{"as_of":"2026-08-18T09:43:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:6eaffb7a5f59caed11a872ce9ea21fd6084e1313e155b3ec159345d2b52c5b63","coverage":[{"denominator":24,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":24,"source":"paper_references, paper_reference_links","source_observed_at":"2026-06-26T10:43:24.973644Z","state":"measured"},{"denominator":24,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":24,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-18T06:34:40.430872+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/2606.22282/citation-record","integrity":"/paper/2606.22282/integrity","json":"/paper/2606.22282/citation-record.json","paper":"/paper/2606.22282"},"outbound":[{"citation":{"cited_paper":{"arxiv_id":"2604.03848","last_updated":"2026-04-04T20:13:53Z","snapshot_observed_at":"2026-07-06T22:52:57.182669Z","submitted_at":"2026-04-04T20:13:53Z","title":"Regularity and singularity of the blow-up curve for a wave equation with a derivative nonlinearity and a scale-invariant damping","version":1},"cited_work":{"arxiv_id":"2604.03848","doi":null,"metadata_source":"pith","pith_arxiv_id":"2604.03848","snapshot_observed_at":"2026-07-04T08:59:42.711001Z","title":"Regularity and singularity of the blow-up curve for a wave equation with a derivative nonlinearity and a scale-invariant damping","venue":"math.AP","work_id":"9f9229a2-5fd3-4f35-b6f1-7b18d936d15c","year":2026},"citing_paper":{"arxiv_id":"2606.22282","last_updated":"2026-06-21T00:16:29Z","snapshot_observed_at":"2026-08-18T06:30:15.514697Z","submitted_at":"2026-06-21T00:16:29Z","title":"Stable blow-up on a sphere for a quadratic-derivative nonlinear wave equation","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-06-26T10:43:24.973644Z"},"links":{"cited_paper":"/paper/2604.03848","citing_paper":"/paper/2606.22282"},"observation_digest":"sha256:59db29a080514c579767bd9f16994149c76b3955e478c002a4136dd93184aabf","observation_id":"3ad86fd0-3933-48c2-9b66-6d96a1c61f18","resolution":{"observed_at":"2026-07-04T08:59:42.712267Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-06-26T10:43:24.973644Z","title":"Radial blow-up standing solutions for the semilinear wave equation.Calculus of Variations and Partial Differential Equations, 65:104, 2026","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2606.22282","last_updated":"2026-06-21T00:16:29Z","snapshot_observed_at":"2026-08-18T06:30:15.514697Z","submitted_at":"2026-06-21T00:16:29Z","title":"Stable blow-up on a sphere for a quadratic-derivative nonlinear wave equation","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-06-26T10:43:24.973644Z"},"links":{"citing_paper":"/paper/2606.22282"},"observation_digest":"sha256:225fafb31e1c41c9bd2df24a6378b85645fa1b5b4d715f10dccf886a4b538490","observation_id":"a08ae62e-0b57-4fcf-877d-d65be645c6d9","resolution":{"observed_at":"2026-06-26T10:43:24.973644Z","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":"2026-06-26T10:43:24.973644Z","title":"Global solutions of nonlinear hyperbolic equations for small initial data.Communications on Pure and Applied Mathematics, 39(2):267–282, 1986","venue":null,"work_id":null,"year":1986},"citing_paper":{"arxiv_id":"2606.22282","last_updated":"2026-06-21T00:16:29Z","snapshot_observed_at":"2026-08-18T06:30:15.514697Z","submitted_at":"2026-06-21T00:16:29Z","title":"Stable blow-up on a sphere for a quadratic-derivative nonlinear wave equation","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-06-26T10:43:24.973644Z"},"links":{"citing_paper":"/paper/2606.22282"},"observation_digest":"sha256:7e895edb2f51943ad5179cfb85bfcd37cea5aa8ca581731f698df74dcc44352c","observation_id":"827f447e-64ce-41de-826a-ea83a402d992","resolution":{"observed_at":"2026-06-26T10:43:24.973644Z","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":"2026-06-26T10:43:24.973644Z","title":"On