground","venue":null,"work_id":"d4c90e24-7e0d-44b6-b15c-2bba103df0ee","year":2007},"citing_paper":{"arxiv_id":"2507.19935","last_updated":"2025-07-29T06:02:32Z","snapshot_observed_at":"2026-08-07T21:46:16.772241Z","submitted_at":"2025-07-26T12:42:53Z","title":"Stability of oppositely-propagating pair of Hill's spherical vortices","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-06T14:05:44.687173Z"},"links":{"citing_paper":"/paper/2507.19935"},"observation_digest":"sha256:a1f1126b31ab0bd4fa9ec0624bfafd22e633cdf38c43369956b915493bdadd2a","observation_id":"9afacb1d-d9b7-4ef8-bd19-193a74e4998f","resolution":{"observed_at":"2026-08-06T14:05:47.242232Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:05:47.229468Z","title":"Kadtke, Ireneusz Zawadzki, Laurence J","venue":null,"work_id":"1817d111-93c5-47f8-8d5d-b28adbfc523e","year":1988},"citing_paper":{"arxiv_id":"2507.19935","last_updated":"2025-07-29T06:02:32Z","snapshot_observed_at":"2026-08-07T21:46:16.772241Z","submitted_at":"2025-07-26T12:42:53Z","title":"Stability of oppositely-propagating pair of Hill's spherical vortices","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-06T14:05:44.817983Z"},"links":{"citing_paper":"/paper/2507.19935"},"observation_digest":"sha256:bcb8034408d4ca598f6725fb2cebecff5c392038b3f7a7c183a8aeffc367293e","observation_id":"ad9224cd-380e-4d25-95cd-a28a7f707ec2","resolution":{"observed_at":"2026-08-06T14:05:47.232428Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:05:47.220707Z","title":"Barry, Glen R","venue":null,"work_id":"dc57a784-c92b-4684-880e-e62d5e0c9e3f","year":2012},"citing_paper":{"arxiv_id":"2507.19935","last_updated":"2025-07-29T06:02:32Z","snapshot_observed_at":"2026-08-07T21:46:16.772241Z","submitted_at":"2025-07-26T12:42:53Z","title":"Stability of oppositely-propagating pair of Hill's spherical vortices","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-06T14:05:44.984345Z"},"links":{"citing_paper":"/paper/2507.19935"},"observation_digest":"sha256:8fb032f25067c6919943c32bb75096b69aef357293decf7624d26f581b453edd","observation_id":"6bd11267-a2d2-4380-a62d-7dceb1d3466d","resolution":{"observed_at":"2026-08-06T14:05:47.223489Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:05:47.210482Z","title":"Behring and Roy H","venue":null,"work_id":"0ceec16a-fc80-47a1-8efe-8fd56eed09dc","year":2019},"citing_paper":{"arxiv_id":"2507.19935","last_updated":"2025-07-29T06:02:32Z","snapshot_observed_at":"2026-08-07T21:46:16.772241Z","submitted_at":"2025-07-26T12:42:53Z","title":"Stability of oppositely-propagating pair of Hill's spherical vortices","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-06T14:05:45.203573Z"},"links":{"citing_paper":"/paper/2507.19935"},"observation_digest":"sha256:c09c51d8bc843c1188bf6d9195f472bd26bb0d87955a2012f99d98c2ac04a51b","observation_id":"cda42bb5-3b88-475b-964f-3864ac1a502b","resolution":{"observed_at":"2026-08-06T14:05:47.213945Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:05:47.201005Z","title":"Leapfrogging vortex rings as scaling limit of Euler equations","venue":null,"work_id":"3226ae30-f4e3-4ee4-9366-78212b45105e","year":2025},"citing_paper":{"arxiv_id":"2507.19935","last_updated":"2025-07-29T06:02:32Z","snapshot_observed_at":"2026-08-07T21:46:16.772241Z","submitted_at":"2025-07-26T12:42:53Z","title":"Stability of oppositely-propagating pair of Hill's spherical vortices","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-06T14:05:45.329713Z"},"links":{"citing_paper":"/paper/2507.19935"},"observation_digest":"sha256:767ff7f27a769645102d040e5bad4c2484545e8b9d96e23157e7a8fa3fe913d3","observation_id":"4d97929a-e8eb-4d87-afd5-b178eb8efef6","resolution":{"observed_at":"2026-08-06T14:05:47.204392Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:05:47.191852Z","title":null,"venue":null,"work_id":"33fdcd1f-0924-45a5-ac10-7748ee6ed1c4","year":1999},"citing_paper":{"arxiv_id":"2507.19935","last_updated":"2025-07-29T06:02:32Z","snapshot_observed_at":"2026-08-07T21:46:16.772241Z","submitted_at":"2025-07-26T12:42:53Z","title":"Stability of oppositely-propagating pair of Hill's spherical vortices","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-06T14:05:45.494342Z"},"links":{"citing_paper":"/paper/2507.19935"},"observation_digest":"sha256:d70828d9912cd7cd49f2cc2820f4567f0331aadbcb4c8e9b25f0dabec7874ef8","observation_id":"5202bbe2-2c0a-4cb5-ab86-81390346ba41","resolution":{"observed_at":"2026-08-06T14:05:47.194942Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2505.12240","last_updated":"2025-07-11T02:48:49Z","snapshot_observed_at":"2026-08-07T15:43:45.534867Z","submitted_at":"2025-05-18T05:33:36Z","title":"Dynamics and leapfrogging phenomena of multiple helical vortices for 3D incompressible Euler equations","version":4},"cited_work":{"arxiv_id":"2505.12240","doi":null,"metadata_source":"pith","pith_arxiv_id":"2505.12240","snapshot_observed_at":"2026-08-06T14:05:46.764582Z","title":"Dynamics and leapfrogging phenomena of multiple helical vortices for 3D incompressible Euler equations","venue":"math.AP","work_id":"59ed5ab7-474a-4157-aac1-c827646cfbd8","year":2025},"citing_paper":{"arxiv_id":"2507.19935","last_updated":"2025-07-29T06:02:32Z","snapshot_observed_at":"2026-08-07T21:46:16.772241Z","submitted_at":"2025-07-26T12:42:53Z","title":"Stability of oppositely-propagating pair of Hill's spherical vortices","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-06T14:05:45.646345Z"},"links":{"cited_paper":"/paper/2505.12240","citing_paper":"/paper/2507.19935"},"observation_digest":"sha256:3d50e1ce50f535a50695974adfd3a286f34b4065269df161b4c63867c1241c90","observation_id":"2927a73f-d0f8-4b51-a96e-451c7f8b3e64","resolution":{"observed_at":"2026-08-06T14:05:46.768414Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:05:47.182809Z","title":"Traveling vortex pairs for 2D incompressible Euler equations","venue":null,"work_id":"1bb5649c-4565-4f94-82a9-f9ae94acad14","year":2021},"citing_paper":{"arxiv_id":"2507.19935","last_updated":"2025-07-29T06:02:32Z","snapshot_observed_at":"2026-08-07T21:46:16.772241Z","submitted_at":"2025-07-26T12:42:53Z","title":"Stability of oppositely-propagating pair of Hill's spherical