{"as_of":"2026-08-09T05:06:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:62974a6eed0534a762c043233fcc0dcc589cd279d81ead293ef25e1602661bef","coverage":[{"denominator":87,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":87,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T18:31:09.058829Z","state":"measured"},{"denominator":87,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":87,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-08T06:32:00.761636+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/2507.08326/citation-record","integrity":"/paper/2507.08326/integrity","json":"/paper/2507.08326/citation-record.json","paper":"/paper/2507.08326"},"outbound":[{"citation":{"cited_paper":{"arxiv_id":"1903.03859","last_updated":"2025-04-16T16:41:05Z","snapshot_observed_at":"2026-08-08T21:43:19.067967Z","submitted_at":"2019-03-09T19:43:37Z","title":"Stability for linearized gravity on the Kerr spacetime","version":3},"cited_work":{"arxiv_id":"1903.03859","doi":null,"metadata_source":"pith","pith_arxiv_id":"1903.03859","snapshot_observed_at":"2026-08-06T18:31:09.546139Z","title":"Stability for linearized gravity on the Kerr spacetime","venue":"math.AP","work_id":"4f26718b-ba46-47dd-8503-6f67f9cfa798","year":2019},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:07.197580Z"},"links":{"cited_paper":"/paper/1903.03859","citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:a634da030c594d931e7cb4e8f62378b87122aac351c5e762b7333da1198c9ddc","observation_id":"214ae38e-9e3b-45ea-bda2-d8c39d52ddf4","resolution":{"observed_at":"2026-08-06T18:31:09.548283Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"0908.2265","last_updated":"2015-09-03T15:53:12Z","snapshot_observed_at":"2026-07-06T01:56:49.388663Z","submitted_at":"2009-08-16T22:05:01Z","title":"Hidden symmetries and decay for the wave equation on the Kerr spacetime","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"0908.2265","snapshot_observed_at":"2026-08-06T18:31:07.367876Z","title":null,"venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:07.367876Z"},"links":{"cited_paper":"/paper/0908.2265","citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:922aa8c269b6ffaa79a17d9a08f6b442e45f27b9146433cdcdd462f4e6ba4b4d","observation_id":"bac07c76-f0a1-4e5a-8727-3ef08fa4fa01","resolution":{"observed_at":"2026-08-06T18:31:07.367876Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1310.2664","last_updated":"2015-09-03T15:24:58Z","snapshot_observed_at":"2026-07-06T03:25:14.020835Z","submitted_at":"2013-10-09T23:58:03Z","title":"Uniform energy bound and asymptotics for the Maxwell field on a slowly rotating Kerr black hole exterior","version":3},"cited_work":{"arxiv_id":"1310.2664","doi":null,"metadata_source":"pith","pith_arxiv_id":"1310.2664","snapshot_observed_at":"2026-08-06T18:31:09.532743Z","title":"Uniform energy bound and asymptotics for the Maxwell field on a slowly rotating Kerr black hole exterior","venue":"math.AP","work_id":"cae72366-aade-4423-8ff0-0d2984d6da81","year":2013},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:07.529304Z"},"links":{"cited_paper":"/paper/1310.2664","citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:e3fa505ff7793665c357784c2d5cdd1f2d78cb07b942f59135041352c178cb78","observation_id":"af13dc18-bfe8-49c8-af0f-2b8c789565ae","resolution":{"observed_at":"2026-08-06T18:31:09.535684Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1501.00616","last_updated":"2017-06-27T19:38:39Z","snapshot_observed_at":"2026-08-06T23:16:18.625792Z","submitted_at":"2015-01-04T00:55:34Z","title":"Global Regularity for the 2+1 Dimensional Equivariant Einstein-Wave Map System","version":4},"cited_work":{"arxiv_id":"1501.00616","doi":null,"metadata_source":"pith","pith_arxiv_id":"1501.00616","snapshot_observed_at":"2026-08-06T18:31:09.524814Z","title":"Global Regularity for the 2+1 Dimensional Equivariant Einstein-Wave Map System","venue":"math.AP","work_id":"25a8327a-802d-42f9-9c65-eb745855b849","year":2015},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:07.692222Z"},"links":{"cited_paper":"/paper/1501.00616","citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:2449f1c02a2605a988168749ce9d06a5cf4ce45130de1aa8e4a91f66188ca6dd","observation_id":"3a70a4a9-8cc6-4c1a-a968-923e2cc47158","resolution":{"observed_at":"2026-08-06T18:31:09.527053Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"gr-qc/0405109","last_updated":"2004-05-19T17:49:35Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2004-05-19T17:49:35Z","title":"The Dynamics of General Relativity","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"gr-qc/0405109","snapshot_observed_at":"2026-08-06T18:31:07.847939Z","title":null,"venue":null,"work_id":null,"year":1962},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:07.847939Z"},"links":{"cited_paper":"/paper/gr-qc/0405109","citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:35c7fe7ade8757083c828552938917dcf65e13bca999ace22d91b00db506823d","observation_id":"544e1359-5f2d-4ad8-a663-c4b6464f8858","resolution":{"observed_at":"2026-08-06T18:31:07.847939Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"gr-qc/9406040","last_updated":"1994-06-22T19:51:49Z","snapshot_observed_at":"2026-07-07T03:24:45.763672Z","submitted_at":"1994-06-22T19:51:49Z","title":"A Striking Property of the Gravitational Hamiltonian","version":1},"cited_work":{"arxiv_id":"gr-qc/9406040","doi":null,"metadata_source":"pith","pith_arxiv_id":"gr-qc/9406040","snapshot_observed_at":"2026-08-06T18:31:09.511821Z","title":"A Striking Property of the Gravitational Hamiltonian","venue":"gr-qc","work_id":"2abed784-f944-4e4e-9220-b34b589c20d7","year":1994},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:07.858146Z"},"links":{"cited_paper":"/paper/gr-qc/9406040","citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:10923c38b63378e83e148a7ffa6aeeca895b26853df5acf1810a4b8f68599621","observation_id":"9303aee3-6a42-4cc9-8fc2-1242af8d6f9d","resolution":{"observed_at":"2026-08-06T18:31:09.514188Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"0710.4102","last_updated":"2007-10-22T16:50:47Z","snapshot_observed_at":"2026-07-06T01:31:36.843459Z","submitted_at":"2007-10-22T16:50:47Z","title":"Decay of the Maxwell field on the Schwarzschild manifold","version":1},"cited_work":{"arxiv_id":"0710.4102","doi":null,"metadata_source":"pith","pith_arxiv_id":"0710.4102","snapshot_observed_at":"2026-08-06T18:31:09.503934Z","title":"Decay of the Maxwell field on the Schwarzschild manifold","venue":"math.AP","work_id":"df11d39b-4bbc-443b-9ff8-842e5d70247b","year":2007},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:07.989083Z"},"links":{"cited_paper":"/paper/0710.4102","citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:188963a7f55f8b79c8fb028e1fbff5e7b602d85fea168a3cc5ecee075adb80cb","observation_id":"11c08c42-660a-42ab-8332-b219158b5681","resolution":{"observed_at":"2026-08-06T18:31:09.506332Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T18:31:08.149105Z","title":"Physics 7 (1959), 466–483","venue":null,"work_id":null,"year":1959},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:08.149105Z"},"links":{"citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:e7b2f32137a1bf350624a9e72cd84dab028b79a265346ecadbde8c0cd8ee3194","observation_id":"0859905f-6e60-400d-90db-9fcdda49b0c9","resolution":{"observed_at":"2026-08-06T18:31:08.149105Z","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":"2026-08-06T18:31:08.299318Z","title":"Thesis, University of New England, 