{"as_of":"2026-08-10T02:52:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:e7a6985aefd391d103ad37429537c0f1ca26eaf0e6efa298e4f65dea833a36a4","coverage":[{"denominator":51,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":51,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T17:25:02.431184Z","state":"measured"},{"denominator":51,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":51,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-09T06:31:02.800959+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2507.11248/citation-record","integrity":"/paper/2507.11248/integrity","json":"/paper/2507.11248/citation-record.json","paper":"/paper/2507.11248"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T17:24:58.827943Z","title":"Self-similar blow-up profiles for slightly supercritical nonlinear Schrödinger equations.Ann","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2507.11248","last_updated":"2025-07-15T12:22:36Z","snapshot_observed_at":"2026-08-10T01:18:57.444408Z","submitted_at":"2025-07-15T12:22:36Z","title":"Mode stability for self-similar blowup of slightly supercritical NLS: I. low-energy spectrum","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-06T17:24:58.827943Z"},"links":{"citing_paper":"/paper/2507.11248"},"observation_digest":"sha256:70e64ace01fba231af8a4a0fff23b166da25708eaa6eed7e48f932072df1d8f1","observation_id":"db7e2470-f179-4007-b9f0-96009f22e801","resolution":{"observed_at":"2026-08-06T17:24:58.827943Z","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":"2026-08-06T17:25:10.595809Z","title":"Turán type inequalities for modified Bessel functions.Bull","venue":null,"work_id":"fbac56f1-ef48-44ab-a97e-232c1489bac4","year":2010},"citing_paper":{"arxiv_id":"2507.11248","last_updated":"2025-07-15T12:22:36Z","snapshot_observed_at":"2026-08-10T01:18:57.444408Z","submitted_at":"2025-07-15T12:22:36Z","title":"Mode stability for self-similar blowup of slightly supercritical NLS: I. low-energy spectrum","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-06T17:24:58.930494Z"},"links":{"citing_paper":"/paper/2507.11248"},"observation_digest":"sha256:0f98c5130b516c428625fc056f0783f452905b8a2949f9b362440b7285bbab6e","observation_id":"bd3c4d87-ba4a-4d44-8446-fd79f53aaf6f","resolution":{"observed_at":"2026-08-06T17:25:10.641721Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T17:25:10.445763Z","title":"New estimates for a time-dependent schrödinger equation.Duke Mathemat- ical Journal, 159(3):417–477, 2011","venue":null,"work_id":"f4c11e2a-da72-4bba-89d3-95a57ee62b74","year":2011},"citing_paper":{"arxiv_id":"2507.11248","last_updated":"2025-07-15T12:22:36Z","snapshot_observed_at":"2026-08-10T01:18:57.444408Z","submitted_at":"2025-07-15T12:22:36Z","title":"Mode stability for self-similar blowup of slightly supercritical NLS: I. low-energy spectrum","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-06T17:24:59.013813Z"},"links":{"citing_paper":"/paper/2507.11248"},"observation_digest":"sha256:283d538c1b1be2c8cb5e32a673ab5a2e84f5d59d170cfb1c3137aa40ade7c0ed","observation_id":"b4ea5688-60ef-4b91-b177-f2045288b209","resolution":{"observed_at":"2026-08-06T17:25:10.514128Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T17:25:10.267738Z","title":"Universi- text","venue":null,"work_id":"3c8daead-5d05-4965-a09e-56f2dfc01f71","year":2011},"citing_paper":{"arxiv_id":"2507.11248","last_updated":"2025-07-15T12:22:36Z","snapshot_observed_at":"2026-08-10T01:18:57.444408Z","submitted_at":"2025-07-15T12:22:36Z","title":"Mode stability for self-similar blowup of slightly supercritical NLS: I. low-energy spectrum","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-06T17:24:59.064941Z"},"links":{"citing_paper":"/paper/2507.11248"},"observation_digest":"sha256:3252fe2aa8f92d5d572633f1124d4e2a4577954ce8547c945749f107388a7230","observation_id":"99c195c3-0d59-42e6-9733-ecd7732951cb","resolution":{"observed_at":"2026-08-06T17:25:10.343129Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T17:25:10.111181Z","title":null,"venue":null,"work_id":"0032d4eb-056e-40cc-84b9-65474ad5ecaa","year":1995},"citing_paper":{"arxiv_id":"2507.11248","last_updated":"2025-07-15T12:22:36Z","snapshot_observed_at":"2026-08-10T01:18:57.444408Z","submitted_at":"2025-07-15T12:22:36Z","title":"Mode stability for self-similar blowup of slightly supercritical NLS: I. low-energy spectrum","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-06T17:24:59.127791Z"},"links":{"citing_paper":"/paper/2507.11248"},"observation_digest":"sha256:2de422784ad251148e72bf6c17329dfbf0755ce90b300d09740cbae67a15315c","observation_id":"51aafa9f-2f42-435a-b499-fa10ab51c7f8","resolution":{"observed_at":"2026-08-06T17:25:10.195959Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T17:25:09.971078Z","title":"New York University, Courant Institute of Mathematical Sciences, New York; American Mathematical Society, Providence, RI, 2003","venue":null,"work_id":"0971d05f-72c5-449d-9315-741dbd3b3338","year":2003},"citing_paper":{"arxiv_id":"2507.11248","last_updated":"2025-07-15T12:22:36Z","snapshot_observed_at":"2026-08-10T01:18:57.444408Z","submitted_at":"2025-07-15T12:22:36Z","title":"Mode stability for self-similar blowup of slightly supercritical NLS: I. low-energy spectrum","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-06T17:24:59.225979Z"},"links":{"citing_paper":"/paper/2507.11248"},"observation_digest":"sha256:28c5b5ec99a79ad08303f2a56d29b36f6b164ee2f136a144b71588b180214c40","observation_id":"24dbdd06-4f42-43a9-86bc-1027433aea50","resolution":{"observed_at":"2026-08-06T17:25:10.042075Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T17:25:09.823727Z","title":"Spectra