vortices","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-06T14:05:45.846306Z"},"links":{"citing_paper":"/paper/2507.19935"},"observation_digest":"sha256:7aa9a1f6b857a8fa630876823e13adf4aada37b5110b4cff1a8ad60154714d53","observation_id":"d6be1d2c-0abe-469e-82fa-71e9a1dcf1af","resolution":{"observed_at":"2026-08-06T14:05:47.185839Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:05:47.173686Z","title":"Celli, E","venue":null,"work_id":"d1bdcba9-1d29-400b-9275-4b22eb9edc6f","year":2011},"citing_paper":{"arxiv_id":"2507.19935","last_updated":"2025-07-29T06:02:32Z","snapshot_observed_at":"2026-08-07T21:46:16.772241Z","submitted_at":"2025-07-26T12:42:53Z","title":"Stability of oppositely-propagating pair of Hill's spherical vortices","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-06T14:05:46.022186Z"},"links":{"citing_paper":"/paper/2507.19935"},"observation_digest":"sha256:2aa9129f8032c063dce075e8bb95572adf7721b2ef84e7570fdf36e453222c4e","observation_id":"d609aa47-c404-422b-8f3e-fac10b343322","resolution":{"observed_at":"2026-08-06T14:05:47.177201Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:05:47.164484Z","title":"Cheng, J","venue":null,"work_id":"fcfe62b5-ac34-404b-b99f-5d70d17216d3","year":2018},"citing_paper":{"arxiv_id":"2507.19935","last_updated":"2025-07-29T06:02:32Z","snapshot_observed_at":"2026-08-07T21:46:16.772241Z","submitted_at":"2025-07-26T12:42:53Z","title":"Stability of oppositely-propagating pair of Hill's spherical vortices","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-06T14:05:46.190598Z"},"links":{"citing_paper":"/paper/2507.19935"},"observation_digest":"sha256:2117ef66e631558aebbdb81fea3901486b5d86e574cd68fbd4a1ef04a875751c","observation_id":"dfc9d421-112c-4483-b4e9-2deb189ada80","resolution":{"observed_at":"2026-08-06T14:05:47.167954Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:05:47.155048Z","title":"Stability of Hill’s spherical vortex","venue":null,"work_id":"69a00271-4447-4dc1-a67a-1b7be55899ba","year":2024},"citing_paper":{"arxiv_id":"2507.19935","last_updated":"2025-07-29T06:02:32Z","snapshot_observed_at":"2026-08-07T21:46:16.772241Z","submitted_at":"2025-07-26T12:42:53Z","title":"Stability of oppositely-propagating pair of Hill's spherical vortices","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-06T14:05:46.376614Z"},"links":{"citing_paper":"/paper/2507.19935"},"observation_digest":"sha256:4f413409ddf6e7492a070cb5c46dc59f8d5e1551f0fb217c60bdbef3947d4cca","observation_id":"4aef28a6-9af6-498b-aa92-d4e12821df6f","resolution":{"observed_at":"2026-08-06T14:05:47.158623Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2110.09079","last_updated":"2021-11-26T07:09:49Z","snapshot_observed_at":"2026-08-04T14:43:33.073976Z","submitted_at":"2021-10-18T08:04:01Z","title":"On vortex stretching for anti-parallel axisymmetric flows","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2110.09079","snapshot_observed_at":"2026-08-06T14:05:46.419260Z","title":"On vortex stretching for anti-parallel axisymmetric flows","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2507.19935","last_updated":"2025-07-29T06:02:32Z","snapshot_observed_at":"2026-08-07T21:46:16.772241Z","submitted_at":"2025-07-26T12:42:53Z","title":"Stability of oppositely-propagating pair of Hill's spherical vortices","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-06T14:05:46.419260Z"},"links":{"cited_paper":"/paper/2110.09079","citing_paper":"/paper/2507.19935"},"observation_digest":"sha256:f2a7b0f79d09a2f4b8486f60a080bc215f30ae0a4d7c50b3a7419df6b442189f","observation_id":"1e28a232-5057-47f1-9b47-a9fb4082817e","resolution":{"observed_at":"2026-08-06T14:05:46.419260Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:05:47.146779Z","title":"Infinite growth in vorticity gradient of compactly supported planar vorticity near Lamb dipole","venue":null,"work_id":"9aa5b562-642a-4434-8fef-7ca48a49bbe2","year":2022},"citing_paper":{"arxiv_id":"2507.19935","last_updated":"2025-07-29T06:02:32Z","snapshot_observed_at":"2026-08-07T21:46:16.772241Z","submitted_at":"2025-07-26T12:42:53Z","title":"Stability of oppositely-propagating pair of Hill's spherical vortices","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-06T14:05:46.422518Z"},"links":{"citing_paper":"/paper/2507.19935"},"observation_digest":"sha256:c252a79bccf8c8375d0ac0e5d1d121cc44b653f1652fc6f7a86744f2a6d83448","observation_id":"8728a1dd-5653-47ae-8a72-3c37a37679ef","resolution":{"observed_at":"2026-08-06T14:05:47.149784Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:05:47.137654Z","title":"Filamentation near Hill’s vortex","venue":null,"work_id":"e70815eb-2014-4f84-b537-de0a5c73400e","year":2023},"citing_paper":{"arxiv_id":"2507.19935","last_updated":"2025-07-29T06:02:32Z","snapshot_observed_at":"2026-08-07T21:46:16.772241Z","submitted_at":"2025-07-26T12:42:53Z","title":"Stability of oppositely-propagating pair of Hill's spherical vortices","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-06T14:05:46.425167Z"},"links":{"citing_paper":"/paper/2507.19935"},"observation_digest":"sha256:494f742adf57e62ba1cc35cea38ebf1661b3eb2e21fc8760ca84a16a5797b4ca","observation_id":"dca80566-e4d0-4954-8296-e8d57b75ad84","resolution":{"observed_at":"2026-08-06T14:05:47.140689Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:05:47.128438Z","title":"On Existence of Sadovskii Vortex Patch: A Touching Pair of Symmetric Counter-Rotating Uniform Vortices","venue":null,"work_id":"07c09980-ec9e-4b89-9d1e-241989472c1f","year":2025},"citing_paper":{"arxiv_id":"2507.19935","last_updated":"2025-07-29T06:02:32Z","snapshot_observed_at":"2026-08-07T21:46:16.772241Z","submitted_at":"2025-07-26T12:42:53Z","title":"Stability of oppositely-propagating pair of Hill's spherical vortices","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-06T14:05:46.428371Z"},"links":{"citing_paper":"/paper/2507.19935"},"observation_digest":"sha256:70a56ae8b598429651ba27dd015cb4575a62833bcda7beedccf0cc25ab090815","observation_id":"c9392123-7b3a-48df-a8fa-2f6ad83e850e","resolution":{"observed_at":"2026-08-06T14:05:47.132184Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2409.19822","last_updated":"2024-09-29T23:07:57Z","snapshot_observed_at":"2026-07-06T19:24:12.811792Z","submitted_at":"2024-09-29T23:07:57Z","title":"Stability of vortex