blowup for the supercritical quadratic wave equation.Analysis & PDE, 17(2):617–680, 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2606.22282","last_updated":"2026-06-21T00:16:29Z","snapshot_observed_at":"2026-08-18T06:30:15.514697Z","submitted_at":"2026-06-21T00:16:29Z","title":"Stable blow-up on a sphere for a quadratic-derivative nonlinear wave equation","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-06-26T10:43:24.973644Z"},"links":{"citing_paper":"/paper/2606.22282"},"observation_digest":"sha256:8ebb7fdb69e4eb69a683cc2cf25100b1486620d5404d27283c8b543588843ec1","observation_id":"238a06b9-b5b6-4787-abf0-e6e09966a70f","resolution":{"observed_at":"2026-06-26T10:43:24.973644Z","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":"2601.19516","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-04T08:59:42.722783Z","title":"Blowup stability of wave maps without symmetry","venue":null,"work_id":"5727daeb-5228-4ce4-8ab4-62615579f613","year":2026},"citing_paper":{"arxiv_id":"2606.22282","last_updated":"2026-06-21T00:16:29Z","snapshot_observed_at":"2026-08-18T06:30:15.514697Z","submitted_at":"2026-06-21T00:16:29Z","title":"Stable blow-up on a sphere for a quadratic-derivative nonlinear wave equation","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-06-26T10:43:24.973644Z"},"links":{"citing_paper":"/paper/2606.22282"},"observation_digest":"sha256:a4fff9b5b762c718bb87a01a094aab8437f33a720bbd3107f4869269294ce088","observation_id":"cff2ee91-6988-49d9-9987-3736b8655323","resolution":{"observed_at":"2026-07-04T08:59:42.724340Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-06-26T10:43:24.973644Z","title":"Stable blowup for wave equations in odd space dimensions.Annales de l’Institut Henri Poincaré C, Analyse non linéaire, 34(5):1181–1213, 2017","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2606.22282","last_updated":"2026-06-21T00:16:29Z","snapshot_observed_at":"2026-08-18T06:30:15.514697Z","submitted_at":"2026-06-21T00:16:29Z","title":"Stable blow-up on a sphere for a quadratic-derivative nonlinear wave equation","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-06-26T10:43:24.973644Z"},"links":{"citing_paper":"/paper/2606.22282"},"observation_digest":"sha256:dd65ad325616cb79930403721bb2a12d544f807e2d94a818c7ec35d8030234ba","observation_id":"350fd10f-a111-41e6-beaf-4ed38b2855d1","resolution":{"observed_at":"2026-06-26T10:43:24.973644Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2503.04425","last_updated":"2025-03-06T13:34:00Z","snapshot_observed_at":"2026-08-16T12:52:30.342304Z","submitted_at":"2025-03-06T13:34:00Z","title":"Stable blowup for supercritical wave maps into perturbed spheres","version":1},"cited_work":{"arxiv_id":"2503.04425","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2503.04425","snapshot_observed_at":"2026-07-04T08:59:42.724620Z","title":"Stable blowup for supercritical wave maps into per- turbed spheres.arXiv preprint arXiv:2503.04425, 2025","venue":null,"work_id":"cc6c3f0d-b2c2-41c7-a4f1-1bf980bc0b7c","year":2025},"citing_paper":{"arxiv_id":"2606.22282","last_updated":"2026-06-21T00:16:29Z","snapshot_observed_at":"2026-08-18T06:30:15.514697Z","submitted_at":"2026-06-21T00:16:29Z","title":"Stable blow-up on a sphere for a quadratic-derivative nonlinear wave equation","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-06-26T10:43:24.973644Z"},"links":{"cited_paper":"/paper/2503.04425","citing_paper":"/paper/2606.22282"},"observation_digest":"sha256:dcfe259abe8f3e391736e025a4c58a5372ed85f70f956aee37ee015a0fcc5022","observation_id":"a1dfa7fc-e9ac-47ec-934e-c56f9f2c97cc","resolution":{"observed_at":"2026-07-04T08:59:42.726425Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-06-26T10:43:24.973644Z","title":"Instabilities appearing in