1983","venue":null,"work_id":null,"year":1983},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:08.299318Z"},"links":{"citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:cc5609e23baa2bf9adcca9842d1600d17d1bbbf879a957913e080824623d8759","observation_id":"ccfc151a-6dcb-4e53-b057-21ab3386cb0d","resolution":{"observed_at":"2026-08-06T18:31:08.299318Z","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":"2026-08-06T18:31:08.351120Z","title":null,"venue":null,"work_id":null,"year":1971},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:08.351120Z"},"links":{"citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:7e1c99d2d225ca104dc5a45012899298a83353a44441c65283e3c1c2783c6a28","observation_id":"29ce73b6-25c6-4675-b56c-3a4e5df08431","resolution":{"observed_at":"2026-08-06T18:31:08.351120Z","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":"2026-08-06T18:31:08.435085Z","title":null,"venue":null,"work_id":null,"year":1983},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:08.435085Z"},"links":{"citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:135372210b7f0a89688345c83e81eee3e541d19ed54bb43b284e42098bf1c7d3","observation_id":"34fa9714-685d-4806-a160-ffea0fd2d88e","resolution":{"observed_at":"2026-08-06T18:31:08.435085Z","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":"2026-08-06T18:31:08.597381Z","title":null,"venue":null,"work_id":null,"year":1969},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:08.597381Z"},"links":{"citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:4a2baafadc1e24a4037d6f52a3d379ee8ceefe5022863d6a73435770f4d71ae0","observation_id":"3948ea24-bce9-49e5-9c9a-86a0a34a47e9","resolution":{"observed_at":"2026-08-06T18:31:08.597381Z","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":"2026-08-06T18:31:08.709995Z","title":null,"venue":null,"work_id":null,"year":1994},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:08.709995Z"},"links":{"citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:9f6cb7c30fd579c506c9c2c44bda95c3c6ce6897f8a4fd6a571d2b8d1f3f42fa","observation_id":"abf6ab13-423e-4602-896a-20ca222abfb4","resolution":{"observed_at":"2026-08-06T18:31:08.709995Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"gr-qc/0112049","last_updated":"2001-12-19T12:53:41Z","snapshot_observed_at":"2026-07-07T03:15:09.086095Z","submitted_at":"2001-12-19T12:53:41Z","title":"Future Global in time einsteinian spacetimes with U(1) isometry group","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"gr-qc/0112049","snapshot_observed_at":"2026-08-06T18:31:08.849770Z","title":"Henri Poincar´ e2 (2001), 1007–1064, arXiv:gr-qc/0112049","venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:08.849770Z"},"links":{"cited_paper":"/paper/gr-qc/0112049","citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:7dda7f50912b45bb6aff3719c67672cc1e53f3990684336f44f40e741daed2b1","observation_id":"62fa0add-3dc4-4d3d-9573-9e3d9cc5ccff","resolution":{"observed_at":"2026-08-06T18:31:08.849770Z","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":"2026-08-06T18:31:08.898933Z","title":"Pure Appl","venue":null,"work_id":null,"year":1993},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:08.898933Z"},"links":{"citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:e782c43e7e90e5b2556ddb4b9a0f78cd72c22766cc3fc7dfc92ec17816f74c70","observation_id":"4403a3a1-b8aa-4662-bbe5-8987b5672e2e","resolution":{"observed_at":"2026-08-06T18:31:08.898933Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1711.07944","last_updated":"2017-11-21T18:15:42Z","snapshot_observed_at":"2026-07-06T06:10:36.816766Z","submitted_at":"2017-11-21T18:15:42Z","title":"Boundedness and decay for the Teukolsky equation on Kerr spacetimes I: the case $|a|\\ll M$","version":1},"cited_work":{"arxiv_id":"1711.07944","doi":null,"metadata_source":"pith","pith_arxiv_id":"1711.07944","snapshot_observed_at":"2026-08-06T18:31:09.491158Z","title":"Boundedness and decay for the Teukolsky equation on Kerr spacetimes I: the case $|a|\\ll M$","venue":"gr-qc","work_id":"411cd00f-a521-49b0-bd09-0b7af8825999","year":2017},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:08.901500Z"},"links":{"cited_paper":"/paper/1711.07944","citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:231845d1476d4cae15f48bbf3195db576acb82a38b1fb904f2aa5b7b9207c647","observation_id":"0d11a25e-41cd-46a7-a690-7b70f4648ae0","resolution":{"observed_at":"2026-08-06T18:31:09.493269Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1601.06467","last_updated":"2016-01-25T02:38:24Z","snapshot_observed_at":"2026-07-06T04:43:54.315116Z","submitted_at":"2016-01-25T02:38:24Z","title":"The linear stability of the Schwarzschild solution to gravitational perturbations","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1601.06467","snapshot_observed_at":"2026-08-06T18:31:08.904329Z","title":"222 (2019), 1–214, arXiv:1601.06467","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:08.904329Z"},"links":{"cited_paper":"/paper/1601.06467","citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:49b4ad6bdd04c20cebe599d1adb4db6040c633cbc10d627138b8b12b70f5eff1","observation_id":"26d0c5bf-e2b6-4309-8d0e-aa5d09fe2eed","resolution":{"observed_at":"2026-08-06T18:31:08.904329Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2104.08222","last_updated":"2021-04-16T16:57:31Z","snapshot_observed_at":"2026-07-06T11:00:25.253720Z","submitted_at":"2021-04-16T16:57:31Z","title":"The non-linear stability of the Schwarzschild family of black holes","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2104.08222","snapshot_observed_at":"2026-08-06T18:31:08.906868Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:08.906868Z"},"links":{"cited_paper":"/paper/2104.08222","citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:30823adbfa0757839757cd7cbf84bb8baad3664fb240997bd526d8c358b21e40","observation_id":"79c0537e-92d9-4b60-91f0-3f684c9b9723","resolution":{"observed_at":"2026-08-06T18:31:08.906868Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"0805.4309","last_updated":"2008-05-28T11:02:00Z","snapshot_observed_at":"2026-07-06T01:37:55.988709Z","submitted_at":"2008-05-28T11:02:00Z","title":"A proof of the uniform boundedness of solutions to the wave equation on slowly rotating Kerr backgrounds","version":1},"cited_work":{"arxiv_id":"0805.4309","doi":null,"metadata_source":"pith","pith_arxiv_id":"0805.4309","snapshot_observed_at":"2026-08-06T18:31:09.471540Z","title":"A proof of the uniform boundedness of solutions to the wave equation on slowly rotating Kerr backgrounds","venue":"gr-qc","work_id":"bc2275b1-861b-41ea-82ee-2ac1aa1f16fa","year":2008},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:08.909273Z"},"links":{"cited_paper":"/paper/0805.4309","citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:f8af127a0345f8d6ad8b35fd0fb99cff632447372a0a9d320a376cd145fa7bba","observation_id":"213c2098-72c7-4e58-b00f-9462aeba2885","resolution":{"observed_at":"2026-08-06T18:31:09.473784Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1402.7034","last_updated":"2014-12-29T15:08:48Z","snapshot_observed_at":"2026-07-06T03:37:12.405200Z","submitted_at":"2014-02-27T19:33:02Z","title":"Decay for solutions of the wave equation on Kerr exterior spacetimes III: The full subextremal case |a| < M","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1402.7034","snapshot_observed_at":"2026-08-06T18:31:08.911114Z","title":null,"venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:08.911114Z"},"links":{"cited_paper":"/paper/1402.7034","citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:1ad3c278552ef72fe9d3400b5d2b61673650ab8bead6eda69b024d1a07328433","observation_id":"c425bca4-6ac7-4acf-99b7-9bc626bfae21","resolution":{"observed_at":"2026-08-06T18:31:08.911114Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"0804.2679","last_updated":"2009-06-02T13:38:55Z","snapshot_observed_at":"2026-08-08T16:38:07.836610Z","submitted_at":"2008-04-16T20:37:34Z","title":"Axisymmetric evolution of Einstein equations and mass conservation","version":3},"cited_work":{"arxiv_id":"0804.2679","doi":null,"metadata_source":"pith","pith_arxiv_id":"0804.2679","snapshot_observed_at":"2026-08-06T18:31:09.459038Z","title":"Axisymmetric evolution of Einstein equations and mass