quadrupoles with odd-odd symmetry","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2409.19822","snapshot_observed_at":"2026-08-06T14:05:46.430963Z","title":"Stability of vortex quadrupoles with odd-odd symmetry","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.19935","last_updated":"2025-07-29T06:02:32Z","snapshot_observed_at":"2026-08-07T21:46:16.772241Z","submitted_at":"2025-07-26T12:42:53Z","title":"Stability of oppositely-propagating pair of Hill's spherical vortices","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-06T14:05:46.430963Z"},"links":{"cited_paper":"/paper/2409.19822","citing_paper":"/paper/2507.19935"},"observation_digest":"sha256:a8c6a067ff451fab363b9bdfb5df5d6216efbd730b9ba1b9beb1532c12ea1830","observation_id":"dce1d102-f951-4035-8daa-94f48743a8dd","resolution":{"observed_at":"2026-08-06T14:05:46.430963Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:05:46.434007Z","title":"Existence and stability of Sadovskii vortices: from vortex patches to regular vorticity","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.19935","last_updated":"2025-07-29T06:02:32Z","snapshot_observed_at":"2026-08-07T21:46:16.772241Z","submitted_at":"2025-07-26T12:42:53Z","title":"Stability of oppositely-propagating pair of Hill's spherical vortices","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-06T14:05:46.434007Z"},"links":{"citing_paper":"/paper/2507.19935"},"observation_digest":"sha256:12d1905a20c3c4b3dd7ebcf7b4d8bd2e4127a7e8ad536d5c9e921df54b0e45b4","observation_id":"3595b6c5-cb9d-4055-ab3f-57f07d9ee1ae","resolution":{"observed_at":"2026-08-06T14:05:46.434007Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:05:47.119860Z","title":"Head-on collision of two coaxial vortex rings: experiment and computation","venue":null,"work_id":"16a97636-34e2-4e52-b184-ab52107d9c06","year":1995},"citing_paper":{"arxiv_id":"2507.19935","last_updated":"2025-07-29T06:02:32Z","snapshot_observed_at":"2026-08-07T21:46:16.772241Z","submitted_at":"2025-07-26T12:42:53Z","title":"Stability of oppositely-propagating pair of Hill's spherical vortices","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-06T14:05:46.436809Z"},"links":{"citing_paper":"/paper/2507.19935"},"observation_digest":"sha256:e56caeb14ae6e5c84dbb9f571668c1bd0ec93007139d8b71236ed00e82b43e3f","observation_id":"0aac4959-6c08-4c36-966d-27fe0e3470cb","resolution":{"observed_at":"2026-08-06T14:05:47.123030Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:05:47.111106Z","title":"Leapfrogging vortex rings for the three-dimensional incompressible Euler equations","venue":null,"work_id":"67348516-00e3-4e2a-9f25-311d4e7eed3b","year":2024},"citing_paper":{"arxiv_id":"2507.19935","last_updated":"2025-07-29T06:02:32Z","snapshot_observed_at":"2026-08-07T21:46:16.772241Z","submitted_at":"2025-07-26T12:42:53Z","title":"Stability of oppositely-propagating pair of Hill's spherical vortices","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-06T14:05:46.439658Z"},"links":{"citing_paper":"/paper/2507.19935"},"observation_digest":"sha256:0c300909e1dd66d19d9899fcbf191c5c65ec988f1a9be774206738227ef305fc","observation_id":"e0c7da1e-8e4b-4088-9869-0bccbe6b0635","resolution":{"observed_at":"2026-08-06T14:05:47.114057Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:05:47.102556Z","title":null,"venue":null,"work_id":"79ec5a07-6923-4072-a16e-379da669d381","year":1992},"citing_paper":{"arxiv_id":"2507.19935","last_updated":"2025-07-29T06:02:32Z","snapshot_observed_at":"2026-08-07T21:46:16.772241Z","submitted_at":"2025-07-26T12:42:53Z","title":"Stability of oppositely-propagating pair of Hill's spherical vortices","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-06T14:05:46.442403Z"},"links":{"citing_paper":"/paper/2507.19935"},"observation_digest":"sha256:f45095d4bbb1e9869dd8f8f5caaa6057f6439afa95e3b75fa67e838af81f17c8","observation_id":"98582235-db6b-4aab-940f-0b29fe53c6de","resolution":{"observed_at":"2026-08-06T14:05:47.105156Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2503.21604","last_updated":"2025-06-19T16:37:18Z","snapshot_observed_at":"2026-08-07T16:32:32.687903Z","submitted_at":"2025-03-27T15:24:00Z","title":"On the dynamics of leapfrogging vortex rings","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2503.21604","snapshot_observed_at":"2026-08-06T14:05:46.445775Z","title":"On the dynamics of leapfrogging vortex rings.arXiv:2503.21604, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.19935","last_updated":"2025-07-29T06:02:32Z","snapshot_observed_at":"2026-08-07T21:46:16.772241Z","submitted_at":"2025-07-26T12:42:53Z","title":"Stability of oppositely-propagating pair of Hill's spherical vortices","version":2},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-06T14:05:46.445775Z"},"links":{"cited_paper":"/paper/2503.21604","citing_paper":"/paper/2507.19935"},"observation_digest":"sha256:76187159cbe7a5537f0a14e07671d15959077643f58f926d1571e617784de2b9","observation_id":"557f515c-07d9-4570-8362-d2cf51346c23","resolution":{"observed_at":"2026-08-06T14:05:46.445775Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:05:46.449128Z","title":"Global in Time Vortex Configurations for the 2D Euler equations","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2507.19935","last_updated":"2025-07-29T06:02:32Z","snapshot_observed_at":"2026-08-07T21:46:16.772241Z","submitted_at":"2025-07-26T12:42:53Z","title":"Stability of oppositely-propagating pair of Hill's spherical vortices","version":2},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-06T14:05:46.449128Z"},"links":{"citing_paper":"/paper/2507.19935"},"observation_digest":"sha256:87f760e930628a786820bffe2f34f9559de54c7dc97f7ada48a6c15a4dd96fb3","observation_id":"0de7886e-831e-4b84-b9bb-c0895508a7e2","resolution":{"observed_at":"2026-08-06T14:05:46.449128Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2410.18220","last_updated":"2024-10-23T18:45:42Z","snapshot_observed_at":"2026-07-06T19:38:44.045121Z","submitted_at":"2024-10-23T18:45:42Z","title":"An Expanding Self-Similar Vortex Configuration for the 2D Euler Equations","version":1},"cited_work":{"arxiv_id":"2410.18220","doi":null,"metadata_source":"pith","pith_arxiv_id":"2410.18220","snapshot_observed_at":"2026-08-06T14:05:46.593489Z","title":"An