{"as_of":"2026-08-10T11:55:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:6c555f74c1c093cb7456cb258743d62251ae1d7d88846cd0f7fdce41cd36a3e2","coverage":[{"denominator":63,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":63,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T12:39:35.381953Z","state":"measured"},{"denominator":67,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":67,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-10T06:31:04.303077+00:00","state":"measured"},{"denominator":4,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":4,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-05T12:30:11.837039Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"pith","source_observed_at":"2026-07-10T08:26:59.067411Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2505.24271","last_updated":"2025-05-30T06:48:06Z","snapshot_observed_at":"2026-08-09T11:54:16.310893Z","submitted_at":"2025-05-30T06:48:06Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2505.24271","snapshot_observed_at":"2026-08-05T12:30:11.837039Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2509.01650","last_updated":"2025-09-01T17:52:10Z","snapshot_observed_at":"2026-08-07T08:19:18.572526Z","submitted_at":"2025-09-01T17:52:10Z","title":"Sharp unconditional well-posedness of the 2-$d$ periodic cubic hyperbolic nonlinear Schr\\\"odinger equation","version":1},"reference_index":67,"source":"pdf_text","source_observed_at":"2026-08-05T12:30:11.837039Z"},"links":{"cited_paper":"/paper/2505.24271","citing_paper":"/paper/2509.01650"},"observation_digest":"sha256:f9aa324f647218068906a3ef8af3b06606f7bb676d6c1e3a07d9fb2926276c72","observation_id":"1496a6f9-a256-440f-b636-2ad5f58eeb86","resolution":{"observed_at":"2026-08-05T12:30:11.837039Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2505.24271","last_updated":"2025-05-30T06:48:06Z","snapshot_observed_at":"2026-08-09T11:54:16.310893Z","submitted_at":"2025-05-30T06:48:06Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS","version":1},"cited_work":{"arxiv_id":"2505.24271","doi":null,"metadata_source":"pith","pith_arxiv_id":"2505.24271","snapshot_observed_at":"2026-07-10T08:26:59.067411Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS","venue":"math.AP","work_id":"fe03c94e-7ba0-4577-a9ed-e32d9176a6a2","year":2025},"citing_paper":{"arxiv_id":"2607.07618","last_updated":"2026-07-08T16:33:53Z","snapshot_observed_at":"2026-08-06T15:12:27.514394Z","submitted_at":"2026-07-08T16:33:53Z","title":"Fourier restriction norm method adapted to controlled paths: stochastic wave equations","version":1},"reference_index":143,"source":"pdf_text","source_observed_at":"2026-07-09T05:21:50.042171Z"},"links":{"cited_paper":"/paper/2505.24271","citing_paper":"/paper/2607.07618"},"observation_digest":"sha256:edbb5b8570491c1f4e88043acb7702faf7c30b2e6eb2d05c8aff019bc195aa17","observation_id":"abd02811-7771-4423-b462-5784bb11fd26","resolution":{"observed_at":"2026-07-09T05:26:02.055696Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2505.24271","last_updated":"2025-05-30T06:48:06Z","snapshot_observed_at":"2026-08-09T11:54:16.310893Z","submitted_at":"2025-05-30T06:48:06Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS","version":1},"cited_work":{"arxiv_id":"2505.24271","doi":null,"metadata_source":"pith","pith_arxiv_id":"2505.24271","snapshot_observed_at":"2026-07-10T08:26:59.067411Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS","venue":"math.AP","work_id":"fe03c94e-7ba0-4577-a9ed-e32d9176a6a2","year":2025},"citing_paper":{"arxiv_id":"2607.08385","last_updated":"2026-07-09T12:03:44Z","snapshot_observed_at":"2026-08-09T08:26:31.956894Z","submitted_at":"2026-07-09T12:03:44Z","title":"Nonlinear PDEs with modulated dispersion III: multiplicative noises","version":1},"reference_index":67,"source":"pdf_text","source_observed_at":"2026-07-10T08:18:29.415024Z"},"links":{"cited_paper":"/paper/2505.24271","citing_paper":"/paper/2607.08385"},"observation_digest":"sha256:f45e7e94fa1cce02c859b2237735f1ef29ab2a6ddb01487859c588d50a8bb06c","observation_id":"dd304ae3-23c7-4963-82b7-1f63908541b3","resolution":{"observed_at":"2026-07-10T08:26:59.068610Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2505.24271","last_updated":"2025-05-30T06:48:06Z","snapshot_observed_at":"2026-08-09T11:54:16.310893Z","submitted_at":"2025-05-30T06:48:06Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2505.24271","snapshot_observed_at":"2026-07-13T00:51:17.670636Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.09033","last_updated":"2026-07-10T01:44:13Z","snapshot_observed_at":"2026-08-06T08:54:27.994887Z","submitted_at":"2026-07-10T01:44:13Z","title":"A remark on pathwise well-posedness of the 1-$d$ stochastic heat equation","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-07-13T00:51:17.670636Z"},"links":{"cited_paper":"/paper/2505.24271","citing_paper":"/paper/2607.09033"},"observation_digest":"sha256:1b020bc1cc9da189bee19099401565267418c68eb234a8e8cfa5b991b974f4c1","observation_id":"7244c0bb-23a5-4aaf-bc31-32fe782ad388","resolution":{"observed_at":"2026-07-13T00:51:17.670636Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2505.24271/citation-record","integrity":"/paper/2505.24271/integrity","json":"/paper/2505.24271/citation-record.json","paper":"/paper/2505.24271"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:39:49.819048Z","title":"B´ enyi, T","venue":null,"work_id":"2f57a5d1-b920-45a4-bc79-ebfee265f039","year":2011},"citing_paper":{"arxiv_id":"2505.24271","last_updated":"2025-05-30T06:48:06Z","snapshot_observed_at":"2026-08-09T11:54:16.310893Z","submitted_at":"2025-05-30T06:48:06Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-07T12:39:28.839372Z"},"links":{"citing_paper":"/paper/2505.24271"},"observation_digest":"sha256:d4b9b87dde16d430f6c18de49e76235bce156e77edc4f4f8344a3498bd9d332d","observation_id":"b6f5a51d-8d99-4cb0-bb19-8caf12660a09","resolution":{"observed_at":"2026-08-07T12:39:49.950002Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T12:39:49.531353Z","title":"B´ enyi, T","venue":null,"work_id":"6d5bcbff-557e-42dd-bc28-2cf51eb3c6f0","year":2015},"citing_paper":{"arxiv_id":"2505.24271","last_updated":"2025-05-30T06:48:06Z","snapshot_observed_at":"2026-08-09T11:54:16.310893Z","submitted_at":"2025-05-30T06:48:06Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-07T12:39:28.916953Z"},"links":{"citing_paper":"/paper/2505.24271"},"observation_digest":"sha256:1499b4f63d602bd11e5ce3321e9b07864ae844ecef8ee6a63b673d27bfbf00ee","observation_id":"7be915e3-5233-4e95-8167-0409bb9f7da1","resolution":{"observed_at":"2026-08-07T12:39:49.635371Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T12:39:49.290301Z","title":"B´ enyi, T","venue":null,"work_id":"5821e5ee-516a-447e-976b-eb70743d9d00","year":2019},"citing_paper":{"arxiv_id":"2505.24271","last_updated":"2025-05-30T06:48:06Z","snapshot_observed_at":"2026-08-09T11:54:16.310893Z","submitted_at":"2025-05-30T06:48:06Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-07T12:39:29.021253Z"},"links":{"citing_paper":"/paper/2505.24271"},"observation_digest":"sha256:3c4a2761e919e0674eb743722d5a4566c6b5f3a5ce6a43667a4804487385c254","observation_id":"eda10b93-79b1-4f02-befb-c78618262be9","resolution":{"observed_at":"2026-08-07T12:39:49.414272Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T12:39:49.008322Z","title":"Bourgain, Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations","venue":null,"work_id":"66128708-9bf8-4394-841d-019c35c3fe44","year":1993},"citing_paper":{"arxiv_id":"2505.24271","last_updated":"2025-05-30T06:48:06Z","snapshot_observed_at":"2026-08-09T11:54:16.310893Z","submitted_at":"2025-05-30T06:48:06Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-07T12:39:29.113365Z"},"links":{"citing_paper":"/paper/2505.24271"},"observation_digest":"sha256:6e6f1b0f94917ab1441f1a210a35b28824b87048cf76ae8ca866f4d3e39fc254","observation_id":"72604e0b-ba4e-4a8d-938b-43fdfae6a3f3","resolution":{"observed_at":"2026-08-07T12:39:49.144736Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T12:39:48.713510Z","title":"Bourgain, Periodic nonlinear Schr¨ odinger equation and invariant measures, Comm","venue":null,"work_id":"4110850f-a26a-43c5-af3d-902e28188eab","year":1994},"citing_paper":{"arxiv_id":"2505.24271","last_updated":"2025-05-30T06:48:06Z","snapshot_observed_at":"2026-08-09T11:54:16.310893Z","submitted_at":"2025-05-30T06:48:06Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-07T12:39:29.187940Z"},"links":{"citing_paper":"/paper/2505.24271"},"observation_digest":"sha256:bca2f09765fea9b2ac7cc40147b80023aad6919c65c079986d9097281b0dc25d","observation_id":"92519b6d-62c8-478c-9f8f-2dee03c8a60d","resolution":{"observed_at":"2026-08-07T12:39:48.882878Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T12:39:48.461881Z","title":"Bourgain, Invariant measures for the 2D-defocusing nonlinear Schr¨ odinger equation, Comm","venue":null,"work_id":"dd0fed19-0707-44e5-8cb4-d2a1022115bb","year":1996},"citing_paper":{"arxiv_id":"2505.24271","last_updated":"2025-05-30T06:48:06Z","snapshot_observed_at":"2026-08-09T11:54:16.310893Z","submitted_at":"2025-05-30T06:48:06Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-07T12:39:29.265529Z"},"links":{"citing_paper":"/paper/2505.24271"},"observation_digest":"sha256:04c1c68d600425ba90c9be6767c64acf219efaf22bdabaab681f02e1aa915a6a","observation_id":"0b4506c3-d79c-425e-a444-5cd16e9ef267","resolution":{"observed_at":"2026-08-07T12:39:48.564744Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T12:39:48.226484Z","title":"Bremner, Lattice basis reduction","venue":null,"work_id":"62360b8a-5d75-4961-81f2-4c48b21e9f05","year":2012},"citing_paper":{"arxiv_id":"2505.24271","last_updated":"2025-05-30T06:48:06Z","snapshot_observed_at":"2026-08-09T11:54:16.310893Z","submitted_at":"2025-05-30T06:48:06Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-07T12:39:29.341028Z"},"links":{"citing_paper":"/paper/2505.24271"},"observation_digest":"sha256:0b87e2d9eeffc31d2f7f14c9eb94ee2e871d540b8dd0b687bc6cc2fb67a31a7e","observation_id":"1dfa599b-d0b2-4c7c-a1fc-73a41062664d","resolution":{"observed_at":"2026-08-07T12:39:48.341768Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T12:39:48.045769Z","title":"Bringmann, Almost sure local well-posedness for a derivative nonlinear wave equation , Int","venue":null,"work_id":"93069210-a516-4aa2-8585-afe221666803","year":2021},"citing_paper":{"arxiv_id":"2505.24271","last_updated":"2025-05-30T06:48:06Z","snapshot_observed_at":"2026-08-09T11:54:16.310893Z","submitted_at":"2025-05-30T06:48:06Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-07T12:39:29.407429Z"},"links":{"citing_paper":"/paper/2505.24271"},"observation_digest":"sha256:35416638d7b42a232a874114a19e3165005a49f114baed60c07e299774139aa0","observation_id":"81ca0689-7856-445a-95e8-6d035e9f72b2","resolution":{"observed_at":"2026-08-07T12:39:48.126619Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T12:39:47.729257Z","title":"Bringmann, Invariant Gibbs measures for the three-dimensional wave equation with a Hartree nonlin- earity II: dynamics , J","venue":null,"work_id":"aa02a72b-385c-42c1-bd3e-7b92e59e596f","year":2024},"citing_paper":{"arxiv_id":"2505.24271","last_updated":"2025-05-30T06:48:06Z","snapshot_observed_at":"2026-08-09T11:54:16.310893Z","submitted_at":"2025-05-30T06:48:06Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-07T12:39:29.480914Z"},"links":{"citing_paper":"/paper/2505.24271"},"observation_digest":"sha256:62d8fc2c2a38330b347d1a0a142b12072a8e1f3d0f3778b27a38a209aa3f0c43","observation_id":"ec9f70b5-311a-4877-8443-8ca8a392b718","resolution":{"observed_at":"2026-08-07T12:39:47.899032Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T12:39:47.434933Z","title":"Bringmann, Y","venue":null,"work_id":"c58dff55-508f-4a09-96dd-e4e879c11e54","year":2024},"citing_paper":{"arxiv_id":"2505.24271","last_updated":"2025-05-30T06:48:06Z","snapshot_observed_at":"2026-08-09T11:54:16.310893Z","submitted_at":"2025-05-30T06:48:06Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-07T12:39:29.542195Z"},"links":{"citing_paper":"/paper/2505.24271"},"observation_digest":"sha256:e1c7d86f90ea304eb1e5f8bf3b8e36bc112657409eac249965b78c0d494fc04f","observation_id":"f5a8daeb-23e3-4133-9a1b-d22f5ac87207","resolution":{"observed_at":"2026-08-07T12:39:47.581986Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T12:39:47.210934Z","title":"Brydges, G","venue":null,"work_id":"b4d54fe7-c7e3-4021-93cf-d9aec9594853","year":1996},"citing_paper":{"arxiv_id":"2505.24271","last_updated":"2025-05-30T06:48:06Z","snapshot_observed_at":"2026-08-09T11:54:16.310893Z","submitted_at":"2025-05-30T06:48:06Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-07T12:39:29.622935Z"},"links":{"citing_paper":"/paper/2505.24271"},"observation_digest":"sha256:97e0a225bacdb04e65ba04361b52455752f90e3e6bc8fc51f65162ac93766ee5","observation_id":"eafb516f-67a9-4f32-b0bb-b49421321cc4","resolution":{"observed_at":"2026-08-07T12:39:47.358172Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T12:39:47.019361Z","title":null,"venue":null,"work_id":"0cc8de66-3a80-4dae-9f52-235c774c7de2","year":2008},"citing_paper":{"arxiv_id":"2505.24271","last_updated":"2025-05-30T06:48:06Z","snapshot_observed_at":"2026-08-09T11:54:16.310893Z","submitted_at":"2025-05-30T06:48:06Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-07T12:39:29.705593Z"},"links":{"citing_paper":"/paper/2505.24271"},"observation_digest":"sha256:f39b9b5faf9a80fb74ecd147a645db4ce91671c7fc4524044896a37adccccc9a","observation_id":"ee4f0b48-ca87-4e5b-a30c-cd816bcb49fc","resolution":{"observed_at":"2026-08-07T12:39:47.086467Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T12:39:46.771687Z","title":null,"venue":null,"work_id":"20519254-cdb8-4485-bfd1-15cdea04de2b","year":2008},"citing_paper":{"arxiv_id":"2505.24271","last_updated":"2025-05-30T06:48:06Z","snapshot_observed_at":"2026-08-09T11:54:16.310893Z","submitted_at":"2025-05-30T06:48:06Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-07T12:39:29.785908Z"},"links":{"citing_paper":"/paper/2505.24271"},"observation_digest":"sha256:ad2b802ba96c3bd271e67a7eeb72c430f585abf50ec4d30575bb3dce4243adcf","observation_id":"afd16050-37d1-45fc-ab2a-e7f06e0ae850","resolution":{"observed_at":"2026-08-07T12:39:46.905007Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T12:39:46.609526Z","title":null,"venue":null,"work_id":"8b3c0514-6dd8-455f-91a1-6d0d04d4351e","year":2014},"citing_paper":{"arxiv_id":"2505.24271","last_updated":"2025-05-30T06:48:06Z","snapshot_observed_at":"2026-08-09T11:54:16.310893Z","submitted_at":"2025-05-30T06:48:06Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-07T12:39:29.945167Z"},"links":{"citing_paper":"/paper/2505.24271"},"observation_digest":"sha256:3fdba619632961fe7210210f5364eec37c66eb94db8c467fb584f6e331156dd0","observation_id":"261fb234-7862-4701-a419-bd52aed8a078","resolution":{"observed_at":"2026-08-07T12:39:46.700476Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T12:39:30.061264Z","title":"Chapouto, M","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.24271","last_updated":"2025-05-30T06:48:06Z","snapshot_observed_at":"2026-08-09T11:54:16.310893Z","submitted_at":"2025-05-30T06:48:06Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-07T12:39:30.061264Z"},"links":{"citing_paper":"/paper/2505.24271"},"observation_digest":"sha256:18ae60ba0e62e616bed7413696a1cfacd500d609ab952c332d7fb53d601da155","observation_id":"2d182df7-1bda-4c68-b7c4-6d5a5780fd32","resolution":{"observed_at":"2026-08-07T12:39:30.061264Z","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":"2026-08-07T12:39:46.388940Z","title":"Chapouto, J","venue":null,"work_id":"7bd1462c-a401-4ae3-a9c9-5109102e43e9","year":null},"citing_paper":{"arxiv_id":"2505.24271","last_updated":"2025-05-30T06:48:06Z","snapshot_observed_at":"2026-08-09T11:54:16.310