conservation","venue":"gr-qc","work_id":"769a1336-caa1-4b11-95f8-c6e21696565f","year":2008},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:08.913206Z"},"links":{"cited_paper":"/paper/0804.2679","citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:f2526cd4b90c42e9574f6e9e2ca78ebc0d989369abb81ce3d68c1e5d56428ee2","observation_id":"53b50442-6402-4ad2-bea0-ad244abaaf5b","resolution":{"observed_at":"2026-08-06T18:31:09.460986Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T18:31:09.713729Z","title":null,"venue":null,"work_id":"15afdf77-adbd-442b-ae43-c5db09866249","year":2014},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:08.915301Z"},"links":{"citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:9da8584d704033c97e6b54dd050c66cd017d55a2484e906db169394353f142a8","observation_id":"6806a1c3-25ef-468f-ae3a-cbc8d62f7ea9","resolution":{"observed_at":"2026-08-06T18:31:09.715741Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"0801.3471","last_updated":"2008-02-14T15:52:43Z","snapshot_observed_at":"2026-07-06T01:34:44.763166Z","submitted_at":"2008-01-23T11:52:09Z","title":"Black Holes in Higher Dimensions","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"0801.3471","snapshot_observed_at":"2026-08-06T18:31:08.917433Z","title":null,"venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:08.917433Z"},"links":{"cited_paper":"/paper/0801.3471","citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:71f22406625f802fba241fd7f4a4a4fb08090c08a7fbb583504fe09e82337edf","observation_id":"a8647a31-4770-4ce1-aa6f-00365e5fa022","resolution":{"observed_at":"2026-08-06T18:31:08.917433Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"gr-qc/0310024","last_updated":"2008-03-06T20:20:13Z","snapshot_observed_at":"2026-07-07T03:18:25.113340Z","submitted_at":"2003-10-04T22:52:51Z","title":"An Integral Spectral Representation of the Propagator for the Wave Equation in the Kerr Geometry","version":5},"cited_work":{"arxiv_id":"gr-qc/0310024","doi":null,"metadata_source":"pith","pith_arxiv_id":"gr-qc/0310024","snapshot_observed_at":"2026-08-06T18:31:09.446344Z","title":"An Integral Spectral Representation of the Propagator for the Wave Equation in the Kerr Geometry","venue":"gr-qc","work_id":"1cb22d52-280e-46cd-bf7c-d98c533f5464","year":2003},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:08.919390Z"},"links":{"cited_paper":"/paper/gr-qc/0310024","citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:0bb6b498e6e49462f0293d05df243fe9fc9caa00c00cea7650a9ac2a59c04c37","observation_id":"f6d43b33-220d-48d9-aa48-b19c9ba4d4b4","resolution":{"observed_at":"2026-08-06T18:31:09.448872Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"gr-qc/0504047","last_updated":"2008-03-16T21:10:12Z","snapshot_observed_at":"2026-07-07T03:20:49.015991Z","submitted_at":"2005-04-12T07:34:15Z","title":"Decay of Solutions of the Wave Equation in the Kerr Geometry","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"gr-qc/0504047","snapshot_observed_at":"2026-08-06T18:31:08.921301Z","title":null,"venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:08.921301Z"},"links":{"cited_paper":"/paper/gr-qc/0504047","citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:78a46bb73fcd337648f9a56de38899df1d0c8ee12c503e2cc71e6507794f4cc8","observation_id":"63569d31-205f-4bb2-9443-1970c8434ef5","resolution":{"observed_at":"2026-08-06T18:31:08.921301Z","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":"2026-08-06T18:31:09.708536Z","title":"Decay of solutions of the wave equation in the Kerr geometry","venue":null,"work_id":"e0c87f36-640b-40f5-a4ca-19189d2ac276","year":2008},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:08.924451Z"},"links":{"citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:842a64a643dfe57358875e471ba5e8faa69b067b7310250a39457e72dfe2d49a","observation_id":"b32f9a56-c29f-48ba-839e-b1ecf2632db0","resolution":{"observed_at":"2026-08-06T18:31:09.710417Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"gr-qc/0701018","last_updated":"2008-05-22T09:44:15Z","snapshot_observed_at":"2026-07-07T03:23:34.977372Z","submitted_at":"2007-01-01T21:59:50Z","title":"A Rigorous Treatment of Energy Extraction from a Rotating Black Hole","version":3},"cited_work":{"arxiv_id":"gr-qc/0701018","doi":null,"metadata_source":"pith","pith_arxiv_id":"gr-qc/0701018","snapshot_observed_at":"2026-08-06T18:31:09.433656Z","title":"A Rigorous Treatment of Energy Extraction from a Rotating Black Hole","venue":"gr-qc","work_id":"65e35c53-aadd-402d-9f96-059471fec41e","year":2007},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:08.927132Z"},"links":{"cited_paper":"/paper/gr-qc/0701018","citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:e8778ca407232788da46c8ce4e4fdfe39ba87fa565dd99393b5568ed0a492b5e","observation_id":"3e56fd96-f9be-4685-9b9e-d6dadd2b7233","resolution":{"observed_at":"2026-08-06T18:31:09.436047Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T18:31:09.703508Z","title":null,"venue":null,"work_id":"668843c5-920c-4e05-b609-1adb11a5ac1c","year":1975},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:08.929057Z"},"links":{"citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:15c788d8a76b28cbdbe0627de8104444d3b37dd1306366f3910a920ce114791c","observation_id":"cec68aea-272e-4f3f-a642-1751344bf859","resolution":{"observed_at":"2026-08-06T18:31:09.705304Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T18:31:09.698231Z","title":null,"venue":null,"work_id":"94989e69-5267-405a-8546-7615bd2e3f10","year":1980},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:08.931014Z"},"links":{"citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:4dd459e4a615b2037e1f869d23ae9b52ad3244071ec1d42f333b00f8c75cad66","observation_id":"dd9a6c3f-8a99-4575-8415-e9b0358477e4","resolution":{"observed_at":"2026-08-06T18:31:09.700089Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T18:31:09.692771Z","title":null,"venue":null,"work_id":"675a3313-142b-4910-aa7e-a27d9ef8867e","year":1971},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:08.933465Z"},"links":{"citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:e2c3001f756ad294e97ed5dfea6eb632564afb9d8eca4be3ba0c3fcc2dd97b7e","observation_id":"f285723f-0fcd-4a01-b7c1-2a451556822f","resolution":{"observed_at":"2026-08-06T18:31:09.694569Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2002.02740","last_updated":"2020-02-07T12:39:18Z","snapshot_observed_at":"2026-08-08T23:53:05.861732Z","submitted_at":"2020-02-07T12:39:18Z","title":"A general formalism for the stability of Kerr","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2002.02740","snapshot_observed_at":"2026-08-06T18:31:08.935375Z","title":null,"venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:08.935375Z"},"links":{"cited_paper":"/paper/2002.02740","citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:bcb77e3e33e07b03a2ea41e668e79fea02360a7c9e21d537e5514c475540a680","observation_id":"7862129d-d4c9-41b9-8834-8499fe44e2e5","resolution":{"observed_at":"2026-08-06T18:31:08.935375Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2205.14808","last_updated":"2022-05-30T02:09:43Z","snapshot_observed_at":"2026-07-06T13:15:14.206185Z","submitted_at":"2022-05-30T02:09:43Z","title":"Wave equations estimates and the nonlinear stability of slowly rotating Kerr black holes","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2205.14808","snapshot_observed_at":"2026-08-06T18:31:08.937333Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:08.937333Z"},"links":{"cited_paper":"/paper/2205.14808","citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:2baf9ef71c7e21ed1f588a0b299a9ee59dd28f62565fcac2133fadcda2cf089b","observation_id":"20e3a173-4476-4420-9a24-9c929b693adb","resolution":{"observed_at":"2026-08-06T18:31:08.937333Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1311.4495","last_updated":"2013-11-18T19:09:25Z","snapshot_observed_at":"2026-07-06T03:28:32.028517Z","submitted_at":"2013-11-18T19:09:25Z","title":"On the Cauchy Problem for Energy Critical Self-Gravitating Wave Maps","version":1},"cited_work":{"arxiv_id":"1311.4495","doi":null,"metadata_source":"pith","pith_arxiv_id":"1311.4495","snapshot_observed_at":"2026-08-06T18:31:09.416586Z","title":"On the Cauchy Problem for Energy Critical Self-Gravitating Wave