Expanding Self-Similar Vortex Configuration for the 2D Euler Equations","venue":"math.AP","work_id":"ee61cdab-26e7-471a-9215-e67796b1de71","year":2024},"citing_paper":{"arxiv_id":"2507.19935","last_updated":"2025-07-29T06:02:32Z","snapshot_observed_at":"2026-08-07T21:46:16.772241Z","submitted_at":"2025-07-26T12:42:53Z","title":"Stability of oppositely-propagating pair of Hill's spherical vortices","version":2},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-06T14:05:46.452051Z"},"links":{"cited_paper":"/paper/2410.18220","citing_paper":"/paper/2507.19935"},"observation_digest":"sha256:a9d5f443219919674495048f3f40c933ae03b07f3af536763b65436c10a6a456","observation_id":"787a30b5-43da-4022-bba1-94bdb9d05720","resolution":{"observed_at":"2026-08-06T14:05:46.598521Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:05:47.094060Z","title":"On the Cauchy problem for axi-symmetric vortex rings","venue":null,"work_id":"230b775c-7fe6-4f1c-9947-5bf9d09b1fb5","year":2015},"citing_paper":{"arxiv_id":"2507.19935","last_updated":"2025-07-29T06:02:32Z","snapshot_observed_at":"2026-08-07T21:46:16.772241Z","submitted_at":"2025-07-26T12:42:53Z","title":"Stability of oppositely-propagating pair of Hill's spherical vortices","version":2},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-06T14:05:46.454877Z"},"links":{"citing_paper":"/paper/2507.19935"},"observation_digest":"sha256:254e1f7180525018078f8664386d6378b2af07ad7d29726975b6257bd2a0230a","observation_id":"d1ad5470-327f-4601-be46-4ea47ba2a20f","resolution":{"observed_at":"2026-08-06T14:05:47.097125Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:05:47.085929Z","title":null,"venue":null,"work_id":"7f44a4b6-e1dd-4169-a3d8-68e3120eaf76","year":1972},"citing_paper":{"arxiv_id":"2507.19935","last_updated":"2025-07-29T06:02:32Z","snapshot_observed_at":"2026-08-07T21:46:16.772241Z","submitted_at":"2025-07-26T12:42:53Z","title":"Stability of oppositely-propagating pair of Hill's spherical vortices","version":2},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-06T14:05:46.457468Z"},"links":{"citing_paper":"/paper/2507.19935"},"observation_digest":"sha256:1457237b181b0bc55ff43dcd5a3803f52c748159750a13925f9300bfdfb2607d","observation_id":"6271b8e9-7342-46ce-9a59-31487dd4f0a8","resolution":{"observed_at":"2026-08-06T14:05:47.088532Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:05:47.077516Z","title":"Parker, Andrew W","venue":null,"work_id":"e130aeeb-d1f5-4cc9-b6be-b670b3ed23f1","year":2021},"citing_paper":{"arxiv_id":"2507.19935","last_updated":"2025-07-29T06:02:32Z","snapshot_observed_at":"2026-08-07T21:46:16.772241Z","submitted_at":"2025-07-26T12:42:53Z","title":"Stability of oppositely-propagating pair of Hill's spherical vortices","version":2},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-06T14:05:46.460401Z"},"links":{"citing_paper":"/paper/2507.19935"},"observation_digest":"sha256:fa792a7fca51034834e9804cf23e1a393a60c65c14dd2a6777a2a17268dd24b4","observation_id":"19c0cb97-97a1-49ae-bbed-44b3487ec19a","resolution":{"observed_at":"2026-08-06T14:05:47.080526Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:05:47.068977Z","title":"V ortex patches choreography for active scalar equations.J","venue":null,"work_id":"71d5236a-6a0b-4d54-b6fd-baa1aaea3cbc","year":2021},"citing_paper":{"arxiv_id":"2507.19935","last_updated":"2025-07-29T06:02:32Z","snapshot_observed_at":"2026-08-07T21:46:16.772241Z","submitted_at":"2025-07-26T12:42:53Z","title":"Stability of oppositely-propagating pair of Hill's spherical vortices","version":2},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-06T14:05:46.463020Z"},"links":{"citing_paper":"/paper/2507.19935"},"observation_digest":"sha256:1671914c30af55d19a75ef8b434cd91c216c9847d13ea38c726194269db11b78","observation_id":"5dbd0f6a-6ae0-4101-bbc6-d46528b0c433","resolution":{"observed_at":"2026-08-06T14:05:47.072112Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:05:47.060892Z","title":null,"venue":null,"work_id":"31f3d437-ccd6-469e-b77e-82cf2968bdbd","year":2023},"citing_paper":{"arxiv_id":"2507.19935","last_updated":"2025-07-29T06:02:32Z","snapshot_observed_at":"2026-08-07T21:46:16.772241Z","submitted_at":"2025-07-26T12:42:53Z","title":"Stability of oppositely-propagating pair of Hill's spherical vortices","version":2},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-06T14:05:46.465643Z"},"links":{"citing_paper":"/paper/2507.19935"},"observation_digest":"sha256:0172ddee1bb69b63e3895872dd8f0a32699d23519b735435c33e501c9df9dcb0","observation_id":"4cea7672-6cd7-4322-a737-1d4f1b32be0b","resolution":{"observed_at":"2026-08-06T14:05:47.063634Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:05:47.052686Z","title":"Co-rotating vortices with N fold symmetry for the inviscid surface quasi- geostrophic equation","venue":null,"work_id":"7ee2a3cc-9f4f-4cc3-b09d-ba5db940b7ba","year":2023},"citing_paper":{"arxiv_id":"2507.19935","last_updated":"2025-07-29T06:02:32Z","snapshot_observed_at":"2026-08-07T21:46:16.772241Z","submitted_at":"2025-07-26T12:42:53Z","title":"Stability of oppositely-propagating pair of Hill's spherical vortices","version":2},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-06T14:05:46.468371Z"},"links":{"citing_paper":"/paper/2507.19935"},"observation_digest":"sha256:149e2db680cb69a208d04cfa8dd106e5e53f43f9412bb09c6012cb5053e58f74","observation_id":"184266bc-797e-489f-a931-0c8b9d770140","resolution":{"observed_at":"2026-08-06T14:05:47.055613Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:05:47.044201Z","title":"Numerical simulations of two coaxial vortex rings head-on collision","venue":null,"work_id":"6f4d1d2f-6f01-4f67-a9d6-533e2ca5e477","year":2016},"citing_paper":{"arxiv_id":"2507.19935","last_updated":"2025-07-29T06:02:32Z","snapshot_observed_at":"2026-08-07T21:46:16.772241Z","submitted_at":"2025-07-26T12:42:53Z","title":"Stability of oppositely-propagating pair of Hill's spherical vortices","version":2},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-06T14:05:46.471109Z"},"links":{"citing_paper":"/paper/2507.19935"},"observation_digest":"sha256:dbe692205ffd5fadfb4a7a0537dcc8b644e64471341f5b0b90b81293bee86de7","observation_id":"eef249e3-1ea4-4ea7-8283-ce8770cde2ec","resolution":{"observed_at":"2026-08-06T14:05:47.047167Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:05:47.036039Z","title":"Steady