of lin- earized operators for nls solitary waves.SIAM Journal on Mathematical Analysis, 39(4):1070– 1111, 2008","venue":null,"work_id":"be4c73fa-aaca-4639-b90b-42795b1a5de2","year":2008},"citing_paper":{"arxiv_id":"2507.11248","last_updated":"2025-07-15T12:22:36Z","snapshot_observed_at":"2026-08-10T01:18:57.444408Z","submitted_at":"2025-07-15T12:22:36Z","title":"Mode stability for self-similar blowup of slightly supercritical NLS: I. low-energy spectrum","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-06T17:24:59.269433Z"},"links":{"citing_paper":"/paper/2507.11248"},"observation_digest":"sha256:46ac490d1fcb043fbf522f9c5bf688bf8a3df63ffae7f00d0075a8f06b0e1eae","observation_id":"a52cc8dd-c897-4991-a577-04f81319cc25","resolution":{"observed_at":"2026-08-06T17:25:09.891431Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T17:25:09.622555Z","title":"Co-dimension one stable blowup for the quadratic wave equation beyond the light cone.Com- mun","venue":null,"work_id":"6fa75f56-26dc-4cd8-b3d1-f6e8a87a19c0","year":2024},"citing_paper":{"arxiv_id":"2507.11248","last_updated":"2025-07-15T12:22:36Z","snapshot_observed_at":"2026-08-10T01:18:57.444408Z","submitted_at":"2025-07-15T12:22:36Z","title":"Mode stability for self-similar blowup of slightly supercritical NLS: I. low-energy spectrum","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-06T17:24:59.327423Z"},"links":{"citing_paper":"/paper/2507.11248"},"observation_digest":"sha256:3f3413c3c8973b4a3c55f6f8609cb6b032e51dd6087da51842d954c01ae52aa7","observation_id":"07aed708-36a7-41c1-8d61-83ad1506e209","resolution":{"observed_at":"2026-08-06T17:25:09.714363Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T17:25:09.390209Z","title":"Spectral analysis for singularity formation of the two dimensional Keller-Segel system.Ann","venue":null,"work_id":"465e3b5f-a26a-493d-87d0-cb4c8864c4b9","year":2022},"citing_paper":{"arxiv_id":"2507.11248","last_updated":"2025-07-15T12:22:36Z","snapshot_observed_at":"2026-08-10T01:18:57.444408Z","submitted_at":"2025-07-15T12:22:36Z","title":"Mode stability for self-similar blowup of slightly supercritical NLS: I. low-energy spectrum","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-06T17:24:59.401541Z"},"links":{"citing_paper":"/paper/2507.11248"},"observation_digest":"sha256:a6cb491043a69d4e2c269cda0380a13dfde13b9cd65b8b96b67267f4092ec8ac","observation_id":"3ecc23db-80b4-468a-b066-4f249d173ddc","resolution":{"observed_at":"2026-08-06T17:25:09.496842Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2409.05363","last_updated":"2026-07-06T04:50:08Z","snapshot_observed_at":"2026-07-09T23:17:36.571485Z","submitted_at":"2024-09-09T06:51:26Z","title":"Singularity formed by the collision of two collapsing solitons in interaction for the 2D Keller-Segel system","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2409.05363","snapshot_observed_at":"2026-08-06T17:24:59.439584Z","title":"Singularity formed by the collision of two collapsing solitons in interaction for the 2d Keller-Segel system","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.11248","last_updated":"2025-07-15T12:22:36Z","snapshot_observed_at":"2026-08-10T01:18:57.444408Z","submitted_at":"2025-07-15T12:22:36Z","title":"Mode stability for self-similar blowup of slightly supercritical NLS: I. low-energy spectrum","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-06T17:24:59.439584Z"},"links":{"cited_paper":"/paper/2409.05363","citing_paper":"/paper/2507.11248"},"observation_digest":"sha256:826f3ab3541a17782ac079d9ee0ca30a1cb7998b8701eaa1cfa379b59eefc3a1","observation_id":"fb0c2967-aa3d-4e75-b061-407cd9c3c9eb","resolution":{"observed_at":"2026-08-06T17:24:59.439584Z","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":"2026-08-06T17:25:09.155775Z","title":"Strongly anisotropic type II blow up at an isolated point.J","venue":null,"work_id":"c8a5f92e-d5ce-41d8-8bb0-ff963edd4aeb","year":2020},"citing_paper":{"arxiv_id":"2507.11248","last_updated":"2025-07-15T12:22:36Z","snapshot_observed_at":"2026-08-10T01:18:57.444408Z","submitted_at":"2025-07-15T12:22:36Z","title":"Mode stability for self-similar blowup of slightly supercritical NLS: I. low-energy spectrum","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-06T17:24:59.491298Z"},"links":{"citing_paper":"/paper/2507.11248"},"observation_digest":"sha256:019694889d53699689e6209a3933ce1845d1c7229a23771e23ea6da44f2e0078","observation_id":"695cd958-3ab4-43a3-a5d9-bdba2d2749c3","resolution":{"observed_at":"2026-08-06T17:25:09.243950Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T17:25:08.994395Z","title":"On the stability of type I blow up for the energy super critical heat equation.Mem","venue":null,"work_id":"d9fa8691-aed3-434c-99ac-99e06e59d092","year":2019},"citing_paper":{"arxiv_id":"2507.11248","last_updated":"2025-07-15T12:22:36Z","snapshot_observed_at":"2026-08-10T01:18:57.444408Z","submitted_at":"2025-07-15T12:22:36Z","title":"Mode stability for self-similar blowup of slightly supercritical NLS: I. low-energy spectrum","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-06T17:24:59.539281Z"},"links":{"citing_paper":"/paper/2507.11248"},"observation_digest":"sha256:b65c096218abc5059bef5dcc71aa7a40b013bcdba5cadbf4ea5834ef4c4d9bd1","observation_id":"a7115162-30f6-4c69-af10-d6ba4ba6e11b","resolution":{"observed_at":"2026-08-06T17:25:09.071541Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T17:25:08.738481Z","title":"Mode