Maps","venue":"math.AP","work_id":"b46a7b49-9543-4084-9e53-b7fd9a155aa1","year":2013},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:08.939288Z"},"links":{"cited_paper":"/paper/1311.4495","citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:678a0590b15e26e3661be28ee3e6c585905e84c5f59b850cc63303b17041ed32","observation_id":"636d3138-2f43-4b00-9d4e-4022e780316c","resolution":{"observed_at":"2026-08-06T18:31:09.418799Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1702.07950","last_updated":"2017-02-25T21:21:11Z","snapshot_observed_at":"2026-07-06T05:31:24.400512Z","submitted_at":"2017-02-25T21:21:11Z","title":"A Note on the Dimensional Reduction of Axisymmetric Spacetimes","version":1},"cited_work":{"arxiv_id":"1702.07950","doi":null,"metadata_source":"pith","pith_arxiv_id":"1702.07950","snapshot_observed_at":"2026-08-06T18:31:09.408996Z","title":"A Note on the Dimensional Reduction of Axisymmetric Spacetimes","venue":"math.AP","work_id":"ca932a4e-4f89-4d81-be95-8fff1cef7f20","year":2017},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:08.941884Z"},"links":{"cited_paper":"/paper/1702.07950","citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:17a61b2934d910d09555bd4bac3c6f7883429b85115e4b0606d278036671cb2b","observation_id":"db7d4270-23e4-48e4-9af2-d9ba60eae41d","resolution":{"observed_at":"2026-08-06T18:31:09.411253Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1904.09670","last_updated":"2019-04-21T22:33:51Z","snapshot_observed_at":"2026-07-06T07:47:29.276335Z","submitted_at":"2019-04-21T22:33:51Z","title":"Axially Symmetric Perturbations of Kerr Black Holes I: A gauge-invariant construction of ADM Energy","version":1},"cited_work":{"arxiv_id":"1904.09670","doi":null,"metadata_source":"pith","pith_arxiv_id":"1904.09670","snapshot_observed_at":"2026-08-06T18:31:09.401665Z","title":"Axially Symmetric Perturbations of Kerr Black Holes I: A gauge-invariant construction of ADM Energy","venue":"gr-qc","work_id":"2a1ced78-d57c-4856-875e-6efe60ac2094","year":2019},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:08.945611Z"},"links":{"cited_paper":"/paper/1904.09670","citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:cb9b3641db2aa942e7ea68538df4c85d99062f1294fb76d59a75afc675a08e9c","observation_id":"a410b4dd-d1d5-4435-a68a-e91245787167","resolution":{"observed_at":"2026-08-06T18:31:09.403879Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2109.02131","last_updated":"2021-09-05T17:55:59Z","snapshot_observed_at":"2026-07-06T11:44:29.732714Z","submitted_at":"2021-09-05T17:55:59Z","title":"Axially Symmetric Perturbations of Kerr Black Holes II: Boundary Behaviour of the Dynamics in the Orbit Space","version":1},"cited_work":{"arxiv_id":"2109.02131","doi":null,"metadata_source":"pith","pith_arxiv_id":"2109.02131","snapshot_observed_at":"2026-08-06T18:31:09.394192Z","title":"Axially Symmetric Perturbations of Kerr Black Holes II: Boundary Behaviour of the Dynamics in the Orbit Space","venue":"gr-qc","work_id":"ce4dea82-403c-47c3-a923-7d3b8ee69846","year":2021},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:08.948067Z"},"links":{"cited_paper":"/paper/2109.02131","citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:dbf7d2eda9050a5716b54a616073f7ab7f5ec041e3f59b94f8b9665768ad98ac","observation_id":"db0d84e6-792d-4ba6-90b9-9d8d6781f3b9","resolution":{"observed_at":"2026-08-06T18:31:09.396606Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1710.11294","last_updated":"2018-07-20T17:21:41Z","snapshot_observed_at":"2026-07-06T06:06:54.331476Z","submitted_at":"2017-10-31T01:52:24Z","title":"A Positive-Definite Energy Functional for Axially Symmetric Maxwell's Equations on Kerr-de Sitter Black Hole Spacetimes","version":2},"cited_work":{"arxiv_id":"1710.11294","doi":null,"metadata_source":"pith","pith_arxiv_id":"1710.11294","snapshot_observed_at":"2026-08-06T18:31:09.386586Z","title":"A Positive-Definite Energy Functional for Axially Symmetric Maxwell's Equations on Kerr-de Sitter Black Hole Spacetimes","venue":"gr-qc","work_id":"53d31d6c-16b6-4a83-a854-2bdd2b17e792","year":2017},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:08.950152Z"},"links":{"cited_paper":"/paper/1710.11294","citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:1ef52c5c35f4e7950914834cfcd4acbbad15baf705478de05db50f864ee5061f","observation_id":"211da8c7-5001-4d61-a4ce-5ee381fc3119","resolution":{"observed_at":"2026-08-06T18:31:09.388827Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1703.06331","last_updated":"2017-03-18T18:24:43Z","snapshot_observed_at":"2026-07-06T05:34:13.993772Z","submitted_at":"2017-03-18T18:24:43Z","title":"On 3+1 Lorentzian Einstein Manifolds with One Rotational Isometry","version":1},"cited_work":{"arxiv_id":"1703.06331","doi":null,"metadata_source":"pith","pith_arxiv_id":"1703.06331","snapshot_observed_at":"2026-08-06T18:31:09.378744Z","title":"On 3+1 Lorentzian Einstein Manifolds with One Rotational Isometry","venue":"gr-qc","work_id":"a550c280-cd69-435a-b2a6-29e5d85a9ae9","year":2017},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:08.952064Z"},"links":{"cited_paper":"/paper/1703.06331","citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:2b11cf9f2fc9d0ee0dee551c0891cb19a3446f678cf9402c7785e4f5284c9255","observation_id":"6119d802-8723-4653-a2cd-29d2ecc20f09","resolution":{"observed_at":"2026-08-06T18:31:09.380765Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1806.09162","last_updated":"2018-06-24T15:21:47Z","snapshot_observed_at":"2026-07-06T06:46:30.513785Z","submitted_at":"2018-06-24T15:21:47Z","title":"A Conserved Energy for Axially Symmetric Newman-Penrose-Maxwell Scalars on Kerr Black Holes","version":1},"cited_work":{"arxiv_id":"1806.09162","doi":null,"metadata_source":"pith","pith_arxiv_id":"1806.09162","snapshot_observed_at":"2026-08-06T18:31:09.370510Z","title":"A Conserved Energy for Axially Symmetric Newman-Penrose-Maxwell Scalars on Kerr Black Holes","venue":"gr-qc","work_id":"427ffa99-4700-4187-9974-fbbb558c7111","year":2018},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:08.954453Z"},"links":{"cited_paper":"/paper/1806.09162","citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:16cbcc8beee019f5070e852190a656fdea79a57fc3f5851cc1158d29cf1905e8","observation_id":"408d43c1-25a6-43f1-9785-c323628d2e06","resolution":{"observed_at":"2026-08-06T18:31:09.372701Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1906.00860","last_updated":"2019-07-15T21:22:33Z","snapshot_observed_at":"2026-07-06T07:57:32.030864Z","submitted_at":"2019-06-03T15:13:03Z","title":"Linear stability of slowly rotating Kerr black holes","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1906.00860","snapshot_observed_at":"2026-08-06T18:31:08.956456Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:08.956456Z"},"links":{"cited_paper":"/paper/1906.00860","citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:147701c8313f9ada0a6b9195a6660aee3007cb70a5533f695c3764801bce12a0","observation_id":"2b301837-e970-4e97-9323-b59766ff9da7","resolution":{"observed_at":"2026-08-06T18:31:08.956456Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1206.1164","last_updated":"2012-08-30T11:52:48Z","snapshot_observed_at":"2026-07-06T02:49:25.791902Z","submitted_at":"2012-06-06T09:55:59Z","title":"Black hole uniqueness theorems in higher dimensional spacetimes","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1206.1164","snapshot_observed_at":"2026-08-06T18:31:08.958270Z","title":null,"venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:08.958270Z"},"links":{"cited_paper":"/paper/1206.1164","citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:3fbd35ebe5c00957c2362b6376d61537cba30c00290ecad9050ccfd249940aa8","observation_id":"28d3cc34-f2a5-42eb-ad35-306274141610","resolution":{"observed_at":"2026-08-06T18:31:08.958270Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1201.0463","last_updated":"2012-09-04T10:50:33Z","snapshot_observed_at":"2026-08-08T16:24:07.036175Z","submitted_at":"2012-01-02T13:24:16Z","title":"Stability of Black Holes and Black