asymmetric vortex pairs for Euler equations","venue":null,"work_id":"16d40c02-0a6a-4f0f-bcdf-b6b8cd073db9","year":1939},"citing_paper":{"arxiv_id":"2507.19935","last_updated":"2025-07-29T06:02:32Z","snapshot_observed_at":"2026-08-07T21:46:16.772241Z","submitted_at":"2025-07-26T12:42:53Z","title":"Stability of oppositely-propagating pair of Hill's spherical vortices","version":2},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-06T14:05:46.473836Z"},"links":{"citing_paper":"/paper/2507.19935"},"observation_digest":"sha256:0bb703557878158492842d089adb57b429e9c9a7871cec1484edd1795c61ed74","observation_id":"3d19c583-c749-4fb7-bf1c-56776a9c1726","resolution":{"observed_at":"2026-08-06T14:05:47.038875Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2311.15765","last_updated":"2023-12-05T16:52:59Z","snapshot_observed_at":"2026-07-06T16:53:01.773461Z","submitted_at":"2023-11-27T12:35:27Z","title":"Rigorous derivation of the leapfrogging motion for planar Euler equations","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2311.15765","snapshot_observed_at":"2026-08-06T14:05:46.476478Z","title":"Rigorous derivation of the leapfrogging motion for planar Euler equations","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2507.19935","last_updated":"2025-07-29T06:02:32Z","snapshot_observed_at":"2026-08-07T21:46:16.772241Z","submitted_at":"2025-07-26T12:42:53Z","title":"Stability of oppositely-propagating pair of Hill's spherical vortices","version":2},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-06T14:05:46.476478Z"},"links":{"cited_paper":"/paper/2311.15765","citing_paper":"/paper/2507.19935"},"observation_digest":"sha256:69c5e4c7e8fa95ca09717df1f4ff4893043c952af83e19dbb8785967765df5e1","observation_id":"5b1e229a-1c50-47c1-b8cd-1aae77f220e6","resolution":{"observed_at":"2026-08-06T14:05:46.476478Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:05:47.027459Z","title":null,"venue":null,"work_id":"532c8f82-168f-43c3-ae1c-7544f3ea0bff","year":2022},"citing_paper":{"arxiv_id":"2507.19935","last_updated":"2025-07-29T06:02:32Z","snapshot_observed_at":"2026-08-07T21:46:16.772241Z","submitted_at":"2025-07-26T12:42:53Z","title":"Stability of oppositely-propagating pair of Hill's spherical vortices","version":2},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-06T14:05:46.479258Z"},"links":{"citing_paper":"/paper/2507.19935"},"observation_digest":"sha256:b03ec78d4d3ab34b1eba8d8e806d0a0725ba20e57cec2ba0e9541edbe036a125","observation_id":"82bbd6e6-6bd1-46ee-ad6a-d0b3e81d0816","resolution":{"observed_at":"2026-08-06T14:05:47.030515Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:05:47.019138Z","title":null,"venue":null,"work_id":"330f2a26-ec86-44fa-81ff-d25ba7753529","year":1931},"citing_paper":{"arxiv_id":"2507.19935","last_updated":"2025-07-29T06:02:32Z","snapshot_observed_at":"2026-08-07T21:46:16.772241Z","submitted_at":"2025-07-26T12:42:53Z","title":"Stability of oppositely-propagating pair of Hill's spherical vortices","version":2},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-06T14:05:46.481675Z"},"links":{"citing_paper":"/paper/2507.19935"},"observation_digest":"sha256:bd9274fa2f02715b30dfd7ad69d601585d12260e73d50dd82ddd0c5279933398","observation_id":"2b4ce889-2bf6-44af-84dc-52c4176e4153","resolution":{"observed_at":"2026-08-06T14:05:47.021944Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:05:47.010589Z","title":"Helmholtz","venue":null,"work_id":"7202a023-f30e-43d4-ada8-a12ec5a2e610","year":null},"citing_paper":{"arxiv_id":"2507.19935","last_updated":"2025-07-29T06:02:32Z","snapshot_observed_at":"2026-08-07T21:46:16.772241Z","submitted_at":"2025-07-26T12:42:53Z","title":"Stability of oppositely-propagating pair of Hill's spherical vortices","version":2},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-06T14:05:46.484198Z"},"links":{"citing_paper":"/paper/2507.19935"},"observation_digest":"sha256:ef75ad9960df68f87695536ff153015eaa7453820263fcc6e37e02763c7cb0bc","observation_id":"0ac2a119-5c6a-49f7-84fd-3427cad43838","resolution":{"observed_at":"2026-08-06T14:05:47.013653Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:05:47.001598Z","title":null,"venue":null,"work_id":"cd19fddb-98f3-4fce-9fb1-fb519e61914b","year":null},"citing_paper":{"arxiv_id":"2507.19935","last_updated":"2025-07-29T06:02:32Z","snapshot_observed_at":"2026-08-07T21:46:16.772241Z","submitted_at":"2025-07-26T12:42:53Z","title":"Stability of oppositely-propagating pair of Hill's spherical vortices","version":2},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-06T14:05:46.487194Z"},"links":{"citing_paper":"/paper/2507.19935"},"observation_digest":"sha256:ac7dc17ee0f56321e4e5b9b0416e5a1ef322a0e5336b7e1767b0370a81e506ef","observation_id":"e76a0ada-b852-469b-b7bf-3232fd6c7d73","resolution":{"observed_at":"2026-08-06T14:05:47.004574Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:05:46.993305Z","title":"Existence of corotating and counter-rotating vortex pairs for active scalar equations","venue":null,"work_id":"cd6df0b9-8133-4b48-95d0-c1a15a205c18","year":2017},"citing_paper":{"arxiv_id":"2507.19935","last_updated":"2025-07-29T06:02:32Z","snapshot_observed_at":"2026-08-07T21:46:16.772241Z","submitted_at":"2025-07-26T12:42:53Z","title":"Stability of oppositely-propagating pair of Hill's spherical vortices","version":2},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-06T14:05:46.490264Z"},"links":{"citing_paper":"/paper/2507.19935"},"observation_digest":"sha256:58631ef6956b30c3bcc60982f5202f7543cbdc0ed36e420fdb8202efe9eb6e67","observation_id":"8bf0d025-ef51-48f0-a334-5f52223b63ad","resolution":{"observed_at":"2026-08-06T14:05:46.996349Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:05:46.984538Z","title":"Sideris, and Pascal Gamblin","venue":null,"work_id":"a751f64d-61ff-4a52-a511-92bd341aae82","year":1999},"citing_paper":{"arxiv_id":"2507.19935","last_updated":"2025-07-29T06:02:32Z","snapshot_observed_at":"2026-08-07T21:46:16.772241Z","submitted_at":"2025-07-26T12:42:53Z","title":"Stability of oppositely-propagating pair of Hill's spherical