cosmological effective field theories: when and how?Nonlinearity, 36(9):4844–4861, 2023","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2606.22282","last_updated":"2026-06-21T00:16:29Z","snapshot_observed_at":"2026-08-18T06:30:15.514697Z","submitted_at":"2026-06-21T00:16:29Z","title":"Stable blow-up on a sphere for a quadratic-derivative nonlinear wave equation","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-06-26T10:43:24.973644Z"},"links":{"citing_paper":"/paper/2606.22282"},"observation_digest":"sha256:18e4734d7633ab8d7406c2010757a8ea46fd88ed5cfc821229b9df6d3b795820","observation_id":"3d6981ae-8ae9-4ecd-94ff-5cefd58531ac","resolution":{"observed_at":"2026-06-26T10:43:24.973644Z","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":"2026-06-26T10:43:24.973644Z","title":"Springer, New York, 2000","venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2606.22282","last_updated":"2026-06-21T00:16:29Z","snapshot_observed_at":"2026-08-18T06:30:15.514697Z","submitted_at":"2026-06-21T00:16:29Z","title":"Stable blow-up on a sphere for a quadratic-derivative nonlinear wave equation","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-06-26T10:43:24.973644Z"},"links":{"citing_paper":"/paper/2606.22282"},"observation_digest":"sha256:044f9e217d586e75dea9949b3340526c0d20845bec6277d59382fa980817d3fd","observation_id":"3802ee36-6e02-4288-86cf-184626d8f826","resolution":{"observed_at":"2026-06-26T10:43:24.973644Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2501.07887","last_updated":"2025-01-14T06:54:37Z","snapshot_observed_at":"2026-08-17T21:37:57.050939Z","submitted_at":"2025-01-14T06:54:37Z","title":"Blow-up of the one-dimensional wave equation with quadratic spatial derivative nonlinearity","version":1},"cited_work":{"arxiv_id":"2501.07887","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2501.07887","snapshot_observed_at":"2026-07-04T08:59:42.717445Z","title":"Blow-up of the one-dimensional wave equation with quadratic spatial derivative nonlinearity.arXiv preprint arXiv:2501.07887, 2025","venue":null,"work_id":"076d131a-0043-4eae-9739-d7af0deb0d6b","year":2025},"citing_paper":{"arxiv_id":"2606.22282","last_updated":"2026-06-21T00:16:29Z","snapshot_observed_at":"2026-08-18T06:30:15.514697Z","submitted_at":"2026-06-21T00:16:29Z","title":"Stable blow-up on a sphere for a quadratic-derivative nonlinear wave equation","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-06-26T10:43:24.973644Z"},"links":{"cited_paper":"/paper/2501.07887","citing_paper":"/paper/2606.22282"},"observation_digest":"sha256:e3afd9fa94dc1306ccb09704c93783d73a9ed7dbadca1dacbf93c14a8b70492d","observation_id":"d9222c4e-ecba-49ad-b057-0c21ded2cdeb","resolution":{"observed_at":"2026-07-04T08:59:42.718970Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2512.16623","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-04T08:59:42.720037Z","title":"Existence and stability of discretely self-similar blowup for a wave maps type equation","venue":null,"work_id":"9627caee-732d-4c95-8bd1-e963e420f5e1","year":2025},"citing_paper":{"arxiv_id":"2606.22282","last_updated":"2026-06-21T00:16:29Z","snapshot_observed_at":"2026-08-18T06:30:15.514697Z","submitted_at":"2026-06-21T00:16:29Z","title":"Stable blow-up on a sphere for a quadratic-derivative nonlinear wave equation","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-06-26T10:43:24.973644Z"},"links":{"citing_paper":"/paper/2606.22282"},"observation_digest":"sha256:cf0ef8bf30fcf04177460a9f01fcdcd0247fbcbafd0396a9564ef58b25ef60db","observation_id":"3a0726cd-2e42-4173-b972-1c3c1e801e10","resolution":{"observed_at":"2026-07-04T08:59:42.721724Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2510.14815","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-04T08:59:42.721816Z","title":"Stable Type I blow-up