893Z","submitted_at":"2025-05-30T06:48:06Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-07T12:39:30.127258Z"},"links":{"citing_paper":"/paper/2505.24271"},"observation_digest":"sha256:5500f4087535f236b917aef0e51bbbc3beb7202117f46e8259389447723038d1","observation_id":"8261aaf0-5929-472c-b863-86829ef52cff","resolution":{"observed_at":"2026-08-07T12:39:46.479837Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T12:39:46.062672Z","title":"Chapouto, T","venue":null,"work_id":"170e905b-71c5-4d0f-a436-26e264662e6a","year":null},"citing_paper":{"arxiv_id":"2505.24271","last_updated":"2025-05-30T06:48:06Z","snapshot_observed_at":"2026-08-09T11:54:16.310893Z","submitted_at":"2025-05-30T06:48:06Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-07T12:39:30.181248Z"},"links":{"citing_paper":"/paper/2505.24271"},"observation_digest":"sha256:670a3b04bf61d7ad9d622c2b54bc7517a9ae749f58e5feeaadd43a7b48eb8954","observation_id":"cd9a68ce-38ff-44f0-9189-3a452af65d16","resolution":{"observed_at":"2026-08-07T12:39:46.185852Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T12:39:45.690252Z","title":"Christ, Power series solution of a nonlinear Schr¨ odinger equation, Mathematical aspects of nonlinear dispersive equations, 131–155, Ann","venue":null,"work_id":"b802f166-44c0-4aef-b863-bc53ca8c8d8d","year":2007},"citing_paper":{"arxiv_id":"2505.24271","last_updated":"2025-05-30T06:48:06Z","snapshot_observed_at":"2026-08-09T11:54:16.310893Z","submitted_at":"2025-05-30T06:48:06Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-07T12:39:30.269276Z"},"links":{"citing_paper":"/paper/2505.24271"},"observation_digest":"sha256:46987f877e219fe5049122b7a88ff3a5f555f1a8b5868f23575842efe7483db4","observation_id":"d93ab9cd-f180-4b60-b42e-8aa0bb5353d6","resolution":{"observed_at":"2026-08-07T12:39:45.833547Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T12:39:45.401853Z","title":"Colliander, T","venue":null,"work_id":"6102ec52-8246-4628-9b0e-4b89967b9bd8","year":2012},"citing_paper":{"arxiv_id":"2505.24271","last_updated":"2025-05-30T06:48:06Z","snapshot_observed_at":"2026-08-09T11:54:16.310893Z","submitted_at":"2025-05-30T06:48:06Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-07T12:39:30.377587Z"},"links":{"citing_paper":"/paper/2505.24271"},"observation_digest":"sha256:14ca4f4f9bdeb23af3fb9031779685218a33d293b116daf8b1e9044211886394","observation_id":"1c27ba64-0338-4d63-a868-0d80327eb992","resolution":{"observed_at":"2026-08-07T12:39:45.542967Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T12:39:45.033406Z","title":"Da Prato, A","venue":null,"work_id":"97f198e6-cdfb-4ff3-a963-bed098fbd89d","year":2003},"citing_paper":{"arxiv_id":"2505.24271","last_updated":"2025-05-30T06:48:06Z","snapshot_observed_at":"2026-08-09T11:54:16.310893Z","submitted_at":"2025-05-30T06:48:06Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-07T12:39:30.462759Z"},"links":{"citing_paper":"/paper/2505.24271"},"observation_digest":"sha256:fa4e82804a7971dcb2a2dcf2bf13b1e56ebf7f04535a55d7fb49dccf19076d88","observation_id":"1c7f0738-e249-434c-9336-46cb05e279fd","resolution":{"observed_at":"2026-08-07T12:39:45.214072Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T12:39:44.745123Z","title":"Da Prato, L","venue":null,"work_id":"ef975448-5255-4515-b1f2-ea9f023c1cfb","year":2023},"citing_paper":{"arxiv_id":"2505.24271","last_updated":"2025-05-30T06:48:06Z","snapshot_observed_at":"2026-08-09T11:54:16.310893Z","submitted_at":"2025-05-30T06:48:06Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-07T12:39:30.537890Z"},"links":{"citing_paper":"/paper/2505.24271"},"observation_digest":"sha256:d3ed502b5e8b52b2eca2212e55d401be05e73992443f9ac798ed499cd3d97467","observation_id":"68a3c598-9274-43fc-8e0c-dc2935a558ad","resolution":{"observed_at":"2026-08-07T12:39:44.920401Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T12:39:44.353402Z","title":null,"venue":null,"work_id":"78058cba-8f8e-4f30-8679-4f10516141f9","year":2021},"citing_paper":{"arxiv_id":"2505.24271","last_updated":"2025-05-30T06:48:06Z","snapshot_observed_at":"2026-08-09T11:54:16.310893Z","submitted_at":"2025-05-30T06:48:06Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-07T12:39:30.627198Z"},"links":{"citing_paper":"/paper/2505.24271"},"observation_digest":"sha256:988a154ba18b4b0d761dbd32d7bc09cef01d6c531fdb911d869c9503ad3889dd","observation_id":"982cdc4c-a414-456a-a255-0b806c0f90f5","resolution":{"observed_at":"2026-08-07T12:39:44.547581Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T12:39:43.947434Z","title":null,"venue":null,"work_id":"59d90515-5d33-47b0-9001-12858db6858e","year":2024},"citing_paper":{"arxiv_id":"2505.24271","last_updated":"2025-05-30T06:48:06Z","snapshot_observed_at":"2026-08-09T11:54:16.310893Z","submitted_at":"2025-05-30T06:48:06Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-07T12:39:30.701651Z"},"links":{"citing_paper":"/paper/2505.24271"},"observation_digest":"sha256:66e5c43b67ca77de8284b57258dd42a86cefee89e5b7ffe905e73d985bb90907","observation_id":"cd4ee4a1-509a-4220-b770-7c1248fbe5ac","resolution":{"observed_at":"2026-08-07T12:39:44.130410Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T12:39:43.530786Z","title":null,"venue":null,"work_id":"527974f3-dc2c-4199-b4b0-cc2bea4ddc1d","year":2022},"citing_paper":{"arxiv_id":"2505.24271","last_updated":"2025-05-30T06:48:06Z","snapshot_observed_at":"2026-08-09T11:54:16.310893Z","submitted_at":"2025-05-30T06:48:06Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-07T12:39:30.767906Z"},"links":{"citing_paper":"/paper/2505.24271"},"observation_digest":"sha256:c2ba17d5fe6716785d3d91f2578379f1d01dac260c35b28169ce6b0c88c18371","observation_id":"1e50480b-5258-4762-b03f-bca1c5e11f87","resolution":{"observed_at":"2026-08-07T12:39:43.715280Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T12:39:43.113459Z","title":null,"venue":null,"work_id":"fe127580-d58b-4bb0-b4c1-5a81be9243a6","year":2021},"citing_paper":{"arxiv_id":"2505.24271","last_updated":"2025-05-30T06:48:06Z","snapshot_observed_at":"2026-08-09T11:54:16.310893Z","submitted_at":"2025-05-30T06:48:06Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-07T12:39:30.829154Z"},"links":{"citing_paper":"/paper/2505.24271"},"observation_digest":"sha256:9325c0e1e9fe219b3c8c60b1311ee98f9fcbda1f33d29ae4f16108da68554247","observation_id":"c399efaf-afcb-4801-9f11-2c2c2c29550a","resolution":{"observed_at":"2026-08-07T12:39:43.301777Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T12:39:42.644078Z","title":null,"venue":null,"work_id":"7548490c-9120-4147-96b7-38b178f1db96","year":2021},"citing_paper":{"arxiv_id":"2505.24271","last_updated":"2025-05-30T06:48:06Z","snapshot_observed_at":"2026-08-09T11:54:16.310893Z","submitted_at":"2025-05-30T06:48:06Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-07T12:39:30.941276Z"},"links":{"citing_paper":"/paper/2505.24271"},"observation_digest":"sha256:3a770e4f326aaa075ab9eaf881f0a322c4a05585c67778daf0c34b351f775d2c","observation_id":"c94a626f-c8c7-4e89-9ff3-a016e6e4772e","resolution":{"observed_at":"2026-08-07T12:39:42.888839Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T12:39:31.024324Z","title":"Forlano, T","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2505.24271","last_updated":"2025-05-30T06:48:06Z","snapshot_observed_at":"2026-08-09T11:54:16.310893Z","submitted_at":"2025-05-30T06:48:06Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-07T12:39:31.024324Z"},"links":{"citing_paper":"/paper/2505.24271"},"observation_digest":"sha256:321da2eaf7872d8206c350bf6274aff168fe709ebc4c9fe764c639d42aac7fb3","observation_id":"0eafac55-0bc9-433a-bd3d-0a9a878c26b6","resolution":{"observed_at":"2026-08-07T12:39:31.024324Z","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":"2026-08-07T12:39:42.403910Z","title":"Ginibre, Y","venue":null,"work_id":"4250adb0-f76e-4a95-ba53-baaa6879531a","year":1997},"citing_paper":{"arxiv_id":"2505.24271","last_updated":"2025-05-30T06:48:06Z","snapshot_observed_at":"2026-08-09T11:54:16.310893Z","submitted_at":"2025-05-30T06:48:06Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-07T12:39:31.166617Z"},"links":{"citing_paper":"/paper/2505.24271"},"observation_digest":"sha256:def7be5e58edcd61d5666262d491aca3818d0db25164641048120fe730cafa85","observation_id":"66a928a2-4c38-4c88-bc81-bebf658db9ec","resolution":{"observed_at":"2026-08-07T12:39:42.466302Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2412.09790","last_updated":"2025-05-30T06:48:18Z","snapshot_observed_at":"2026-07-06T20:06:17.706151Z","submitted_at":"2024-12-13T02:11:33Z","title":"Critical threshold for weakly interacting log-correlated focusing Gibbs measures","version":2},"cited_work":{"arxiv_id":"2412.09790","doi":null,"metadata_source":"pith","pith_arxiv_id":"2412.09790","snapshot_observed_at":"2026-08-07T12:39:35.807878Z","title":"Critical threshold for weakly interacting log-correlated focusing Gibbs measures","venue":"math.PR","work_id":"740db0b0-d97c-4a94-a034-fd62250e4f07","year":2024},"citing_paper":{"arxiv_id":"2505.24271","last_updated":"2025-05-30T06:48:06Z","snapshot_observed_at":"2026-08-09T11:54:16.310893Z","submitted_at":"2025-05-30T06:48:06Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-07T12:39:31.306847Z"},"links":{"cited_paper":"/paper/2412.09790","citing_paper":"/paper/2505.24271"},"observation_digest":"sha256:11c1bd7ea6e9f0ff4aef347cb2feded99c8c4e2e8cb3f1ff9f5abffc99f360c7","observation_id":"d72ec0c8-2166-46d6-b246-652eb4962874","resolution":{"observed_at":"2026-08-07T12:39:35.890506Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T12:39:31.420869Z","title":"Gr¨ unrock, S","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2505.24271","last_updated":"2025-05-30T06:48:06Z","snapshot_observed_at":"2026-08-09T11:54:16.310893Z","submitted_at":"2025-05-30T06:48:06Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-07T12:39:31.420869Z"},"links":{"citing_paper":"/paper/2505.24271"},"observation_digest":"sha256:f9d33ca3ef975dcf928d624ca6ccbd3a389b19c2b6a02a931c773557030d38db","observation_id":"0c9f7f7d-f526-4c55-abcc-2eca7c3468f9","resolution":{"observed_at":"2026-08-07T12:39:31.420869Z","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":"2026-08-07T12:39:42.116453Z","title":"Gubinelli, H","venue":null,"work_id":"c1579d78-9369-4dd6-90f3-edfbbac5e230","year":2018},"citing_paper":{"arxiv_id":"2505.24271","last_updated":"2025-05-30T06:48:06Z","snapshot_observed_at":"2026-08-09T11:54:16.310893Z","submitted_at":"2025-05-30T06:48:06Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-07T12:39:31.542007Z"},"links":{"citing_paper":