stability of self-similar wave maps in higher dimensions.Comm","venue":null,"work_id":"acaeff08-1aa3-454b-b5a7-38e08ef53f92","year":2017},"citing_paper":{"arxiv_id":"2507.11248","last_updated":"2025-07-15T12:22:36Z","snapshot_observed_at":"2026-08-10T01:18:57.444408Z","submitted_at":"2025-07-15T12:22:36Z","title":"Mode stability for self-similar blowup of slightly supercritical NLS: I. low-energy spectrum","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-06T17:24:59.596598Z"},"links":{"citing_paper":"/paper/2507.11248"},"observation_digest":"sha256:fbaa3c84063abf40867944cfb8ef6530f695a6377bfec824ad9d1d42deb4d5ce","observation_id":"5940686d-9cdb-4aee-b083-fbfcd1bc3188","resolution":{"observed_at":"2026-08-06T17:25:08.857407Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T17:25:08.467459Z","title":null,"venue":null,"work_id":"64a0d00b-465a-4bb8-8eec-e2b3af89ad06","year":2016},"citing_paper":{"arxiv_id":"2507.11248","last_updated":"2025-07-15T12:22:36Z","snapshot_observed_at":"2026-08-10T01:18:57.444408Z","submitted_at":"2025-07-15T12:22:36Z","title":"Mode stability for self-similar blowup of slightly supercritical NLS: I. low-energy spectrum","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-06T17:24:59.651722Z"},"links":{"citing_paper":"/paper/2507.11248"},"observation_digest":"sha256:f68b8e945b71b4f42511cf52f56d0a2bfe29f9d4243d13a641b803c84534e790","observation_id":"55ad8ef8-dc7c-4aab-82f7-72f2947a816e","resolution":{"observed_at":"2026-08-06T17:25:08.603970Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T17:25:08.280265Z","title":null,"venue":null,"work_id":"f3661aba-957d-4c83-b0a4-176b11986d9b","year":2024},"citing_paper":{"arxiv_id":"2507.11248","last_updated":"2025-07-15T12:22:36Z","snapshot_observed_at":"2026-08-10T01:18:57.444408Z","submitted_at":"2025-07-15T12:22:36Z","title":"Mode stability for self-similar blowup of slightly supercritical NLS: I. low-energy spectrum","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-06T17:24:59.696843Z"},"links":{"citing_paper":"/paper/2507.11248"},"observation_digest":"sha256:f2a67551337530d7a9912da699bd6362a7c51ac5b4cfb8cacc461da165932523","observation_id":"e4d90cc4-9af4-43bf-966f-9655427d6e7b","resolution":{"observed_at":"2026-08-06T17:25:08.349347Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T17:25:07.993128Z","title":"On blowup in supercritical wave equations.Comm","venue":null,"work_id":"4d793b33-fd42-4e2b-af87-ffc0759b2f6c","year":2016},"citing_paper":{"arxiv_id":"2507.11248","last_updated":"2025-07-15T12:22:36Z","snapshot_observed_at":"2026-08-10T01:18:57.444408Z","submitted_at":"2025-07-15T12:22:36Z","title":"Mode stability for self-similar blowup of slightly supercritical NLS: I. low-energy spectrum","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-06T17:24:59.749877Z"},"links":{"citing_paper":"/paper/2507.11248"},"observation_digest":"sha256:4ad0bbc7ddacc20c2ffa788f548a1eaab403c56e96ba2dc9ae072292b0ffc982","observation_id":"716aa14e-f8f5-4c3c-a5e5-ac53d3a39a19","resolution":{"observed_at":"2026-08-06T17:25:08.152477Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T17:25:07.683129Z","title":"Fedoryuk.Asymptotic analysis: linear ordinary differential equations","venue":null,"work_id":"0cbb3a6c-120b-459f-96b0-423bdc94cabb","year":1993},"citing_paper":{"arxiv_id":"2507.11248","last_updated":"2025-07-15T12:22:36Z","snapshot_observed_at":"2026-08-10T01:18:57.444408Z","submitted_at":"2025-07-15T12:22:36Z","title":"Mode stability for self-similar blowup of slightly supercritical NLS: I. low-energy spectrum","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-06T17:24:59.797144Z"},"links":{"citing_paper":"/paper/2507.11248"},"observation_digest":"sha256:27024169250142933e6e34eb9532f4984e062412e2a5409869de76eb5a082690","observation_id":"45783007-b8b9-464b-824a-4fe370b5926e","resolution":{"observed_at":"2026-08-06T17:25:07.814572Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T17:25:07.471573Z","title":"Singular ring solutions of critical and super- critical nonlinear Schrödinger equations.Phys","venue":null,"work_id":"43cede49-d348-4d51-bc09-8aeaf5c52649","year":2007},"citing_paper":{"arxiv_id":"2507.11248","last_updated":"2025-07-15T12:22:36Z","snapshot_observed_at":"2026-08-10T01:18:57.444408Z","submitted_at":"2025-07-15T12:22:36Z","title":"Mode stability for self-similar blowup of slightly supercritical NLS: I. low-energy spectrum","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-06T17:24:59.842656Z"},"links":{"citing_paper":"/paper/2507.11248"},"observation_digest":"sha256:b4e3d9d6ed10bfcea7fb74c334fb38003d58e9f34f0a06b8397443d5dad490dc","observation_id":"9709d7dc-b012-4072-837d-4d4c1bad157d","resolution":{"observed_at":"2026-08-06T17:25:07.579886Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T17:25:07.156614Z","title":"Nonlinear stability of homothetically shrinking Yang- Mills solitons in the equivariant case.Comm","venue":null,"work_id":"2e2776a8-5fb5-46a5-a5d9-97a22ac15171","year":2020},"citing_paper":{"arxiv_id":"2507.11248","last_updated":"2025-07-15T12:22:36Z","snapshot_observed_at":"2026-08-10T01:18:57.444408Z","submitted_at":"2025-07-15T12:22:36Z","title":"Mode stability for self-similar blowup of slightly supercritical NLS: I. low-energy spectrum","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-06T17:24:59.892540Z"},"links":{"citing_paper":"/paper/2507.11248"},"observation_digest":"sha256:d348f3572a3ddf99786864d72103caa4a671ef65616354ce2967f2305c906bee","observation_id":"a31309a5-2644-4b9a-b6db-b657a33b28cf","resolution":{"observed_at":"2026-08-06T17:25:07.324965Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T17:25:06.886297Z","title":"Stable