for the one-dimensional wave equation with time-derivative nonlinearity.arXiv preprint arXiv:2510.14815, 2025","venue":null,"work_id":"8949d283-68de-4676-b37f-466a29637caf","year":2025},"citing_paper":{"arxiv_id":"2606.22282","last_updated":"2026-06-21T00:16:29Z","snapshot_observed_at":"2026-08-18T06:30:15.514697Z","submitted_at":"2026-06-21T00:16:29Z","title":"Stable blow-up on a sphere for a quadratic-derivative nonlinear wave equation","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-06-26T10:43:24.973644Z"},"links":{"citing_paper":"/paper/2606.22282"},"observation_digest":"sha256:7bad719bc95041415a398ce227d7ffc9d14b3a46a945f2110080a97ea760907d","observation_id":"58fda796-3871-455d-a1d6-618e7edbb6da","resolution":{"observed_at":"2026-07-04T08:59:42.723433Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-06-26T10:43:24.973644Z","title":"New nonlinear instability for scalar fields","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2606.22282","last_updated":"2026-06-21T00:16:29Z","snapshot_observed_at":"2026-08-18T06:30:15.514697Z","submitted_at":"2026-06-21T00:16:29Z","title":"Stable blow-up on a sphere for a quadratic-derivative nonlinear wave equation","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-06-26T10:43:24.973644Z"},"links":{"citing_paper":"/paper/2606.22282"},"observation_digest":"sha256:de39ba3ef00966d29c5bd7c268a4dbdf1c1fe11ed302bb7ff4c1be1d18afe8c4","observation_id":"9d8a9f07-3008-4c74-ace8-5d33ad3c912a","resolution":{"observed_at":"2026-06-26T10:43:24.973644Z","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":"2026-06-26T10:43:24.973644Z","title":"Small-data shock formation in solutions to 3D quasilinear wave equations: An overview.Journal of Hyperbolic Differential Equations, 13(1):1–105, 2016","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2606.22282","last_updated":"2026-06-21T00:16:29Z","snapshot_observed_at":"2026-08-18T06:30:15.514697Z","submitted_at":"2026-06-21T00:16:29Z","title":"Stable blow-up on a sphere for a quadratic-derivative nonlinear wave equation","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-06-26T10:43:24.973644Z"},"links":{"citing_paper":"/paper/2606.22282"},"observation_digest":"sha256:594f7e5e7ac64ae667480b39f15c356b27a8551e2701be3de3b638a9dc264b17","observation_id":"913efba8-b3aa-481b-9de7-be8685e5d66c","resolution":{"observed_at":"2026-06-26T10:43:24.973644Z","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":"2026-06-26T10:43:24.973644Z","title":"Blow-up of solutions of nonlinear wave equations in three space dimensions.Manuscripta Mathematica, 28:235– 268, 1979","venue":null,"work_id":null,"year":1979},"citing_paper":{"arxiv_id":"2606.22282","last_updated":"2026-06-21T00:16:29Z","snapshot_observed_at":"2026-08-18T06:30:15.514697Z","submitted_at":"2026-06-21T00:16:29Z","title":"Stable blow-up on a sphere for a quadratic-derivative nonlinear wave equation","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-06-26T10:43:24.973644Z"},"links":{"citing_paper":"/paper/2606.22282"},"observation_digest":"sha256:39d839181a6f73fa480631a8c29ef5990465d2269dbd4d03762f68902a5c1575","observation_id":"791d8dc3-9a55-4f90-bd6c-e13fe2f629aa","resolution":{"observed_at":"2026-06-26T10:43:24.973644Z","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":"2026-06-26T10:43:24.973644Z","title":"Springer Berlin Heidelberg, 2013","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2606.22282","last_updated":"2026-06-21T00:16:29Z","snapshot_observed_at":"2026-08-18T06:30:15.514697Z","submitted_at":"2026-06-21T00:16:29Z","title":"Stable blow-up on a sphere for a quadratic-derivative nonlinear wave