vortices","version":2},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-06T14:05:46.493122Z"},"links":{"citing_paper":"/paper/2507.19935"},"observation_digest":"sha256:a2561a0c31de9b404a0c26f157c8925fea13ecc5e3af2602fcb951523b21bb98","observation_id":"cf81d041-fe95-42f1-8dcb-f0ee1895491a","resolution":{"observed_at":"2026-08-06T14:05:46.987581Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:05:46.975606Z","title":"V orlesungen¨uber mathematische Physik, volume 1","venue":null,"work_id":"cf94a25d-78d2-4a03-8b7c-11566f40c621","year":null},"citing_paper":{"arxiv_id":"2507.19935","last_updated":"2025-07-29T06:02:32Z","snapshot_observed_at":"2026-08-07T21:46:16.772241Z","submitted_at":"2025-07-26T12:42:53Z","title":"Stability of oppositely-propagating pair of Hill's spherical vortices","version":2},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-06T14:05:46.495565Z"},"links":{"citing_paper":"/paper/2507.19935"},"observation_digest":"sha256:db0501e5e01330b27fd5d73c14a58230813dee8b9b82af536389c9cbf37d585d","observation_id":"763afe03-0693-4c32-9d6d-a964b06b9ed5","resolution":{"observed_at":"2026-08-06T14:05:46.978844Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:05:46.967155Z","title":null,"venue":null,"work_id":"941f1582-4bf8-484f-a2f3-faf5be3a1438","year":2014},"citing_paper":{"arxiv_id":"2507.19935","last_updated":"2025-07-29T06:02:32Z","snapshot_observed_at":"2026-08-07T21:46:16.772241Z","submitted_at":"2025-07-26T12:42:53Z","title":"Stability of oppositely-propagating pair of Hill's spherical vortices","version":2},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-06T14:05:46.498240Z"},"links":{"citing_paper":"/paper/2507.19935"},"observation_digest":"sha256:b6c248a5806ea44b2338434cf4b6e77e282c1aa5d1b970ea5ad8b3e247e7bbd0","observation_id":"6df50821-511d-4641-a836-cb69254ead0e","resolution":{"observed_at":"2026-08-06T14:05:46.969936Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:05:46.958384Z","title":null,"venue":null,"work_id":"b563649c-eeef-4c6b-bf87-dc5f5401224a","year":2010},"citing_paper":{"arxiv_id":"2507.19935","last_updated":"2025-07-29T06:02:32Z","snapshot_observed_at":"2026-08-07T21:46:16.772241Z","submitted_at":"2025-07-26T12:42:53Z","title":"Stability of oppositely-propagating pair of Hill's spherical vortices","version":2},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-06T14:05:46.500706Z"},"links":{"citing_paper":"/paper/2507.19935"},"observation_digest":"sha256:90e6dbc80bdcf66b97b9482031858c4514f6be7c0608bbfccf6803416bd2b1c5","observation_id":"25b27f74-6122-4ed4-9670-55d89bd03cce","resolution":{"observed_at":"2026-08-06T14:05:46.961555Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:05:46.949985Z","title":null,"venue":null,"work_id":"14eb2a50-2d03-4c63-b76e-5e3acd1b70b1","year":2022},"citing_paper":{"arxiv_id":"2507.19935","last_updated":"2025-07-29T06:02:32Z","snapshot_observed_at":"2026-08-07T21:46:16.772241Z","submitted_at":"2025-07-26T12:42:53Z","title":"Stability of oppositely-propagating pair of Hill's spherical vortices","version":2},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-06T14:05:46.503676Z"},"links":{"citing_paper":"/paper/2507.19935"},"observation_digest":"sha256:f256a0c19ba2f0ad50edd6d69ec0e7bbab344c70b44125e8b6cefe85fcf275b5","observation_id":"ca7f31a6-1ea4-41d9-9c74-3aabf9edccce","resolution":{"observed_at":"2026-08-06T14:05:46.952780Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:05:46.941630Z","title":null,"venue":null,"work_id":"8619dfd1-3444-41c2-ac87-6b2c2f3649b1","year":2002},"citing_paper":{"arxiv_id":"2507.19935","last_updated":"2025-07-29T06:02:32Z","snapshot_observed_at":"2026-08-07T21:46:16.772241Z","submitted_at":"2025-07-26T12:42:53Z","title":"Stability of oppositely-propagating pair of Hill's spherical vortices","version":2},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-06T14:05:46.506174Z"},"links":{"citing_paper":"/paper/2507.19935"},"observation_digest":"sha256:de678b214e9f3837edd2a847d4c5455f9848e3912b7fd8d3a840cb632f6d1ee8","observation_id":"08be6f88-3d59-4c19-97ae-471577253cca","resolution":{"observed_at":"2026-08-06T14:05:46.944468Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:05:46.932596Z","title":"Hydrodynamics","venue":null,"work_id":"218fa69d-d3e3-46cd-b14e-44aa1bbda649","year":1993},"citing_paper":{"arxiv_id":"2507.19935","last_updated":"2025-07-29T06:02:32Z","snapshot_observed_at":"2026-08-07T21:46:16.772241Z","submitted_at":"2025-07-26T12:42:53Z","title":"Stability of oppositely-propagating pair of Hill's spherical vortices","version":2},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-06T14:05:46.509106Z"},"links":{"citing_paper":"/paper/2507.19935"},"observation_digest":"sha256:b435eda737b45cf6adf6afa3179588d3a5d7de66b26fc3e55731fa372f151b76","observation_id":"337c17ef-82eb-476e-a8c1-88383e8189fa","resolution":{"observed_at":"2026-08-06T14:05:46.935644Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:05:46.924351Z","title":"Leoncini, L","venue":null,"work_id":"6cd5471f-5a8c-41ab-a29d-63f06de3be1d","year":1911},"citing_paper":{"arxiv_id":"2507.19935","last_updated":"2025-07-29T06:02:32Z","snapshot_observed_at":"2026-08-07T21:46:16.772241Z","submitted_at":"2025-07-26T12:42:53Z","title":"Stability of oppositely-propagating pair of Hill's spherical vortices","version":2},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-06T14:05:46.511598Z"},"links":{"citing_paper":"/paper/2507.19935"},"observation_digest":"sha256:0a3e450c26e9ec6bcd5c9e7df03da031081dd3a27343f4800945059a12f1edac","observation_id":"dbde9e99-f02b-486e-b36a-3090e24ca362","resolution":{"observed_at":"2026-08-06T14:05:46.927126Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:05:46.916078Z","title":null,"venue":null,"work_id":"e6b44f7e-c298-4180-8468-4ffe02272b91","year":1941},"citing_paper":{"arxiv_id":"2507.19935","last_updated":"2025-07-29T06:02:32Z","snapshot_observed_at":"2026-08-07T21:46:16.772241Z","submitted_at":"2025-07-26T12:42:53Z","title":"Stability of oppositely-propagating pair of Hill's spherical