Singularity Formation for the Keller–Segel System in Three Dimensions.Arch","venue":null,"work_id":"84c23641-32ca-4b0d-a3d5-7a8c8b578a9f","year":2024},"citing_paper":{"arxiv_id":"2507.11248","last_updated":"2025-07-15T12:22:36Z","snapshot_observed_at":"2026-08-10T01:18:57.444408Z","submitted_at":"2025-07-15T12:22:36Z","title":"Mode stability for self-similar blowup of slightly supercritical NLS: I. low-energy spectrum","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-06T17:24:59.947789Z"},"links":{"citing_paper":"/paper/2507.11248"},"observation_digest":"sha256:1544bc07c18c654f78132b857dbd3b2747da0800a70ebfef6a9f1c4d1035abf7","observation_id":"8ded573a-488a-4440-a556-4712faa221d1","resolution":{"observed_at":"2026-08-06T17:25:06.982478Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T17:25:06.698972Z","title":"On melting and freezing for the 2D radial Stefan problem","venue":null,"work_id":"173a1d6c-4d7f-49b0-89a8-38a0b99fc4bc","year":2019},"citing_paper":{"arxiv_id":"2507.11248","last_updated":"2025-07-15T12:22:36Z","snapshot_observed_at":"2026-08-10T01:18:57.444408Z","submitted_at":"2025-07-15T12:22:36Z","title":"Mode stability for self-similar blowup of slightly supercritical NLS: I. low-energy spectrum","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-06T17:25:00.004672Z"},"links":{"citing_paper":"/paper/2507.11248"},"observation_digest":"sha256:ed84e854897f019f4cacdd4dd3fa3c6b64d7672a1b1384b6af833f0dfcb82fbb","observation_id":"d230101d-f51e-4406-a664-e35fafa4045d","resolution":{"observed_at":"2026-08-06T17:25:06.804404Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T17:25:06.403503Z","title":"A solution to the focusing 3d NLS that blows up on a contracting sphere.Trans","venue":null,"work_id":"5327ed3d-3e74-4b79-b1e1-6a34d61d29b2","year":2015},"citing_paper":{"arxiv_id":"2507.11248","last_updated":"2025-07-15T12:22:36Z","snapshot_observed_at":"2026-08-10T01:18:57.444408Z","submitted_at":"2025-07-15T12:22:36Z","title":"Mode stability for self-similar blowup of slightly supercritical NLS: I. low-energy spectrum","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-06T17:25:00.083162Z"},"links":{"citing_paper":"/paper/2507.11248"},"observation_digest":"sha256:51462f2d6853600757b3920d6e4ebc0b10e5b9589bf71951b4755052d5020d82","observation_id":"34c4375b-8b23-4d2e-ae7d-a8993cc7d05c","resolution":{"observed_at":"2026-08-06T17:25:06.531043Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T17:25:06.152690Z","title":null,"venue":null,"work_id":"9898744c-2251-40d6-8346-5e544e089afc","year":1977},"citing_paper":{"arxiv_id":"2507.11248","last_updated":"2025-07-15T12:22:36Z","snapshot_observed_at":"2026-08-10T01:18:57.444408Z","submitted_at":"2025-07-15T12:22:36Z","title":"Mode stability for self-similar blowup of slightly supercritical NLS: I. low-energy spectrum","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-06T17:25:00.148771Z"},"links":{"citing_paper":"/paper/2507.11248"},"observation_digest":"sha256:4eb7d145f1a0e32788586b004ad6ff85cf5cd838df0f9c3c64b2a51c93ec949d","observation_id":"151855af-78d2-4df1-b812-aa8196b75b85","resolution":{"observed_at":"2026-08-06T17:25:06.234893Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T17:25:05.957661Z","title":"Sharp universal rate for stable blow-up of corotational wave maps.Comm","venue":null,"work_id":"97a0ddad-0a52-4d1e-8cb0-870e6a88d001","year":2023},"citing_paper":{"arxiv_id":"2507.11248","last_updated":"2025-07-15T12:22:36Z","snapshot_observed_at":"2026-08-10T01:18:57.444408Z","submitted_at":"2025-07-15T12:22:36Z","title":"Mode stability for self-similar blowup of slightly supercritical NLS: I. low-energy spectrum","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-06T17:25:00.224357Z"},"links":{"citing_paper":"/paper/2507.11248"},"observation_digest":"sha256:74118bf826ac79eb846ba2874f067e756a83dda8cc19b53a988d98d5cfc32380","observation_id":"2d06eb13-d615-4551-8f1d-4b071f55833c","resolution":{"observed_at":"2026-08-06T17:25:06.036957Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T17:25:05.734241Z","title":"Self-similar solutions to super-critical gKdV.Nonlinearity, 28(3):545–575, 2015","venue":null,"work_id":"f61d0b2b-a190-4ef2-b141-4917afa561dd","year":2015},"citing_paper":{"arxiv_id":"2507.11248","last_updated":"2025-07-15T12:22:36Z","snapshot_observed_at":"2026-08-10T01:18:57.444408Z","submitted_at":"2025-07-15T12:22:36Z","title":"Mode stability for self-similar blowup of slightly supercritical NLS: I. low-energy spectrum","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-06T17:25:00.293942Z"},"links":{"citing_paper":"/paper/2507.11248"},"observation_digest":"sha256:c1ab94629721794a2a859a79055af627e93dec5d70fdae23725415ef1fe4a7d3","observation_id":"16ea696f-cfbb-415b-b039-a25031699b08","resolution":{"observed_at":"2026-08-06T17:25:05.848506Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T17:25:05.496623Z","title":"Krieger and W","venue":null,"work_id":"bb785232-a51a-4fec-a272-39746fee4285","year":2006},"citing_paper":{"arxiv_id":"2507.11248","last_updated":"2025-07-15T12:22:36Z","snapshot_observed_at":"2026-08-10T01:18:57.444408Z","submitted_at":"2025-07-15T12:22:36Z","title":"Mode stability for self-similar blowup of slightly supercritical NLS: I. low-energy