equation","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-06-26T10:43:24.973644Z"},"links":{"citing_paper":"/paper/2606.22282"},"observation_digest":"sha256:90a145b69787f6662936fbbe98ce22267f29eccb2ad5e8517fdc6fe95b2b9044","observation_id":"6c0539e9-4b7c-4f51-8037-24606f2d85bc","resolution":{"observed_at":"2026-06-26T10:43:24.973644Z","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":"2026-06-26T10:43:24.973644Z","title":"On self-similar blow up for the energy supercritical semilinear wave equation.Journal de l’Ecole polytechnique — Mathématiques, 11:1483–1542, 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2606.22282","last_updated":"2026-06-21T00:16:29Z","snapshot_observed_at":"2026-08-18T06:30:15.514697Z","submitted_at":"2026-06-21T00:16:29Z","title":"Stable blow-up on a sphere for a quadratic-derivative nonlinear wave equation","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-06-26T10:43:24.973644Z"},"links":{"citing_paper":"/paper/2606.22282"},"observation_digest":"sha256:3cef17b1f894577337a0ee6785a89a6c8189fbdbb9436bac37b3ed09c3c5cd21","observation_id":"55a9ecb3-d9d2-45a4-8738-e3dd37715e84","resolution":{"observed_at":"2026-06-26T10:43:24.973644Z","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":"2026-06-26T10:43:24.973644Z","title":"The null condition and global existence to nonlinear wave equations","venue":null,"work_id":null,"year":1984},"citing_paper":{"arxiv_id":"2606.22282","last_updated":"2026-06-21T00:16:29Z","snapshot_observed_at":"2026-08-18T06:30:15.514697Z","submitted_at":"2026-06-21T00:16:29Z","title":"Stable blow-up on a sphere for a quadratic-derivative nonlinear wave equation","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-06-26T10:43:24.973644Z"},"links":{"citing_paper":"/paper/2606.22282"},"observation_digest":"sha256:9072c8259b10b301b131d4bb02f7f52aff6bdde19da36aae2deba0e06604228f","observation_id":"2418cc06-4b56-4709-abe2-2c021b25846f","resolution":{"observed_at":"2026-06-26T10:43:24.973644Z","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":"2511.13504","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-04T08:59:42.712031Z","title":"arXiv preprint arXiv:2511.13504, 2025","venue":null,"work_id":"5e999197-ad86-402f-862f-30bd42443bf9","year":2025},"citing_paper":{"arxiv_id":"2606.22282","last_updated":"2026-06-21T00:16:29Z","snapshot_observed_at":"2026-08-18T06:30:15.514697Z","submitted_at":"2026-06-21T00:16:29Z","title":"Stable blow-up on a sphere for a quadratic-derivative nonlinear wave equation","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-06-26T10:43:24.973644Z"},"links":{"citing_paper":"/paper/2606.22282"},"observation_digest":"sha256:35bdab9d5f7de808376082a18b4131945d493abe638206a3026f4187266a268a","observation_id":"1e147649-326d-47f8-b612-7d293f247183","resolution":{"observed_at":"2026-07-04T08:59:42.713359Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-06-26T10:43:24.973644Z","title":"On blow up for the energy super critical defocusing nonlinear Schrödinger equations.Inventiones Mathematicae, 227(1):247–413, 2022","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2606.22282","last_updated":"2026-06-21T00:16:29Z","snapshot_observed_at":"2026-08-18T06:30:15.514697Z","submitted_at":"2026-06-21T00:16:29Z","title":"Stable blow-up on a sphere for a quadratic-derivative nonlinear wave equation","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-06-26T10:43:24.973644Z"},"links":{"citing_paper":"/paper/2606.22282"},"observation_digest":"sha256:0c59779b307824d19de07e62fe337bd02ad1ce30a6eac3e20d743f0be1c703b4","observation_id":"54a0bea3-ce1a-492d-aff2-ffbac9057fe5","resolution":{"observed_at":"2026-06-26T10:43:24.973644Z","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":"2026-06-26T10:43:24.973644Z","title":"Existence and universality of the blow-up profile for the semilinear wave equation in one space dimension.Journal of Functional Analysis, 253(1):43–121, 