Branes","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1201.0463","snapshot_observed_at":"2026-08-06T18:31:08.960689Z","title":null,"venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:08.960689Z"},"links":{"cited_paper":"/paper/1201.0463","citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:7f62318be08ce4950480bd58157204b307b9db36394a2a43c46f74c585ef7896","observation_id":"a668b7f1-0747-4110-8ea8-5f586aea7b37","resolution":{"observed_at":"2026-08-06T18:31:08.960689Z","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":"2026-08-06T18:31:09.687111Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes 71","venue":null,"work_id":"5a1cf35c-59c5-4b91-ae53-d9eae184d9c7","year":2016},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:08.962703Z"},"links":{"citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:a42dea66fb42dd101f95684371031ec578a67d277c768c2dfbace146cf02f786","observation_id":"f9f6c920-e33b-4618-b4b2-bff39992be65","resolution":{"observed_at":"2026-08-06T18:31:09.689164Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1702.02843","last_updated":"2018-12-07T14:37:15Z","snapshot_observed_at":"2026-08-03T21:26:42.835874Z","submitted_at":"2017-02-09T14:21:02Z","title":"Linear Stability of Schwarzschild Spacetime: Decay of Metric Coefficients","version":3},"cited_work":{"arxiv_id":"1702.02843","doi":null,"metadata_source":"pith","pith_arxiv_id":"1702.02843","snapshot_observed_at":"2026-08-06T18:31:09.347672Z","title":"Linear Stability of Schwarzschild Spacetime: Decay of Metric Coefficients","venue":"gr-qc","work_id":"2fdde3ef-6ba2-41cb-90dc-92343eb3267c","year":2017},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:08.964823Z"},"links":{"cited_paper":"/paper/1702.02843","citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:af5349d2ec4d4f110335678223e5d341ae3e51245e295a1193c44ab0b58b71f2","observation_id":"00aa6784-6791-4a1a-bc0f-1abe767071fe","resolution":{"observed_at":"2026-08-06T18:31:09.350284Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1412.5679","last_updated":"2014-12-17T23:49:20Z","snapshot_observed_at":"2026-07-06T04:04:00.032931Z","submitted_at":"2014-12-17T23:49:20Z","title":"On the global stability of the wave-map equation in Kerr spaces with small angular momentum","version":1},"cited_work":{"arxiv_id":"1412.5679","doi":null,"metadata_source":"pith","pith_arxiv_id":"1412.5679","snapshot_observed_at":"2026-08-06T18:31:09.339837Z","title":"On the global stability of the wave-map equation in Kerr spaces with small angular momentum","venue":"math.AP","work_id":"ebab6ab5-8e83-4775-ac0d-fd43835ba9cd","year":2014},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:08.967340Z"},"links":{"cited_paper":"/paper/1412.5679","citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:303f59eb7acc1cbd36448ffe1d74fe98bb0abc267a3ea4b5cccfc56e6e14f439","observation_id":"20c9ba96-aabf-49fa-80bb-bf75033bec1a","resolution":{"observed_at":"2026-08-06T18:31:09.342009Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2104.11857","last_updated":"2021-04-24T02:14:35Z","snapshot_observed_at":"2026-07-06T11:03:12.267745Z","submitted_at":"2021-04-24T02:14:35Z","title":"Kerr stability for small angular momentum","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2104.11857","snapshot_observed_at":"2026-08-06T18:31:08.969285Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:08.969285Z"},"links":{"cited_paper":"/paper/2104.11857","citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:fcb4bf112ea652420bdda32dedced9709d95b174f1634cf8159d7500ef1492d7","observation_id":"00698a09-7204-413a-b271-68542ea0666c","resolution":{"observed_at":"2026-08-06T18:31:08.969285Z","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":"2026-08-06T18:31:09.679685Z","title":null,"venue":null,"work_id":"075a2041-5752-4a39-9d05-9eb257cf640c","year":2012},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:08.971284Z"},"links":{"citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:d96bfc5da400ef875c4c8ba3625c1429c77f8d575791bfee68cdae6e80f4fe08","observation_id":"a16f8ebd-213f-4fd6-bcf6-5f83220c4d6c","resolution":{"observed_at":"2026-08-06T18:31:09.681498Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1705.06621","last_updated":"2020-08-27T14:28:20Z","snapshot_observed_at":"2026-07-06T05:43:13.457438Z","submitted_at":"2017-05-18T14:38:49Z","title":"Uniform energy bound and Morawetz estimate for extreme components of spin fields in the exterior of a slowly rotating Kerr black hole I: Maxwell field","version":4},"cited_work":{"arxiv_id":"1705.06621","doi":null,"metadata_source":"pith","pith_arxiv_id":"1705.06621","snapshot_observed_at":"2026-08-06T18:31:09.327018Z","title":"Uniform energy bound and Morawetz estimate for extreme components of spin fields in the exterior of a slowly rotating Kerr black hole I: Maxwell field","venue":"gr-qc","work_id":"ec66ac29-d6d8-42bc-b7d6-4b79d797c49c","year":2017},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:08.973991Z"},"links":{"cited_paper":"/paper/1705.06621","citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:bc6abc69802acc86693c97b242c61d0775f9c6cc1148d7e147d51a3cc08702b4","observation_id":"c2abb345-627e-4b1b-a783-dfb54131bf07","resolution":{"observed_at":"2026-08-06T18:31:09.329413Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1708.07385","last_updated":"2020-08-27T14:24:00Z","snapshot_observed_at":"2026-08-03T17:57:40.593779Z","submitted_at":"2017-08-23T13:05:45Z","title":"Uniform energy bound and Morawetz estimate for extreme components of spin fields in the exterior of a slowly rotating Kerr black hole II: linearized gravity","version":3},"cited_work":{"arxiv_id":"1708.07385","doi":null,"metadata_source":"pith","pith_arxiv_id":"1708.07385","snapshot_observed_at":"2026-08-06T18:31:09.318805Z","title":"Uniform energy bound and Morawetz estimate for extreme components of spin fields in the exterior of a slowly rotating Kerr black hole II: linearized gravity","venue":"gr-qc","work_id":"07cf1fb3-079e-40ca-8d97-0b2a69f642ef","year":2017},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:08.975953Z"},"links":{"cited_paper":"/paper/1708.07385","citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:a09b1e63dc9bdf0007a62b318e46611eb7c70f1ea7c9de01691fc4277d2be767","observation_id":"a8ea6e2c-6f11-47ca-b604-a78754744e63","resolution":{"observed_at":"2026-08-06T18:31:09.321366Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"hep-th/0101012","last_updated":"2000-12-31T23:42:45Z","snapshot_observed_at":"2026-08-04T17:07:01.181789Z","submitted_at":"2000-12-31T23:42:45Z","title":"Black Uniqueness Theorems","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"hep-th/0101012","snapshot_observed_at":"2026-08-06T18:31:08.977952Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:08.977952Z"},"links":{"cited_paper":"/paper/hep-th/0101012","citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:b98759b2eb6a0755c9f49c59e5227537c93c26ec48ee442763f1ce26d0754dfc","observation_id":"c944cbc6-5ffd-433f-bc5d-c2ee20073eb6","resolution":{"observed_at":"2026-08-06T18:31:08.977952Z","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":"2026-08-06T18:31:09.674320Z","title":null,"venue":null,"work_id":"4ae58fdc-2fcd-46a5-8927-cb3a4942bfb9","year":1978},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:08.980072Z"},"links":{"citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:ebb5ce0d361def1025bfa000ff03cd261600f37e98c34efb792783e722aa2c94","observation_id":"362c38ca-aab6-4796-9f7b-7db234506929","resolution":{"observed_at":"2026-08-06T18:31:09.676134Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T18:31:09.669254Z","title":null,"venue":null,"work_id":"aea69f22-8f7e-43f2-8421-c4f548e2c8ba","year":1973},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:08.981751Z"},"links":{"citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:846512b6dcc4f0b610ac6eb5e10cc276b98f3e1b991dc29cc4ab9c4f3beb2ec3","observation_id":"90f18822-b1aa-44fe-81e0-3b22f527007b","resolution":{"observed_at":"2026-08-06T18:31:09.670991Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T18:31:09.663763Z","title":null,"venue":null,"work_id":"eb275a21-d29e-4767-b917-fa1303c894d4","year":1974},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:08.983838Z"},"links":{"citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:8fafbfe2431cc35039155585c391f873c6a7c08a55cd