spectrum","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-06T17:25:00.335387Z"},"links":{"citing_paper":"/paper/2507.11248"},"observation_digest":"sha256:74bc133a91f3cd7723663844a924625a6887e4ab1ce7db755bd683df7160159c","observation_id":"aff5e5bf-c919-4b3d-986c-bd9675351726","resolution":{"observed_at":"2026-08-06T17:25:05.596075Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T17:25:05.260901Z","title":"Uniqueness of positive solutions of∆u − u + up = 0 in RN","venue":null,"work_id":"9e036ea2-3e38-4414-8ab6-cf9d07a67b24","year":1989},"citing_paper":{"arxiv_id":"2507.11248","last_updated":"2025-07-15T12:22:36Z","snapshot_observed_at":"2026-08-10T01:18:57.444408Z","submitted_at":"2025-07-15T12:22:36Z","title":"Mode stability for self-similar blowup of slightly supercritical NLS: I. low-energy spectrum","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-06T17:25:00.397536Z"},"links":{"citing_paper":"/paper/2507.11248"},"observation_digest":"sha256:af3d2b8eda25e4ec5d65205ea10820207f8d4a7000e6cb751ebae9676d3ea5d8","observation_id":"81b4aeae-67d3-4321-b23d-d8f08dad399e","resolution":{"observed_at":"2026-08-06T17:25:05.399044Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T17:25:05.154814Z","title":"Stability of isotropic singularities for the nonlinear schrödinger equation.Physica D: Nonlinear Phenomena, 47(3):393–415, 1991","venue":null,"work_id":"f64a12ca-34bd-4263-a0a0-eb38c722a43d","year":1991},"citing_paper":{"arxiv_id":"2507.11248","last_updated":"2025-07-15T12:22:36Z","snapshot_observed_at":"2026-08-10T01:18:57.444408Z","submitted_at":"2025-07-15T12:22:36Z","title":"Mode stability for self-similar blowup of slightly supercritical NLS: I. low-energy spectrum","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-06T17:25:00.443092Z"},"links":{"citing_paper":"/paper/2507.11248"},"observation_digest":"sha256:54cb41879ffb268593a00cf66f8852ea38f9520e6a678478903ee2b567c6af79","observation_id":"7141b5c9-8f43-4067-a835-ac01bedcfe0d","resolution":{"observed_at":"2026-08-06T17:25:05.194593Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T17:25:04.945129Z","title":"Focusing and multi-focusing solu- tions of the nonlinear schrödinger equation.Physica D: Nonlinear Phenomena, 31(1):78–102, 1988","venue":null,"work_id":"dc94bbea-ac4b-479e-8f58-9c58577f45cb","year":1988},"citing_paper":{"arxiv_id":"2507.11248","last_updated":"2025-07-15T12:22:36Z","snapshot_observed_at":"2026-08-10T01:18:57.444408Z","submitted_at":"2025-07-15T12:22:36Z","title":"Mode stability for self-similar blowup of slightly supercritical NLS: I. low-energy spectrum","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-06T17:25:00.495071Z"},"links":{"citing_paper":"/paper/2507.11248"},"observation_digest":"sha256:112c25238962eb05269b853453c10e793f1e7ace281c55bcc2badf1496a6d0b3","observation_id":"2304d617-525e-4ab0-990c-7c257294492b","resolution":{"observed_at":"2026-08-06T17:25:05.059018Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T17:25:04.756267Z","title":"Mode stability for self-similar blowup of slightly supercritical nls: II","venue":null,"work_id":"574d9f3f-0813-433b-bdb1-7c67358a22b9","year":2025},"citing_paper":{"arxiv_id":"2507.11248","last_updated":"2025-07-15T12:22:36Z","snapshot_observed_at":"2026-08-10T01:18:57.444408Z","submitted_at":"2025-07-15T12:22:36Z","title":"Mode stability for self-similar blowup of slightly supercritical NLS: I. low-energy spectrum","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-06T17:25:00.560086Z"},"links":{"citing_paper":"/paper/2507.11248"},"observation_digest":"sha256:c6b81a3dccd39d4088127dd6cd4c13d962f8da84b3c1a1b50d82a036c5a75e33","observation_id":"e8c2e31b-f324-4d01-9f3a-7e07d7460e9a","resolution":{"observed_at":"2026-08-06T17:25:04.859481Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2304.02078","last_updated":"2024-12-27T12:26:10Z","snapshot_observed_at":"2026-08-10T01:18:31.825573Z","submitted_at":"2023-04-04T19:08:51Z","title":"On stability of self-similar blowup for mass supercritical NLS","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2304.02078","snapshot_observed_at":"2026-08-06T17:25:00.622403Z","title":"On stability of self-similar blowup for mass supercritical nls","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2507.11248","last_updated":"2025-07-15T12:22:36Z","snapshot_observed_at":"2026-08-10T01:18:57.444408Z","submitted_at":"2025-07-15T12:22:36Z","title":"Mode stability for self-similar blowup of slightly supercritical NLS: I. low-energy spectrum","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-06T17:25:00.622403Z"},"links":{"cited_paper":"/paper/2304.02078","citing_paper":"/paper/2507.11248"},"observation_digest":"sha256:5768667c0b18bbd5595030f73773dcf040cb970d4c396ab8c290eafaf2a14759","observation_id":"a2986f80-6c2b-4863-8419-ff95eac74868","resolution":{"observed_at":"2026-08-06T17:25:00.622403Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2501.07073","last_updated":"2025-03-30T15:24:56Z","snapshot_observed_at":"2026-08-09T08:14:26.913441Z","submitted_at":"2025-01-13T06:05:01Z","title":"Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2501.07073","snapshot_observed_at":"2026-08-06T17:25:00.700966Z","title":"Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.11248","last_updated":"2025-07-15T12:22:36Z","snapshot_observed_at":"2026-08-10T01:18:57.444408Z","submitted_at":"2025-07-15T12:22:36Z","title":"Mode stability for self-similar blowup of slightly supercritical NLS: I. low-energy