vortices","version":2},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-06T14:05:46.514608Z"},"links":{"citing_paper":"/paper/2507.19935"},"observation_digest":"sha256:bf701d5954ed5ebf7e0b3a30eedb5f083897fb8d0a7937c73702fb404e8d4e17","observation_id":"23c299f2-f980-4cd6-b3a3-0cac6819b4dc","resolution":{"observed_at":"2026-08-06T14:05:46.918780Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:05:46.907572Z","title":null,"venue":null,"work_id":"3b39b0d6-a79b-45a1-9831-333ebd6eb535","year":1941},"citing_paper":{"arxiv_id":"2507.19935","last_updated":"2025-07-29T06:02:32Z","snapshot_observed_at":"2026-08-07T21:46:16.772241Z","submitted_at":"2025-07-26T12:42:53Z","title":"Stability of oppositely-propagating pair of Hill's spherical vortices","version":2},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-06T14:05:46.517372Z"},"links":{"citing_paper":"/paper/2507.19935"},"observation_digest":"sha256:a4416a6fde2526a8e446fddffe8036cb161091a349958f045d27dbc5aaaf0099","observation_id":"53b8bf82-7003-45e6-8a80-524b906e5d19","resolution":{"observed_at":"2026-08-06T14:05:46.910255Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:05:46.898993Z","title":null,"venue":null,"work_id":"2489415b-5b90-4e17-a216-a0a6203882c7","year":2001},"citing_paper":{"arxiv_id":"2507.19935","last_updated":"2025-07-29T06:02:32Z","snapshot_observed_at":"2026-08-07T21:46:16.772241Z","submitted_at":"2025-07-26T12:42:53Z","title":"Stability of oppositely-propagating pair of Hill's spherical vortices","version":2},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-06T14:05:46.519874Z"},"links":{"citing_paper":"/paper/2507.19935"},"observation_digest":"sha256:599617b7bbf84c4b6c1dbcbcff5cd2156e65974adcd762388ce17b6eba620fc1","observation_id":"06d5117f-42a8-43b5-8b61-b2dd8a0ca6dd","resolution":{"observed_at":"2026-08-06T14:05:46.901805Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:05:46.889782Z","title":null,"venue":null,"work_id":"ec1d4591-d4af-4bdc-8322-8ec44d4ac40a","year":1972},"citing_paper":{"arxiv_id":"2507.19935","last_updated":"2025-07-29T06:02:32Z","snapshot_observed_at":"2026-08-07T21:46:16.772241Z","submitted_at":"2025-07-26T12:42:53Z","title":"Stability of oppositely-propagating pair of Hill's spherical vortices","version":2},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-06T14:05:46.522594Z"},"links":{"citing_paper":"/paper/2507.19935"},"observation_digest":"sha256:dc96ad3d4845c72ddb61a29cbb499079ea060e38b0bb0c16ec1c698c59981d1d","observation_id":"7281ba10-ffe2-4676-b368-1cbe3ace70f8","resolution":{"observed_at":"2026-08-06T14:05:46.893293Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:05:46.880935Z","title":null,"venue":null,"work_id":"42b1612f-80c6-446c-9a66-0e2135aa140a","year":1973},"citing_paper":{"arxiv_id":"2507.19935","last_updated":"2025-07-29T06:02:32Z","snapshot_observed_at":"2026-08-07T21:46:16.772241Z","submitted_at":"2025-07-26T12:42:53Z","title":"Stability of oppositely-propagating pair of Hill's spherical vortices","version":2},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-08-06T14:05:46.525171Z"},"links":{"citing_paper":"/paper/2507.19935"},"observation_digest":"sha256:a38674896d9e951fcf83b0ceedd9adc39fb54fdcf189ad6eb947816c66dc0caa","observation_id":"d2edb037-b3d1-4f6d-addf-486fa78be943","resolution":{"observed_at":"2026-08-06T14:05:46.883805Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:05:46.872487Z","title":null,"venue":null,"work_id":"9733654e-cf75-4580-a2c2-513970621ab0","year":1979},"citing_paper":{"arxiv_id":"2507.19935","last_updated":"2025-07-29T06:02:32Z","snapshot_observed_at":"2026-08-07T21:46:16.772241Z","submitted_at":"2025-07-26T12:42:53Z","title":"Stability of oppositely-propagating pair of Hill's spherical vortices","version":2},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-08-06T14:05:46.527771Z"},"links":{"citing_paper":"/paper/2507.19935"},"observation_digest":"sha256:9c077948e21232e7ef1b0dc447edcc7c21f43f821dddaa4915a4e30c2d89de6d","observation_id":"942a9829-5810-43d8-a49f-7940e627e9cf","resolution":{"observed_at":"2026-08-06T14:05:46.875337Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:05:46.863394Z","title":"Head-on Collision of Two Vortex Rings","venue":null,"work_id":"3245b3b2-0ee0-4162-8d49-5246b1e6d2ea","year":1978},"citing_paper":{"arxiv_id":"2507.19935","last_updated":"2025-07-29T06:02:32Z","snapshot_observed_at":"2026-08-07T21:46:16.772241Z","submitted_at":"2025-07-26T12:42:53Z","title":"Stability of oppositely-propagating pair of Hill's spherical vortices","version":2},"reference_index":58,"source":"pdf_text","source_observed_at":"2026-08-06T14:05:46.530178Z"},"links":{"citing_paper":"/paper/2507.19935"},"observation_digest":"sha256:a9fe3cad3d9dd89c858c8212c1b4c74b7b633792534dcbca2ca27b454f991270","observation_id":"5508da21-5cd3-448f-b914-91a2a00838cc","resolution":{"observed_at":"2026-08-06T14:05:46.866350Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:05:46.854353Z","title":"Pozrikidis","venue":null,"work_id":"d24cc02b-a50b-4fd4-ba8b-5d8c65ed233a","year":1986},"citing_paper":{"arxiv_id":"2507.19935","last_updated":"2025-07-29T06:02:32Z","snapshot_observed_at":"2026-08-07T21:46:16.772241Z","submitted_at":"2025-07-26T12:42:53Z","title":"Stability of oppositely-propagating pair of Hill's spherical vortices","version":2},"reference_index":59,"source":"pdf_text","source_observed_at":"2026-08-06T14:05:46.532637Z"},"links":{"citing_paper":"/paper/2507.19935"},"observation_digest":"sha256:3fa772c82bd4cb352a2128071d1fedc022acad1388fc9252d14408ac10e73b9f","observation_id":"95af3fce-f2db-4e27-847c-7a130914e94d","resolution":{"observed_at":"2026-08-06T14:05:46.857036Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:05:46.845410Z","title":"Linear stability of Hill’s vortex to axisymmetric perturbations","venue":null,"work_id":"44f28afa-7439-4f79-9e93-352fd8337466","year":2016},"citing_paper":{"arxiv_id":"2507.19935","last_updated":"2025-07-29T06:02:32Z","snapshot_observed_at":"2026-08-07T21:46:16.772241Z","submitted_at":"2025-07-26T12:42:53Z","title":"Stability of oppositely-propagating pair of Hill's spherical vortices","version":2},"reference_index":60,"source":"pdf_text","source_observed_at":"2026-08-06T14:05:46.535928Z"},"links":{"citing_paper":"/paper/2507.19935"},"observation_digest":"sha256:4afe6b944b21b8bb21f6ad91f5ba4385da8b023aa47fa374bcc377885eefe255","observation_id":"827aa179-72b9-41e4-a084-02d3d7cf4b7f","resolution":{"observed_at":"2026-08-06T14:05:46.848615Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:05:46.836328Z","title":"V