2007","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2606.22282","last_updated":"2026-06-21T00:16:29Z","snapshot_observed_at":"2026-08-18T06:30:15.514697Z","submitted_at":"2026-06-21T00:16:29Z","title":"Stable blow-up on a sphere for a quadratic-derivative nonlinear wave equation","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-06-26T10:43:24.973644Z"},"links":{"citing_paper":"/paper/2606.22282"},"observation_digest":"sha256:372a37a4c9d1b3f94a53332e796518e6a87a0e5a82f638599560c4bdba14efa6","observation_id":"3e91c146-c54e-4cd4-82ba-f7d0ae2d70ba","resolution":{"observed_at":"2026-06-26T10:43:24.973644Z","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":"2026-06-26T10:43:24.973644Z","title":"Blow-up behavior outside the origin for a semilinear wave equation in the radial case","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2606.22282","last_updated":"2026-06-21T00:16:29Z","snapshot_observed_at":"2026-08-18T06:30:15.514697Z","submitted_at":"2026-06-21T00:16:29Z","title":"Stable blow-up on a sphere for a quadratic-derivative nonlinear wave equation","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-06-26T10:43:24.973644Z"},"links":{"citing_paper":"/paper/2606.22282"},"observation_digest":"sha256:a4626e81d1926ede11b7f41427d4e4e55a0424f1622dd9c82fe0c099e7b2ebec","observation_id":"a8af60e7-9383-4fe2-84c2-115f134e0c63","resolution":{"observed_at":"2026-06-26T10:43:24.973644Z","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":"2026-06-26T10:43:24.973644Z","title":"Stable blowup for focusing semilinear wave equations in all dimensions.Transactions of the American Mathematical Society, 377(7):4727–4778, 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2606.22282","last_updated":"2026-06-21T00:16:29Z","snapshot_observed_at":"2026-08-18T06:30:15.514697Z","submitted_at":"2026-06-21T00:16:29Z","title":"Stable blow-up on a sphere for a quadratic-derivative nonlinear wave equation","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-06-26T10:43:24.973644Z"},"links":{"citing_paper":"/paper/2606.22282"},"observation_digest":"sha256:b0901f9315121a040c1349eb41cbe04fcc0e51403c64d7fcff07d8edc3fc64e5","observation_id":"f7ce4d39-f511-4295-a9d6-44a78b82135f","resolution":{"observed_at":"2026-06-26T10:43:24.973644Z","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":"2026-06-26T10:43:24.973644Z","title":"Stable ODE-type blowup for some quasilinear wave equations with derivative-quadratic nonlinearities.Anal- ysis & PDE, 13(1):93–146, 2020","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2606.22282","last_updated":"2026-06-21T00:16:29Z","snapshot_observed_at":"2026-08-18T06:30:15.514697Z","submitted_at":"2026-06-21T00:16:29Z","title":"Stable blow-up on a sphere for a quadratic-derivative nonlinear wave equation","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-06-26T10:43:24.973644Z"},"links":{"citing_paper":"/paper/2606.22282"},"observation_digest":"sha256:4586c09c2a4cb0c13929664af90edff69147ce65b1710007de1833c61effdbf3","observation_id":"500b464f-4356-4dac-881b-0e65ed7b9af2","resolution":{"observed_at":"2026-06-26T10:43:24.973644Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2606.22282","last_updated":"2026-06-21T00:16:29Z","latest_version":1,"primary_category":"math.AP","snapshot_observed_at":"2026-08-18T06:30:15.514697Z","submitted_at":"2026-06-21T00:16:29Z","title":"Stable blow-up on a sphere for a quadratic-derivative nonlinear wave equation"},"reference_resolution":{"displayed":24,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":17,"verified_exact":7,"verified_fuzzy":0},"total_outbound_references":24},"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":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"thesis":"As of 18 August 2026, this Paper Citation Record lists 24 of 24 outbound references and 0 inbound Pith citation observations for arXiv:2606.22282."}