spectrum","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-06T17:25:00.700966Z"},"links":{"cited_paper":"/paper/2501.07073","citing_paper":"/paper/2507.11248"},"observation_digest":"sha256:84d37e9795087f4166dc7cacd3830f8b624658d1b37893039e99c02a68709f70","observation_id":"9afe58b9-d730-49da-95dd-5695727b4078","resolution":{"observed_at":"2026-08-06T17:25:00.700966Z","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":"2026-08-06T17:25:04.568496Z","title":"Focusing singularity of the cubic schrödinger equation.Physical Review A, 34(2):1200, 1986","venue":null,"work_id":"67bd89ff-4fbd-412d-a30a-5700778c5d4e","year":1986},"citing_paper":{"arxiv_id":"2507.11248","last_updated":"2025-07-15T12:22:36Z","snapshot_observed_at":"2026-08-10T01:18:57.444408Z","submitted_at":"2025-07-15T12:22:36Z","title":"Mode stability for self-similar blowup of slightly supercritical NLS: I. low-energy spectrum","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-06T17:25:00.754817Z"},"links":{"citing_paper":"/paper/2507.11248"},"observation_digest":"sha256:5b759153bb918902895907d6245a77f891adfdbe915f97d3e36fed0723126ea0","observation_id":"ba5cb18c-8d07-40ef-86a8-628c21d4069d","resolution":{"observed_at":"2026-08-06T17:25:04.655325Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T17:25:04.463345Z","title":"Blow up of the critical norm for some radialL2 super critical nonlinear Schrödinger equations.Amer","venue":null,"work_id":"83141460-792b-42d9-8d1f-10f3b0fd01ad","year":2008},"citing_paper":{"arxiv_id":"2507.11248","last_updated":"2025-07-15T12:22:36Z","snapshot_observed_at":"2026-08-10T01:18:57.444408Z","submitted_at":"2025-07-15T12:22:36Z","title":"Mode stability for self-similar blowup of slightly supercritical NLS: I. low-energy spectrum","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-06T17:25:00.869938Z"},"links":{"citing_paper":"/paper/2507.11248"},"observation_digest":"sha256:438b6af2793e086311529a6cfeafd74709b594620b831953c3b07f3fc550ea13","observation_id":"5008b5c5-0ea0-4425-b656-d22c7c515a47","resolution":{"observed_at":"2026-08-06T17:25:04.501538Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T17:25:04.346060Z","title":null,"venue":null,"work_id":"e389fae7-305d-4b78-8373-2e6cb4542044","year":2015},"citing_paper":{"arxiv_id":"2507.11248","last_updated":"2025-07-15T12:22:36Z","snapshot_observed_at":"2026-08-10T01:18:57.444408Z","submitted_at":"2025-07-15T12:22:36Z","title":"Mode stability for self-similar blowup of slightly supercritical NLS: I. low-energy spectrum","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-06T17:25:00.958242Z"},"links":{"citing_paper":"/paper/2507.11248"},"observation_digest":"sha256:c1c9d1f24056ba099e41c482915b69505d467be643c4e4bdfac4e515e37bbeec","observation_id":"51cee145-942e-4f19-a6aa-eea057e1914c","resolution":{"observed_at":"2026-08-06T17:25:04.403098Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T17:25:01.031422Z","title":"Stable self-similar blow-up dynamics for slightly L2 super-critical NLS equations.Geom","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2507.11248","last_updated":"2025-07-15T12:22:36Z","snapshot_observed_at":"2026-08-10T01:18:57.444408Z","submitted_at":"2025-07-15T12:22:36Z","title":"Mode stability for self-similar blowup of slightly supercritical NLS: I. low-energy spectrum","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-06T17:25:01.031422Z"},"links":{"citing_paper":"/paper/2507.11248"},"observation_digest":"sha256:715632beaee73754518ed428d6c4329c0f9e72694e72936bd90150d520bf2103","observation_id":"c681a14f-3ab6-41f0-9c14-60950f3e7a26","resolution":{"observed_at":"2026-08-06T17:25:01.031422Z","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":"2026-08-06T17:25:04.136873Z","title":"On collapsing ring blow-up solutions to the mass supercritical nonlinear Schrödinger equation.Duke Math","venue":null,"work_id":"79e82d25-6bce-4aba-9267-18250e928467","year":2014},"citing_paper":{"arxiv_id":"2507.11248","last_updated":"2025-07-15T12:22:36Z","snapshot_observed_at":"2026-08-10T01:18:57.444408Z","submitted_at":"2025-07-15T12:22:36Z","title":"Mode stability for self-similar blowup of slightly supercritical NLS: I. low-energy spectrum","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-06T17:25:01.157741Z"},"links":{"citing_paper":"/paper/2507.11248"},"observation_digest":"sha256:8cfb91d5fd5cd3000fa87832307c3b063642aaa7aa583b79533e2ec831816551","observation_id":"08728603-94ce-4059-9ef4-2e9d40bd519a","resolution":{"observed_at":"2026-08-06T17:25:04.252324Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T17:25:04.036496Z","title":null,"venue":null,"work_id":"3ba4f09d-fcd0-4752-9a39-32dace27c416","year":1959},"citing_paper":{"arxiv_id":"2507.11248","last_updated":"2025-07-15T12:22:36Z","snapshot_observed_at":"2026-08-10T01:18:57.444408Z","submitted_at":"2025-07-15T12:22:36Z","title":"Mode stability for self-similar blowup of slightly supercritical NLS: I. low-energy spectrum","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-06T17:25:01.262554Z"},"links":{"citing_paper":"/paper/2507.11248"},"observation_digest":"sha256:9923a1c297c128458c885e71764632f0497f392b090a46619bd6eef9c287253f","observation_id":"79a5a377-5aff-4751-a942-13977d50bbaf","resolution":{"observed_at":"2026-08-06T17:25:04.077149Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T17:25:03.929740Z","title":null,"venue":null,"work_id":"7c321623-17f8-40c5-93e0-2530fe520414","year":null},"citing_paper":{"arxiv_id":"2507.11248","last_updated":"2025-07-15T12:22:36Z","snapshot_observed_at":"2026-08-10T01:18:57.444408Z","submitted_at":"2025-07-15T12:22:36Z","title":"Mode stability for self-similar blowup of slightly