90e9305d462cc2fb726c","observation_id":"de59a393-3add-4d27-9ee8-dc9fe3154969","resolution":{"observed_at":"2026-08-06T18:31:09.665832Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T18:31:09.658569Z","title":null,"venue":null,"work_id":"c750bc91-d164-4e27-853a-cb2ac0bb27cf","year":1974},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:08.985774Z"},"links":{"citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:43984f6588417cadef1fc42b0d113aa13e3e18e7780c6ce63a3a443263b886af","observation_id":"2fbc2da1-e694-4b44-9250-33584285e7e2","resolution":{"observed_at":"2026-08-06T18:31:09.660361Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T18:31:09.652111Z","title":null,"venue":null,"work_id":"e2cdf732-9ead-41b2-9ae4-d5c10b895100","year":1974},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:08.987676Z"},"links":{"citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:c967e2139a7e8474878b5ea42035b9c072fa9d9f2f4beb8fa891f36dfa0e07b5","observation_id":"7b0d5c2c-79f7-4c5e-bfdc-41f923a3ae68","resolution":{"observed_at":"2026-08-06T18:31:09.654235Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T18:31:09.647300Z","title":null,"venue":null,"work_id":"c40a5c32-dad9-40af-a5e9-951ae013bc9c","year":1975},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:08.989362Z"},"links":{"citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:095cf179f151f3b5ae610f9bb0bd7b67460d9185eeba16a6591561fe876fc14e","observation_id":"8ec3cc7a-364d-46ba-98b1-79c51c8f4b3b","resolution":{"observed_at":"2026-08-06T18:31:09.649013Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T18:31:09.642203Z","title":null,"venue":null,"work_id":"3477e703-3527-476f-8939-d336edb80814","year":1975},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:08.991087Z"},"links":{"citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:9af98c989f09fb0f16c80f322efd712bec90ecbcd5b4b8ff28a295e065cffd12","observation_id":"1788ff53-4f31-4f37-bb3d-db3e881e983e","resolution":{"observed_at":"2026-08-06T18:31:09.644181Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T18:31:09.636315Z","title":"Physics 167 (1986), 118–142","venue":null,"work_id":"09c895c6-21d7-4468-bdcb-5cd2d27696a0","year":1986},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":58,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:08.993355Z"},"links":{"citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:7c1391bcecce8235cc407ac118a10376099d8ea27adea51d42fef9d296c06292","observation_id":"62bf3b3b-81e2-4372-9305-cdd05f6ae233","resolution":{"observed_at":"2026-08-06T18:31:09.638137Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T18:31:09.631413Z","title":null,"venue":null,"work_id":"8a2e685e-6124-40ee-8624-cef41e88037c","year":1990},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":59,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:08.995274Z"},"links":{"citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:1ae3c5ec39abc7bcc7676fa9919afe4074a3c2c8e8578ced546e2e7cec0b5308","observation_id":"e7dd2b69-b9ea-45b0-b55d-842d9a41e050","resolution":{"observed_at":"2026-08-06T18:31:09.633157Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T18:31:09.626360Z","title":null,"venue":null,"work_id":"20856ff3-a55b-46d3-a5f0-256d22132d22","year":2008},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":60,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:08.997409Z"},"links":{"citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:e67a99fda4b315229878a2d9b23d0ff905eccb3ee29d6d6a09337d7581379795","observation_id":"8fae2a53-b3ac-4210-91e5-176d5655d1eb","resolution":{"observed_at":"2026-08-06T18:31:09.628175Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2105.12632","last_updated":"2021-05-26T15:46:52Z","snapshot_observed_at":"2026-08-08T02:31:29.593035Z","submitted_at":"2021-05-26T15:46:52Z","title":"A Positive-Definite Energy Functional for the Axisymmetric Perturbations of Kerr-Newman Black Holes","version":1},"cited_work":{"arxiv_id":"2105.12632","doi":null,"metadata_source":"pith","pith_arxiv_id":"2105.12632","snapshot_observed_at":"2026-08-06T18:31:09.304438Z","title":"A Positive-Definite Energy Functional for the Axisymmetric Perturbations of Kerr-Newman Black Holes","venue":"gr-qc","work_id":"05e41ca3-2187-4aa9-9f39-209fe58b25b6","year":2021},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":61,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:08.999206Z"},"links":{"cited_paper":"/paper/2105.12632","citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:a993a394c44748ce57525e8489592f2d591b6ee45c35eff9d41c4e3ce57df50c","observation_id":"45f381b9-395f-452b-ad30-740b0a8b66ea","resolution":{"observed_at":"2026-08-06T18:31:09.307447Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1501.02522","last_updated":"2015-08-26T04:24:57Z","snapshot_observed_at":"2026-08-08T06:44:34.785488Z","submitted_at":"2015-01-12T02:03:03Z","title":"Black Hole Instabilities and Exponential Growth","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1501.02522","snapshot_observed_at":"2026-08-06T18:31:09.001430Z","title":null,"venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":62,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:09.001430Z"},"links":{"cited_paper":"/paper/1501.02522","citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:95102c85ad32ed18e1c5ba34493abfc44bd70086cb4fd2e3974af95507e209df","observation_id":"4ae5d5f5-6c8f-42f2-bb52-010f28944556","resolution":{"observed_at":"2026-08-06T18:31:09.001430Z","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":"2026-08-06T18:31:09.621544Z","title":null,"venue":null,"work_id":"b1203c72-baaa-49b5-8692-47c9d2ba3a2b","year":1957},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":63,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:09.003820Z"},"links":{"citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:0a7b3a07d606f82b9f40dfa56fd9ce68342ba4432956d3a997d4ff9a63a63218","observation_id":"ea03589c-f3f1-44de-860a-0bc7f23b40f5","resolution":{"observed_at":"2026-08-06T18:31:09.623333Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"gr-qc/0502037","last_updated":"2005-02-09T15:16:38Z","snapshot_observed_at":"2026-07-07T03:20:33.571415Z","submitted_at":"2005-02-09T15:16:38Z","title":"A strongly hyperbolic and regular reduction of Einstein's equations for axisymmetric spacetimes","version":1},"cited_work":{"arxiv_id":"gr-qc/0502037","doi":null,"metadata_source":"pith","pith_arxiv_id":"gr-qc/0502037","snapshot_observed_at":"2026-08-06T18:31:09.291692Z","title":"A strongly hyperbolic and regular reduction of Einstein's equations for axisymmetric spacetimes","venue":"gr-qc","work_id":"eff260cf-079b-45e8-9839-cc186d7aa19b","year":2005},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":64,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:09.005630Z"},"links":{"cited_paper":"/paper/gr-qc/0502037","citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:728def90efd0cd6329b3a4d20da3285bb90c87f6e4a6178a6928eaa28a0698e9","observation_id":"9296883b-2a18-4758-9866-6477a676793f","resolution":{"observed_at":"2026-08-06T18:31:09.294182Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T18:31:09.616437Z","title":null,"venue":null,"work_id":"df0be7aa-fb05-4c05-b8d9-28ea8c090e3d","year":1974},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":65,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:09.008591Z"},"links":{"citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:9f6ffaff4d3d5a1a466aa30f0d2704621122d61dfd96068104500fafd82897a7","observation_id":"063e7cac-732f-4a4a-b3af-885e9dc874ab","resolution":{"observed_at":"2026-08-06T18:31:09.618323Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T18:31:09.611101Z","title":null,"venue":null,"work_id":"bc30fe4f-1850-464e-b0bd-f249ee517250","year":1979},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":66,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:09.010736Z"},"links":{"citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:af4e823a5eff33d9013a351741ccb255f288ce795bf0f34c9cc8d2128524c93a","observation_id":"96419ff6-eaf3-485c-adf1-1170a9974611","resolution":{"observed_at":"2026-08-06T18:31:09.613116Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T18:31:09.605496Z","title":"II, Comm","venue":null,"work_id":"9eac841d-876c-4024-a73d-4661a5b65cf5","year":1981},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":67,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:09.012885Z"},"links":{"citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:be564e6a086efdeba2921f68a145b6ae2864dcfc1440da80ac862f7cc6148e60","observation_id":"2177b689-acc1-4248-a304-c4972bce945e","resolution":{"observed_at":"2026-08-06T18:31:09.607743Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1209.0019","last_updated":"2012-08-31T21:24:58Z","snapshot_observed_at":"2026-07-06T02:54:44.378468Z","submitted_at":"2012-08-31T21:24:58Z","title":"Convexity