ortex rings","venue":null,"work_id":"812876c4-6851-40c7-9508-dc0199ae74de","year":1992},"citing_paper":{"arxiv_id":"2507.19935","last_updated":"2025-07-29T06:02:32Z","snapshot_observed_at":"2026-08-07T21:46:16.772241Z","submitted_at":"2025-07-26T12:42:53Z","title":"Stability of oppositely-propagating pair of Hill's spherical vortices","version":2},"reference_index":61,"source":"pdf_text","source_observed_at":"2026-08-06T14:05:46.538238Z"},"links":{"citing_paper":"/paper/2507.19935"},"observation_digest":"sha256:017d96e589955ffd5fb7db44837f3f3c0d0d08f64a0acb52122fa4cf65084810","observation_id":"3196bfc7-1c50-4a22-88dc-2704a803c7d3","resolution":{"observed_at":"2026-08-06T14:05:46.839101Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:05:46.826979Z","title":"Zabusky, and Joel H","venue":null,"work_id":"70dccd68-3243-484b-b955-1fce3900c144","year":1988},"citing_paper":{"arxiv_id":"2507.19935","last_updated":"2025-07-29T06:02:32Z","snapshot_observed_at":"2026-08-07T21:46:16.772241Z","submitted_at":"2025-07-26T12:42:53Z","title":"Stability of oppositely-propagating pair of Hill's spherical vortices","version":2},"reference_index":62,"source":"pdf_text","source_observed_at":"2026-08-06T14:05:46.540710Z"},"links":{"citing_paper":"/paper/2507.19935"},"observation_digest":"sha256:87f413a398cc786f358344ab80ce6d8d91bd37fa3ea20ff1a7d2b053cbfb22f3","observation_id":"bb413bdf-6995-4948-b55a-22d6b114edb2","resolution":{"observed_at":"2026-08-06T14:05:46.830157Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:05:46.817262Z","title":"Instability of vortex pair leapfrogging","venue":null,"work_id":"496914cd-7fd7-46ca-9037-ebf9fd70b26a","year":2013},"citing_paper":{"arxiv_id":"2507.19935","last_updated":"2025-07-29T06:02:32Z","snapshot_observed_at":"2026-08-07T21:46:16.772241Z","submitted_at":"2025-07-26T12:42:53Z","title":"Stability of oppositely-propagating pair of Hill's spherical vortices","version":2},"reference_index":63,"source":"pdf_text","source_observed_at":"2026-08-06T14:05:46.543256Z"},"links":{"citing_paper":"/paper/2507.19935"},"observation_digest":"sha256:55a60c0f14d756bc80c3106f1fa96e820bb56546c4d98e1fa42bc2b3c9639c83","observation_id":"7ad8f413-bde2-4e08-85ff-6e7df319a0d2","resolution":{"observed_at":"2026-08-06T14:05:46.820421Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:05:46.546039Z","title":"On steady vortex flow in two dimensions","venue":null,"work_id":null,"year":1983},"citing_paper":{"arxiv_id":"2507.19935","last_updated":"2025-07-29T06:02:32Z","snapshot_observed_at":"2026-08-07T21:46:16.772241Z","submitted_at":"2025-07-26T12:42:53Z","title":"Stability of oppositely-propagating pair of Hill's spherical vortices","version":2},"reference_index":64,"source":"pdf_text","source_observed_at":"2026-08-06T14:05:46.546039Z"},"links":{"citing_paper":"/paper/2507.19935"},"observation_digest":"sha256:93047e272853865de61d0b3839ab6ee6e48f036f74a01e85b2ba1c9ba6a21380","observation_id":"e4764edd-863e-4759-8305-4c0864a3daa5","resolution":{"observed_at":"2026-08-06T14:05:46.546039Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:05:46.802420Z","title":"Variational principles for Hill’s spherical vortex and nearly spherical vortices","venue":null,"work_id":"baed7f78-75d5-46f4-82b3-3954ac0b6728","year":1988},"citing_paper":{"arxiv_id":"2507.19935","last_updated":"2025-07-29T06:02:32Z","snapshot_observed_at":"2026-08-07T21:46:16.772241Z","submitted_at":"2025-07-26T12:42:53Z","title":"Stability of oppositely-propagating pair of Hill's spherical vortices","version":2},"reference_index":65,"source":"pdf_text","source_observed_at":"2026-08-06T14:05:46.548468Z"},"links":{"citing_paper":"/paper/2507.19935"},"observation_digest":"sha256:45534bbd1077be5c55e8f400c69211380faf8b6ba3e7328df97d884148bfdadb","observation_id":"40c760be-f01e-4631-877a-0f2d618af0aa","resolution":{"observed_at":"2026-08-06T14:05:46.805587Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:05:46.793206Z","title":"V ortex motion of the Euler and lake equations.J","venue":null,"work_id":"11d9cb1e-d3fa-4cf2-b5ba-7a6c98871382","year":2021},"citing_paper":{"arxiv_id":"2507.19935","last_updated":"2025-07-29T06:02:32Z","snapshot_observed_at":"2026-08-07T21:46:16.772241Z","submitted_at":"2025-07-26T12:42:53Z","title":"Stability of oppositely-propagating pair of Hill's spherical vortices","version":2},"reference_index":66,"source":"pdf_text","source_observed_at":"2026-08-06T14:05:46.551200Z"},"links":{"citing_paper":"/paper/2507.19935"},"observation_digest":"sha256:6eb6e143feb9e5e2cdd6b5c2d5a9771b1111acd5054f2944f49e796876fb1993","observation_id":"13ecfbd2-5ace-47b3-a2e0-de222fec7853","resolution":{"observed_at":"2026-08-06T14:05:46.796111Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:05:46.784481Z","title":"From point vortices to vortex patches in self-similar expanding configurations","venue":null,"work_id":"26eb38fd-eba2-45f7-b65d-1dd47589c656","year":2021},"citing_paper":{"arxiv_id":"2507.19935","last_updated":"2025-07-29T06:02:32Z","snapshot_observed_at":"2026-08-07T21:46:16.772241Z","submitted_at":"2025-07-26T12:42:53Z","title":"Stability of oppositely-propagating pair of Hill's spherical vortices","version":2},"reference_index":67,"source":"pdf_text","source_observed_at":"2026-08-06T14:05:46.554013Z"},"links":{"citing_paper":"/paper/2507.19935"},"observation_digest":"sha256:5953ce1881cd885d14dd651942488e75e8e85042f2007d9d9b2aa092e7059123","observation_id":"5e410583-7cbd-4e0e-b79b-2b3d84f62175","resolution":{"observed_at":"2026-08-06T14:05:46.787584Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2507.19935","last_updated":"2025-07-29T06:02:32Z","latest_version":2,"primary_category":"math.AP","snapshot_observed_at":"2026-08-07T21:46:16.772241Z","submitted_at":"2025-07-26T12:42:53Z","title":"Stability of oppositely-propagating pair of Hill's spherical vortices"},"reference_resolution":{"displayed":67,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":26,"verified_exact":2,"verified_fuzzy":39},"total_outbound_references":67},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"thesis":"As of 9 August 2026, this Paper Citation Record lists 67 of 67 outbound references and 0 inbound Pith citation observations for arXiv:2507.19935."}