supercritical NLS: I. low-energy spectrum","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-06T17:25:01.377161Z"},"links":{"citing_paper":"/paper/2507.11248"},"observation_digest":"sha256:4572fcaef4ce377f712e2003d9016b879bdfdd1b6dcbda73e2e24b0e10eb2f4a","observation_id":"ff8d1030-e6db-40da-9b47-2a87d49ea8c7","resolution":{"observed_at":"2026-08-06T17:25:03.978246Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T17:25:03.674288Z","title":"On the formation of singularities in solutions of the critical nonlinear Schrödinger equation.Ann","venue":null,"work_id":"8898e8e3-ae48-4d02-83da-df2f395e84d5","year":2001},"citing_paper":{"arxiv_id":"2507.11248","last_updated":"2025-07-15T12:22:36Z","snapshot_observed_at":"2026-08-10T01:18:57.444408Z","submitted_at":"2025-07-15T12:22:36Z","title":"Mode stability for self-similar blowup of slightly supercritical NLS: I. low-energy spectrum","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-06T17:25:01.576513Z"},"links":{"citing_paper":"/paper/2507.11248"},"observation_digest":"sha256:a39db5247c5e5c429bfe36977a3f6581150706c0653977c80295f4a31658a966","observation_id":"ca40d2ce-4d72-43e1-b967-2eee5be4e06c","resolution":{"observed_at":"2026-08-06T17:25:03.747256Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T17:25:03.573671Z","title":"Existence and stability of a solution blowing up on a sphere for an L2- supercritical nonlinear Schrödinger equation.Duke Math","venue":null,"work_id":"147b253c-7686-4003-be0d-6b4152af6373","year":2006},"citing_paper":{"arxiv_id":"2507.11248","last_updated":"2025-07-15T12:22:36Z","snapshot_observed_at":"2026-08-10T01:18:57.444408Z","submitted_at":"2025-07-15T12:22:36Z","title":"Mode stability for self-similar blowup of slightly supercritical NLS: I. low-energy spectrum","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-06T17:25:01.659177Z"},"links":{"citing_paper":"/paper/2507.11248"},"observation_digest":"sha256:bc0671a31e60a464679bda8effe905df49df7700ada2cdc9f579363c31fa2c2a","observation_id":"3515d7f5-a2b4-4da2-8db6-4602d8005743","resolution":{"observed_at":"2026-08-06T17:25:03.615312Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T17:25:03.452982Z","title":null,"venue":null,"work_id":"6342e40f-de5f-4ea9-92ad-1b40ae865329","year":1979},"citing_paper":{"arxiv_id":"2507.11248","last_updated":"2025-07-15T12:22:36Z","snapshot_observed_at":"2026-08-10T01:18:57.444408Z","submitted_at":"2025-07-15T12:22:36Z","title":"Mode stability for self-similar blowup of slightly supercritical NLS: I. low-energy spectrum","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-06T17:25:01.722628Z"},"links":{"citing_paper":"/paper/2507.11248"},"observation_digest":"sha256:4ab80fc9d10fb3cda5cac4a22b5839418134c2f8b1b01d5308fc57acf9dc0483","observation_id":"07cb04d8-ad90-43b9-bda9-8b3c4207e6fe","resolution":{"observed_at":"2026-08-06T17:25:03.498121Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T17:25:03.339793Z","title":"Elsevier, 1972","venue":null,"work_id":"24cb1d18-3f82-407d-af66-7292ea9cdf9f","year":1972},"citing_paper":{"arxiv_id":"2507.11248","last_updated":"2025-07-15T12:22:36Z","snapshot_observed_at":"2026-08-10T01:18:57.444408Z","submitted_at":"2025-07-15T12:22:36Z","title":"Mode stability for self-similar blowup of slightly supercritical NLS: I. low-energy spectrum","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-06T17:25:01.829533Z"},"links":{"citing_paper":"/paper/2507.11248"},"observation_digest":"sha256:88b76e3ce372af4f0d22e23126ada191db089824042b6baf70f07bb1c325ce81","observation_id":"7daa412e-a467-4cca-8274-88458821c900","resolution":{"observed_at":"2026-08-06T17:25:03.392973Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T17:25:03.206619Z","title":"Stein and Guido Weiss.Introduction to Fourier analysis on Euclidean spaces, volume No","venue":null,"work_id":"f39ae59a-3126-4f8e-870f-efd769fcdbf8","year":1971},"citing_paper":{"arxiv_id":"2507.11248","last_updated":"2025-07-15T12:22:36Z","snapshot_observed_at":"2026-08-10T01:18:57.444408Z","submitted_at":"2025-07-15T12:22:36Z","title":"Mode stability for self-similar blowup of slightly supercritical NLS: I. low-energy spectrum","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-06T17:25:01.899023Z"},"links":{"citing_paper":"/paper/2507.11248"},"observation_digest":"sha256:a729d26f1c9dd30eb2690343e0f9b3b82480af8b11eb00c74e69f6542489ee95","observation_id":"bb59f4f4-271f-4e09-b6e7-9331ca76c667","resolution":{"observed_at":"2026-08-06T17:25:03.252023Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T17:25:03.077834Z","title":"Focusing nonlinear Schrödinger equation and wave- packet collapse","venue":null,"work_id":"606095d9-405c-4860-9658-ca744bcb7c1e","year":1996},"citing_paper":{"arxiv_id":"2507.11248","last_updated":"2025-07-15T12:22:36Z","snapshot_observed_at":"2026-08-10T01:18:57.444408Z","submitted_at":"2025-07-15T12:22:36Z","title":"Mode stability for self-similar blowup of slightly supercritical NLS: I. low-energy spectrum","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-06T17:25:01.968381Z"},"links":{"citing_paper":"/paper/2507.11248"},"observation_digest":"sha256:44a4e0a1b1ba326d66c5158750578a492aa3918b738cedb2953de08f5f96e022","observation_id":"adf9f104-2327-4f10-86e1-6f7bfc4680ae","resolution":{"observed_at":"2026-08-06T17:25:03.133642Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T17:25:02.955856Z","title":"Springer-Verlag, New York, 