of reduced energy and mass angular momentum inequalities","version":1},"cited_work":{"arxiv_id":"1209.0019","doi":null,"metadata_source":"pith","pith_arxiv_id":"1209.0019","snapshot_observed_at":"2026-08-06T18:31:09.284431Z","title":"Convexity of reduced energy and mass angular momentum inequalities","venue":"math.DG","work_id":"8a7fe746-5464-4305-8749-5a2b1612cc46","year":2012},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":68,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:09.015214Z"},"links":{"cited_paper":"/paper/1209.0019","citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:e16435c896bd7686aabb446ea3a9598f07d49c206138f75a3c828051c9605ce4","observation_id":"650648a4-4d64-410a-80bb-174e2e3dd30a","resolution":{"observed_at":"2026-08-06T18:31:09.286721Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T18:31:09.600078Z","title":"Pure Appl","venue":null,"work_id":"c6781a00-aafe-44da-9c4e-1d6f3fe21637","year":1992},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":69,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:09.017513Z"},"links":{"citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:b8b6d2cb5dc10833ca7c1ff61e4c5435c5ff9a5850aa5bab6aaafd92653aadb7","observation_id":"586ddd3d-a694-4e15-9543-527a78e8e9d8","resolution":{"observed_at":"2026-08-06T18:31:09.601957Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T18:31:09.594584Z","title":"Pure Appl","venue":null,"work_id":"2b30fb5a-4265-407c-b41d-f66a110eb8a5","year":1994},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":70,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:09.019459Z"},"links":{"citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:5d5e3de609927c7e0da1b469d73d7698006fa8580d1faa54bd7d8283afef0b54","observation_id":"f5c340e2-36f9-4650-829d-d608764ea9ce","resolution":{"observed_at":"2026-08-06T18:31:09.596451Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"0906.3384","last_updated":"2009-06-18T09:19:52Z","snapshot_observed_at":"2026-07-06T01:55:44.178956Z","submitted_at":"2009-06-18T09:19:52Z","title":"Energy dispersed large data wave maps in 2+1 dimensions","version":1},"cited_work":{"arxiv_id":"0906.3384","doi":null,"metadata_source":"pith","pith_arxiv_id":"0906.3384","snapshot_observed_at":"2026-08-06T18:31:09.277012Z","title":"Energy dispersed large data wave maps in 2+1 dimensions","venue":"math.AP","work_id":"709c28ce-2a83-4301-b1df-d94b5a11689e","year":2009},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":71,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:09.021704Z"},"links":{"cited_paper":"/paper/0906.3384","citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:6e34f8c43b10b6de2868015e9e98c2df13a33a875e6ebc57fb96ca45620ca9c9","observation_id":"3d99a43a-941f-42a2-b13a-f91610e39f18","resolution":{"observed_at":"2026-08-06T18:31:09.279495Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"0907.3148","last_updated":"2009-07-17T20:12:49Z","snapshot_observed_at":"2026-07-06T01:55:43.498765Z","submitted_at":"2009-07-17T20:12:49Z","title":"Regularity of Wave-Maps in dimension 2+1","version":1},"cited_work":{"arxiv_id":"0907.3148","doi":null,"metadata_source":"pith","pith_arxiv_id":"0907.3148","snapshot_observed_at":"2026-08-06T18:31:09.268237Z","title":"Regularity of Wave-Maps in dimension 2+1","venue":"math.AP","work_id":"22a01cbe-2929-4cc8-b8b5-fb19d7b6714c","year":2009},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":72,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:09.024358Z"},"links":{"cited_paper":"/paper/0907.3148","citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:c9e5cb574e8b5d4a603a9c16c79bbf2605f311e0025f0d2357b67b1c3b698f75","observation_id":"3d801633-7665-4025-97d4-00c37af76753","resolution":{"observed_at":"2026-08-06T18:31:09.271452Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T18:31:09.588991Z","title":null,"venue":null,"work_id":"8fabb0e5-7ba1-4b5f-9bf7-20d7fdd1199b","year":2002},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":73,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:09.026666Z"},"links":{"citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:cc6f2adc523829a10baf384f54d67b74871c6ee0faa589405058621fd8536615","observation_id":"f93c4efd-81bb-4842-9dcc-5bec00ef2ced","resolution":{"observed_at":"2026-08-06T18:31:09.590963Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T18:31:09.582996Z","title":"Pure Appl","venue":null,"work_id":"f30fbff6-5572-4fb3-a686-958cbf4a6ef7","year":2003},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":74,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:09.028919Z"},"links":{"citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:2224aed743e828fc08ab7efa68caa36ae72eadc5ef6e7f94aedc413177377cd5","observation_id":"45af6084-4876-43b8-80cd-e99c7a1707ef","resolution":{"observed_at":"2026-08-06T18:31:09.584987Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T18:31:09.576359Z","title":null,"venue":null,"work_id":"bd233d2f-cc73-406d-b950-dddb4273260b","year":1934},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":75,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:09.031317Z"},"links":{"citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:42c0812d98aa0feb7281498b434896e98dccb618551bc0769b195a46217e529a","observation_id":"da0ed142-17c2-419d-8cc8-51850a6086ae","resolution":{"observed_at":"2026-08-06T18:31:09.578489Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"math.ap/0010068","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:31:09.260373Z","title":null,"venue":null,"work_id":"4566c54c-6b4b-4961-9c66-8d785eb855cd","year":2001},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":76,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:09.033261Z"},"links":{"citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:e14554f01649c70e7da6f384ddf5c8c3612bf53a38d0daa1539d9f648514358b","observation_id":"09e59993-bd04-48df-8b76-c6dcf4a75c1d","resolution":{"observed_at":"2026-08-06T18:31:09.263399Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"math.ap/0011173","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:31:09.188595Z","title":null,"venue":null,"work_id":"d54a5903-18e9-42d3-954a-cbec670c2a65","year":2001},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":77,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:09.035012Z"},"links":{"citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:84bf27432ec3153a2715f0e0e33ef38f0c2eedb5324cf36442e3687fd5eb7918","observation_id":"7f66b136-7b24-4647-8e61-965fda1c1b56","resolution":{"observed_at":"2026-08-06T18:31:09.193008Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"0805.4666","last_updated":"2009-08-08T16:07:38Z","snapshot_observed_at":"2026-07-06T01:38:42.192192Z","submitted_at":"2008-05-30T04:06:22Z","title":"Global regularity of wave maps III. Large energy from $\\R^{1+2}$ to hyperbolic spaces","version":3},"cited_work":{"arxiv_id":"0805.4666","doi":null,"metadata_source":"pith","pith_arxiv_id":"0805.4666","snapshot_observed_at":"2026-08-06T18:31:09.120551Z","title":"Global regularity of wave maps III. Large energy from $\\R^{1+2}$ to hyperbolic