1999","venue":null,"work_id":"813d1bea-4114-489a-ac40-629f5dd7fa0c","year":1999},"citing_paper":{"arxiv_id":"2507.11248","last_updated":"2025-07-15T12:22:36Z","snapshot_observed_at":"2026-08-10T01:18:57.444408Z","submitted_at":"2025-07-15T12:22:36Z","title":"Mode stability for self-similar blowup of slightly supercritical NLS: I. low-energy spectrum","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-06T17:25:02.019059Z"},"links":{"citing_paper":"/paper/2507.11248"},"observation_digest":"sha256:b6b10287e692e865dc58f31ac791f2df5ffa5b3702a9e92a1b2c531b5674d30b","observation_id":"6ebd8bfb-3b63-452c-8d40-39bac28b408c","resolution":{"observed_at":"2026-08-06T17:25:03.016540Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T17:25:02.792355Z","title":"Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 2006","venue":null,"work_id":"a9762304-84fd-4211-a7c9-80c7af77e19c","year":2006},"citing_paper":{"arxiv_id":"2507.11248","last_updated":"2025-07-15T12:22:36Z","snapshot_observed_at":"2026-08-10T01:18:57.444408Z","submitted_at":"2025-07-15T12:22:36Z","title":"Mode stability for self-similar blowup of slightly supercritical NLS: I. low-energy spectrum","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-06T17:25:02.126729Z"},"links":{"citing_paper":"/paper/2507.11248"},"observation_digest":"sha256:6733f800b71ea4f99cd9e44dfeec9a2e570ac67079ac7456419bdc04663990a5","observation_id":"86d0a4f7-55d5-4f4e-81ae-489bd7c0f791","resolution":{"observed_at":"2026-08-06T17:25:02.883145Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T17:25:02.224696Z","title":null,"venue":null,"work_id":null,"year":1944},"citing_paper":{"arxiv_id":"2507.11248","last_updated":"2025-07-15T12:22:36Z","snapshot_observed_at":"2026-08-10T01:18:57.444408Z","submitted_at":"2025-07-15T12:22:36Z","title":"Mode stability for self-similar blowup of slightly supercritical NLS: I. low-energy spectrum","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-06T17:25:02.224696Z"},"links":{"citing_paper":"/paper/2507.11248"},"observation_digest":"sha256:3fdffda158a015b13af69d49665d384623a5ae182192bc0bbe1b4cd5b96074dd","observation_id":"564684c3-39a1-4153-81cd-b9e525b1dde9","resolution":{"observed_at":"2026-08-06T17:25:02.224696Z","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":"2026-08-06T17:25:02.624524Z","title":"Weinstein","venue":null,"work_id":"8f7f0da8-dcdd-4b6f-b7a8-17f957ff1a8d","year":1985},"citing_paper":{"arxiv_id":"2507.11248","last_updated":"2025-07-15T12:22:36Z","snapshot_observed_at":"2026-08-10T01:18:57.444408Z","submitted_at":"2025-07-15T12:22:36Z","title":"Mode stability for self-similar blowup of slightly supercritical NLS: I. low-energy spectrum","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-06T17:25:02.339184Z"},"links":{"citing_paper":"/paper/2507.11248"},"observation_digest":"sha256:990e1825347252f06aae12219a6f62bf057bf0fa20b6b76da92f0f4fe396cab4","observation_id":"48c438c5-4c88-4bb0-b7ff-f68016b4b0f0","resolution":{"observed_at":"2026-08-06T17:25:02.679355Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2503.02632","last_updated":"2025-03-04T13:57:42Z","snapshot_observed_at":"2026-08-07T17:30:22.227344Z","submitted_at":"2025-03-04T13:57:42Z","title":"Mode stability of blow-up for wave maps in the absence of symmetry","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2503.02632","snapshot_observed_at":"2026-08-06T17:25:02.431184Z","title":"Mode stability of blow-up for wave maps in the absence of symmetry","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.11248","last_updated":"2025-07-15T12:22:36Z","snapshot_observed_at":"2026-08-10T01:18:57.444408Z","submitted_at":"2025-07-15T12:22:36Z","title":"Mode stability for self-similar blowup of slightly supercritical NLS: I. low-energy spectrum","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-06T17:25:02.431184Z"},"links":{"cited_paper":"/paper/2503.02632","citing_paper":"/paper/2507.11248"},"observation_digest":"sha256:58545d0a865b1291978d5e9ac4d2e0bb7cf494c7d71516c2b4625f72c38aff0f","observation_id":"82e633a3-4667-424d-bba4-bd9011816766","resolution":{"observed_at":"2026-08-06T17:25:02.431184Z","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":"2026-08-06T17:25:03.834989Z","title":null,"venue":null,"work_id":"6b1320de-9a03-40b5-b34a-2ae5b52b3a3e","year":null},"citing_paper":{"arxiv_id":"2507.11248","last_updated":"2025-07-15T12:22:36Z","snapshot_observed_at":"2026-08-10T01:18:57.444408Z","submitted_at":"2025-07-15T12:22:36Z","title":"Mode stability for self-similar blowup of slightly supercritical NLS: I. low-energy spectrum","version":1},"reference_index":2010,"source":"pdf_text","source_observed_at":"2026-08-06T17:25:01.501387Z"},"links":{"citing_paper":"/paper/2507.11248"},"observation_digest":"sha256:d93d8467ed1067d731a62697a85dbe082bb63c89eac1f5be73fe2dedbe7db816","observation_id":"a224101d-9ef3-44a6-a7a6-1eb36548a6f8","resolution":{"observed_at":"2026-08-06T17:25:03.871178Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2507.11248","last_updated":"2025-07-15T12:22:36Z","latest_version":1,"primary_category":"math.AP","snapshot_observed_at":"2026-08-10T01:18:57.444408Z","submitted_at":"2025-07-15T12:22:36Z","title":"Mode stability for self-similar blowup of slightly supercritical NLS: I. low-energy spectrum"},"reference_resolution":{"displayed":51,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":16,"verified_exact":0,"verified_fuzzy":35},"total_outbound_references":51},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"thesis":"As of 10 August 2026, this Paper Citation Record lists 51 of 51 outbound references and 0 inbound Pith citation observations for arXiv:2507.11248."}