spaces","venue":"math.AP","work_id":"05eec2d2-b9f2-4249-9741-44ce195f3e93","year":2008},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":78,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:09.036828Z"},"links":{"cited_paper":"/paper/0805.4666","citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:3dd0a9dd50fb83bc346077c3d6a6bbbb2e3e350dc96f00a2d4029f64d8e60016","observation_id":"a3ba7fb6-65c7-4866-a9dd-1155027f4aac","resolution":{"observed_at":"2026-08-06T18:31:09.124843Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"0806.3592","last_updated":"2009-08-06T00:09:47Z","snapshot_observed_at":"2026-07-06T01:43:42.092551Z","submitted_at":"2008-06-22T21:32:39Z","title":"Global regularity of wave maps IV. Absence of stationary or self-similar solutions in the energy class","version":2},"cited_work":{"arxiv_id":"0806.3592","doi":null,"metadata_source":"pith","pith_arxiv_id":"0806.3592","snapshot_observed_at":"2026-08-06T18:31:09.111667Z","title":"Global regularity of wave maps IV. Absence of stationary or self-similar solutions in the energy class","venue":"math.AP","work_id":"f126ee1c-adc1-4bf9-a03e-8a6527c906f0","year":2008},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":80,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:09.041449Z"},"links":{"cited_paper":"/paper/0806.3592","citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:8dd824927ed57af84641fdfa63fd934fb754e0154c21fecbe0b78e7e48b2393f","observation_id":"b4c037cd-20c9-4081-b307-c09862286ef6","resolution":{"observed_at":"2026-08-06T18:31:09.115209Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"0906.2833","last_updated":"2009-08-06T00:14:07Z","snapshot_observed_at":"2026-07-06T01:57:44.487967Z","submitted_at":"2009-06-16T01:48:39Z","title":"Global regularity of wave maps VI. Abstract theory of minimal-energy blowup solutions","version":2},"cited_work":{"arxiv_id":"0906.2833","doi":null,"metadata_source":"pith","pith_arxiv_id":"0906.2833","snapshot_observed_at":"2026-08-06T18:31:09.103717Z","title":"Global regularity of wave maps VI. Abstract theory of minimal-energy blowup solutions","venue":"math.AP","work_id":"9a80f5f9-3760-46b9-8bff-4bbfd24e894e","year":2009},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":81,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:09.044066Z"},"links":{"cited_paper":"/paper/0906.2833","citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:1dfeddceaf223290c6204763b3342234ce1c19c18c4ad1049d9445c0bca1f2d0","observation_id":"ceefc396-925e-40c3-97c6-6064f2d8cf82","resolution":{"observed_at":"2026-08-06T18:31:09.106200Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"0908.0776","last_updated":"2009-08-08T16:36:48Z","snapshot_observed_at":"2026-07-06T01:59:52.809746Z","submitted_at":"2009-08-06T00:17:57Z","title":"Global regularity of wave maps VII. Control of delocalised or dispersed solutions","version":2},"cited_work":{"arxiv_id":"0908.0776","doi":null,"metadata_source":"pith","pith_arxiv_id":"0908.0776","snapshot_observed_at":"2026-08-06T18:31:09.095254Z","title":"Global regularity of wave maps VII. Control of delocalised or dispersed solutions","venue":"math.AP","work_id":"a9d26ade-83b1-44da-8ad0-6b17a41a0741","year":2009},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":82,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:09.046677Z"},"links":{"cited_paper":"/paper/0908.0776","citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:ef9da91f7f7401d4b6a74266cdf964afef3b3b988d5c723db518978478046877","observation_id":"52cdc5d7-eb8d-494f-9baa-0788baa5212c","resolution":{"observed_at":"2026-08-06T18:31:09.098016Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"0810.5766","last_updated":"2008-11-03T18:00:40Z","snapshot_observed_at":"2026-07-06T01:50:47.082945Z","submitted_at":"2008-10-31T19:22:42Z","title":"Local energy estimate on Kerr black hole backgrounds","version":2},"cited_work":{"arxiv_id":"0810.5766","doi":null,"metadata_source":"pith","pith_arxiv_id":"0810.5766","snapshot_observed_at":"2026-08-06T18:31:09.083869Z","title":"Local energy estimate on Kerr black hole backgrounds","venue":"math.AP","work_id":"8143572e-59b3-43f3-8914-37faa6a22d8c","year":2008},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":83,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:09.048604Z"},"links":{"cited_paper":"/paper/0810.5766","citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:de88f98c122fd482933d28d28fd2a22e9863cb3e1b68a931e477e02e06366cd5","observation_id":"2a72403c-4f69-48ab-b212-08b079293357","resolution":{"observed_at":"2026-08-06T18:31:09.088412Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1410.2130","last_updated":"2015-01-15T23:04:41Z","snapshot_observed_at":"2026-08-05T18:51:26.273866Z","submitted_at":"2014-10-08T14:18:57Z","title":"The Kerr Metric","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1410.2130","snapshot_observed_at":"2026-08-06T18:31:09.050608Z","title":null,"venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":84,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:09.050608Z"},"links":{"cited_paper":"/paper/1410.2130","citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:535a8005f6102a7a98dd88b2804ff0ef161afb74e2b938df61da872bb4c8bd61","observation_id":"9abe2350-b9dc-408f-8547-043df0734ad9","resolution":{"observed_at":"2026-08-06T18:31:09.050608Z","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":"2026-08-06T18:31:09.569910Z","title":null,"venue":null,"work_id":"4a288aaf-7dee-44f7-9b76-d0585cd8f5b9","year":1965},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":85,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:09.052624Z"},"links":{"citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:a24c93f12f777abc19835e0ff895075d17bab4e97db5874b10f73e43817535bb","observation_id":"f397db70-3fe2-413e-a08d-9aa22b0f815b","resolution":{"observed_at":"2026-08-06T18:31:09.571788Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T18:31:09.563560Z","title":null,"venue":null,"work_id":"3c8e85cb-d158-4fbe-9fe4-87263a053bb8","year":1981},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":86,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:09.054479Z"},"links":{"citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:e62fdc689f87a848a8b04972001d5e98bb65c079128523cd672cc42afc64583b","observation_id":"1f6297e5-90af-4a55-a0b9-882ceb547215","resolution":{"observed_at":"2026-08-06T18:31:09.565663Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T18:31:09.557882Z","title":null,"venue":null,"work_id":"39045fdc-4325-488d-b33a-27546509020c","year":1970},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":87,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:09.056495Z"},"links":{"citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:ac15497be82cd4c6576caec19db91b428f86e76e6b23cefbfbe15f165c9d60cc","observation_id":"de031be9-e0b5-42da-b3f3-cf3ec6edc494","resolution":{"observed_at":"2026-08-06T18:31:09.559907Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T18:31:09.552299Z","title":null,"venue":null,"work_id":"29dae518-aeab-4320-9b22-c4f82fa5715f","year":1974},"citing_paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes","version":1},"reference_index":88,"source":"pdf_text","source_observed_at":"2026-08-06T18:31:09.058829Z"},"links":{"citing_paper":"/paper/2507.08326"},"observation_digest":"sha256:fa64b1301f0254c2a2e49889ea5109ee224581ad911ba7648859ed62214fda87","observation_id":"062466dc-aa3c-4c37-8893-6551ca0d4b03","resolution":{"observed_at":"2026-08-06T18:31:09.554154Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2507.08326","last_updated":"2025-07-11T05:33:54Z","latest_version":1,"primary_category":"gr-qc","snapshot_observed_at":"2026-08-08T06:26:29.385101Z","submitted_at":"2025-07-11T05:33:54Z","title":"On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes"},"reference_resolution":{"displayed":87,"state_counts":{"malformed_identifier":0,"metadata_mismatch":8,"parse_uncertain":0,"unresolved":47,"verified_exact":25,"verified_fuzzy":7},"total_outbound_references":87},"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":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"thesis":"As of 9 August 2026, this Paper Citation Record lists 87 of 87 outbound references and 0 inbound Pith citation observations for arXiv:2507.08326."}