"/paper/2505.24271"},"observation_digest":"sha256:e439af16fc998ac712eebf5bf3d4dccd7a8ec793e2bb0a66a4fe61a7fee7ad3e","observation_id":"0c5c2066-9c92-4ee0-b99c-cd1f87724b68","resolution":{"observed_at":"2026-08-07T12:39:42.222113Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T12:39:41.824968Z","title":"Gubinelli, H","venue":null,"work_id":"32366c73-d399-4f24-936b-3c0a1d7afe54","year":2024},"citing_paper":{"arxiv_id":"2505.24271","last_updated":"2025-05-30T06:48:06Z","snapshot_observed_at":"2026-08-09T11:54:16.310893Z","submitted_at":"2025-05-30T06:48:06Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-07T12:39:31.692231Z"},"links":{"citing_paper":"/paper/2505.24271"},"observation_digest":"sha256:30b8d5ab8712160b340ebf6fa89904fd24ba83b52ac09b04e5f7bb3ef4d2d9e7","observation_id":"4f8da9c0-dd99-429c-9328-387801e49b3d","resolution":{"observed_at":"2026-08-07T12:39:41.990464Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T12:39:41.511283Z","title":null,"venue":null,"work_id":"0faa120b-b258-4b11-ae3d-ad650efae1ad","year":2018},"citing_paper":{"arxiv_id":"2505.24271","last_updated":"2025-05-30T06:48:06Z","snapshot_observed_at":"2026-08-09T11:54:16.310893Z","submitted_at":"2025-05-30T06:48:06Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-07T12:39:31.799818Z"},"links":{"citing_paper":"/paper/2505.24271"},"observation_digest":"sha256:4e94318d3ddf8b8adbc17de7bda0d71a14519e8427d2390f7a0635a683edbda9","observation_id":"4f58cc8c-6143-4768-9d4e-fb7126e4888e","resolution":{"observed_at":"2026-08-07T12:39:41.644246Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T12:39:41.241695Z","title":null,"venue":null,"work_id":"c5afb21c-8085-4343-8d6c-b9eed3cca7eb","year":2024},"citing_paper":{"arxiv_id":"2505.24271","last_updated":"2025-05-30T06:48:06Z","snapshot_observed_at":"2026-08-09T11:54:16.310893Z","submitted_at":"2025-05-30T06:48:06Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-07T12:39:31.868846Z"},"links":{"citing_paper":"/paper/2505.24271"},"observation_digest":"sha256:29c20c237c9f40744909877f13906c3c3477396aa7ecf5c133d5801237c1784a","observation_id":"f4e762c8-b081-484b-9789-919281963df2","resolution":{"observed_at":"2026-08-07T12:39:41.345751Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T12:39:40.996823Z","title":"Kenig, G","venue":null,"work_id":"8ce224c4-7ce9-4999-9a59-5c094a6d7f28","year":1993},"citing_paper":{"arxiv_id":"2505.24271","last_updated":"2025-05-30T06:48:06Z","snapshot_observed_at":"2026-08-09T11:54:16.310893Z","submitted_at":"2025-05-30T06:48:06Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-07T12:39:31.962303Z"},"links":{"citing_paper":"/paper/2505.24271"},"observation_digest":"sha256:be134dac3a7099e3a23f54d0dcd7aa5504a3a0f427ed569ee1f28d766a8d4fc9","observation_id":"b7950843-c813-40c9-960d-03fc41fd8716","resolution":{"observed_at":"2026-08-07T12:39:41.121883Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T12:39:40.724474Z","title":"Kishimoto, Remark on the periodic mass critical nonlinear Schr¨ odinger equation, Proc","venue":null,"work_id":"15c3be34-07cd-412c-8c47-2ff11959dd45","year":2014},"citing_paper":{"arxiv_id":"2505.24271","last_updated":"2025-05-30T06:48:06Z","snapshot_observed_at":"2026-08-09T11:54:16.310893Z","submitted_at":"2025-05-30T06:48:06Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-07T12:39:32.027274Z"},"links":{"citing_paper":"/paper/2505.24271"},"observation_digest":"sha256:cab5be69071748a2732b45a83ef17ef4fde7bc93a8738ade18fc685205a84b9b","observation_id":"964daa6a-3b3b-4a9a-a9ca-3c646e8a8ca2","resolution":{"observed_at":"2026-08-07T12:39:40.851673Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T12:39:40.422956Z","title":"Lebowitz, H","venue":null,"work_id":"daceeed3-cd4b-4a22-85bd-e6cd926b97cb","year":1988},"citing_paper":{"arxiv_id":"2505.24271","last_updated":"2025-05-30T06:48:06Z","snapshot_observed_at":"2026-08-09T11:54:16.310893Z","submitted_at":"2025-05-30T06:48:06Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-07T12:39:32.114628Z"},"links":{"citing_paper":"/paper/2505.24271"},"observation_digest":"sha256:55b616e10cdc1fb659ca39e85c9fdcecb9aefbd2511a631986c71c71a41d71ad","observation_id":"ebad2cec-7de0-4c7c-8ec0-846bc152dd51","resolution":{"observed_at":"2026-08-07T12:39:40.590225Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T12:39:40.152692Z","title":"Lenstra, H.W","venue":null,"work_id":"00e9b537-d0a1-411d-a1cd-4fdb7cf275a0","year":1982},"citing_paper":{"arxiv_id":"2505.24271","last_updated":"2025-05-30T06:48:06Z","snapshot_observed_at":"2026-08-09T11:54:16.310893Z","submitted_at":"2025-05-30T06:48:06Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-07T12:39:32.191159Z"},"links":{"citing_paper":"/paper/2505.24271"},"observation_digest":"sha256:74a8f86f541dd856bbb672956057f21d50b6a3a29dde2b966d3bd8ca4334ab47","observation_id":"74de4a7c-abf3-457b-90f0-97961bdbe4f1","resolution":{"observed_at":"2026-08-07T12:39:40.272564Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T12:39:39.914558Z","title":"L¨ uhrmann, D","venue":null,"work_id":"68e6bd67-4a92-44af-ba4a-bcba119aee33","year":2014},"citing_paper":{"arxiv_id":"2505.24271","last_updated":"2025-05-30T06:48:06Z","snapshot_observed_at":"2026-08-09T11:54:16.310893Z","submitted_at":"2025-05-30T06:48:06Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-07T12:39:32.376847Z"},"links":{"citing_paper":"/paper/2505.24271"},"observation_digest":"sha256:54a2c7234607fb5c3e0a24b7e5019077dbe3f6a54abfabfe0fb8d9188fd2778c","observation_id":"ba390f52-f4b0-4c1e-9b0c-bbec65e87ea3","resolution":{"observed_at":"2026-08-07T12:39:40.009755Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T12:39:32.547663Z","title":"Statistical mechanics of nonlinear wave equations. IV. Cubic Schr¨ odinger","venue":null,"work_id":null,"year":1995},"citing_paper":{"arxiv_id":"2505.24271","last_updated":"2025-05-30T06:48:06Z","snapshot_observed_at":"2026-08-09T11:54:16.310893Z","submitted_at":"2025-05-30T06:48:06Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-07T12:39:32.547663Z"},"links":{"citing_paper":"/paper/2505.24271"},"observation_digest":"sha256:29318c7c591773038f30332f2013ee6d8ef32127b7eda3790bc84eb32f0062b7","observation_id":"8c742cd5-2158-4024-887f-f0b9033a4019","resolution":{"observed_at":"2026-08-07T12:39:32.547663Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:39:32.706268Z","title":"Nelson, A quartic interaction in two dimensions , 1966 Mathematical Theory of Elementary Particles (Proc","venue":null,"work_id":null,"year":1966},"citing_paper":{"arxiv_id":"2505.24271","last_updated":"2025-05-30T06:48:06Z","snapshot_observed_at":"2026-08-09T11:54:16.310893Z","submitted_at":"2025-05-30T06:48:06Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-07T12:39:32.706268Z"},"links":{"citing_paper":"/paper/2505.24271"},"observation_digest":"sha256:5677e807f8cde7221ae8fc86d0754662e1a654c9d1db8092ab77032c5b74f607","observation_id":"aeff04a0-fcd2-4250-b3cd-f147f2ddc3ae","resolution":{"observed_at":"2026-08-07T12:39:32.706268Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:39:32.865492Z","title":"Oh, Note on a lower bound of the Weyl sum in Bourgain ’s paper (GAF A ’93) http://www.maths.ed.ac.uk/∼toh","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.24271","last_updated":"2025-05-30T06:48:06Z","snapshot_observed_at":"2026-08-09T11:54:16.310893Z","submitted_at":"2025-05-30T06:48:06Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-07T12:39:32.865492Z"},"links":{"citing_paper":"/paper/2505.24271"},"observation_digest":"sha256:46f94e8620d9e2c654c598d92d2ffa6bacb7d9575f0f62dc8e21b20aae787697","observation_id":"786d9582-8d14-4dcd-a064-3b4f922558fd","resolution":{"observed_at":"2026-08-07T12:39:32.865492Z","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":"2026-08-07T12:39:39.592870Z","title":"Oh, A remark on norm inflation with general initial data for the cubic nonlinear Schr¨ odinger equations in negative Sobolev spaces , Funkcial","venue":null,"work_id":"663807b7-f9c6-4e4e-a52c-9f9ef4d99c3b","year":2017},"citing_paper":{"arxiv_id":"2505.24271","last_updated":"2025-05-30T06:48:06Z","snapshot_observed_at":"2026-08-09T11:54:16.310893Z","submitted_at":"2025-05-30T06:48:06Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-07T12:39:33.009481Z"},"links":{"citing_paper":"/paper/2505.24271"},"observation_digest":"sha256:c3bc3656322d0f190fbbb3c318cf9a49bbc20e9129ce64bfd8ba0e0f0c0b97af","observation_id":"b7733149-f665-4cb1-bec6-efa301cb7f65","resolution":{"observed_at":"2026-08-07T12:39:39.685171Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T12:39:33.177033Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.24271","last_updated":"2025-05-30T06:48:06Z","snapshot_observed_at":"2026-08-09T11:54:16.310893Z","submitted_at":"2025-05-30T06:48:06Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-07T12:39:33.177033Z"},"links":{"citing_paper":"/paper/2505.24271"},"observation_digest":"sha256:1ad8262a8e3b0e4c4e475d085b1a46da79b2ce89a85fc334ddc66c733217a8e2","observation_id":"1c95bedc-fdf8-47ae-aeef-d8c84df0c110","resolution":{"observed_at":"2026-08-07T12:39:33.177033Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:39:33.312177Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2505.24271","last_updated":"2025-05-30T06:48:06Z","snapshot_observed_at":"2026-08-09T11:54:16.310893Z","submitted_at":"2025-05-30T06:48:06Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-07T12:39:33.312177Z"},"links":{"citing_paper":"/paper/2505.24271"},"observation_digest":"sha256:481cec09ff28e6e8b0374cb1db32c5671e797106ec5c5e4faab7599ac1952f25","observation_id":"d40f82c4-0b2a-4dc2-a6cc-725b96375e23","resolution":{"observed_at":"2026-08-07T12:39:33.312177Z","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":"2026-08-07T12:39:39.340360Z","title":null,"venue":null,"work_id":"d4103bc8-75fb-4514-bf7e-1b1cc9d38075","year":2023},"citing_paper":{"arxiv_id":"2505.24271","last_updated":"2025-05-30T06:48:06Z","snapshot_observed_at":"2026-08-09T11:54:16.310893Z","submitted_at":"2025-05-30T06:48:06Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-07T12:39:33.431693Z"},"links":{"citing_paper":"/paper/2505.24271"},"observation_digest":"sha256:a5734a6d5c4d65d82c1f8b99f45d581d74822d0de49a349e1f994cdf70a81159","observation_id":"48400518-2ef0-451a-ae19-3cc8931b8c7e","resolution":{"observed_at":"2026-08-07T12:39:39.423888Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T12:39:39.135331Z","title":null,"venue":null,"work_id":"1785277e-1ac2-4551-916e-9ee7f1c6cccd","year":2024},"citing_paper":{"arxiv_id":"2505.24271","last_updated":"2025-05-30T06:48:06Z","snapshot_observed_at":"2026-08-09T11:54:16.310893Z","submitted_at":"2025-05-30T06:48:06Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-07T12:39:33.531118Z"},"links":{"citing_paper":"/paper/2505.24271"},"observation_digest":"sha256:010ad31fa9454e0e923f9909517dba95dbdc2394540cbc1d3ae77912aced77a8","observation_id":"aade65eb-7fb7-4f10-b8f6-ada7d692a756","resolution":{"observed_at":"2026-08-07T12:39:39.202667Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T12:39:38.848995Z","title":null,"venue":null,"work_id":"98932f62-491b-4fa1-a139-593e9a906b16","year":2022},"citing_paper":{"arxiv_id":"2505.24271","last_updated":"2025-05-30T06:48:06Z","snapshot_observed_at":"2026-08-09T11:54:16.310893Z","submitted_at":"2025-05-30T06:48:06Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-07T12:39:33.660898Z"},"links":{"citing_paper":"/paper/2505.24271"},"observation_digest":"sha256:2db2b469ac265f19f7959cf53840bf751696c768b47f54197b5f31fa7e10fd80","observation_id":"dda5a55e-a0d2-46ad-be0f-3d1dbc06a7ac","resolution":{"observed_at":"2026-08-07T12:39:38.995909Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T12:39:38.550859Z","title":null,"venue":null,"work_id":"ea4032e3-9008-4151-9da9-23125606a25d","year":2012},"citing_paper":{"arxiv_id":"2505.24271","last_updated":"2025-05-30T06:48:06Z","snapshot_observed_at":"2026-08-09T11:54:16.310893Z","submitted_at":"2025-05-30T06:48:06Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-07T12:39:33.756904Z"},"links":{"citing_paper":"/paper/2505.24271"},"observation_digest":"sha256:6c76cdde5ea1298bad5d5da08053970e508466fd2940e95901e06c50eeddbbc6","observation_id":"da5b56b7-1f10-43cd-ab09-ab6265ba74a5","resolution":{"observed_at":"2026-08-07T12:39:38.698660Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T12:39:38.204093Z","title":null,"venue":null,"work_id":"78fa6924-083e-40ce-8633-686c6bec774a","year":2018},"citing_paper":{"arxiv_id":"2505.24271","last_updated":"2025-05-30T06:48:06Z","snapshot_observed_at":"2026-08-09T11:54:16.310893Z","submitted_at":"2025-05-30T06:48:06Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-07T12:39:33.899483Z"},"links":{"citing_paper":"/paper/2505.24271"},"observation_digest":"sha256:04120244baa9b591c062702bd6bfa7dc192d428de78bad8521e8f078ac7a8bd8","observation_id":"6d791f85-4f96-4657-b655-195011c30587","resolution":{"observed_at":"2026-08-07T12:39:38.350892Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T12:39:34.020358Z","title":null,"venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2505.24271","last_updated":"2025-05-30T06:48:06Z","snapshot_observed_at":"2026-08-09T11:54:16.310893Z","submitted_at":"2025-05-30T06:48:06Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS","version":1},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-07T12:39:34.020358Z"},"links":{"citing_paper":"/paper/2505.24271"},"observation_digest":"sha256:01a5a07edd7ef432fadfa3905da199307381318ed0394f9d1cc6e26e9f1d0339","observation_id":"17df0d50-2d37-4068-b000-e73626c9b31a","resolution":{"observed_at":"2026-08-07T12:39:34.020358Z","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":"2026-08-07T12:39:37.822013Z","title":null,"venue":null,"work_id":"d89394c8-afe0-44c2-8291-e5929b03f914","year":2020},"citing_paper":{"arxiv_id":"2505.24271","last_updated":"2025-05-30T06:48:06Z","snapshot_observed_at":"2026-08-09T11:54:16.310893Z","submitted_at":"2025-05-30T06:48:06Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS","version":1},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-07T12:39:34.190694Z"},"links":{"citing_paper":"/paper/2505.24271"},"observation_digest":"sha256:33a055b4964421aa998ba73caf28c47824f00e9a900647ad8db845e822c6dca4","observation_id":"aa73d863-452d-4ac6-8ee0-b1487471f7ad","resolution":{"observed_at":"2026-08-07T12:39:37.985332Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T12:39:34.323718Z","title":null,"venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2505.24271","last_updated":"2025-05-30T06:48:06Z","snapshot_observed_at":"2026-08-09T11:54:16.310893Z","submitted_at":"2025-05-30T06:48:06Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS","version":1},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-07T12:39:34.323718Z"},"links":{"citing_paper":"/paper/2505.24271"},"observation_digest":"sha256:d430d9d06301528fcb899230e44427f04cf30139ffa03781d767b0bc30668cbb","observation_id":"5ab5a0e0-081e-4ab2-844b-601e5f947584","resolution":{"observed_at":"2026-08-07T12:39:34.323718Z","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":"2026-08-07T12:39:37.492248Z","title":null,"venue":null,"work_id":"cfdee626-418f-4776-8ad5-1c439631d0a8","year":2021},"citing_paper":{"arxiv_id":"2505.24271","last_updated":"2025-05-30T06:48:06Z","snapshot_observed_at":"2026-08-09T11:54:16.310893Z","submitted_at":"2025-05-30T06:48:06Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS","version":1},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-07T12:39:34.449123Z"},"links":{"citing_paper":"/paper/2505.24271"},"observation_digest":"sha256:c3a5e9951d1f1c56f4f3789aee530ef9f182a08dd21ee55a21598fd50668da85","observation_id":"a7eb40f6-81e6-4663-a123-e53792801168","resolution":{"observed_at":"2026-08-07T12:39:37.610097Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T12:39:37.205672Z","title":null,"venue":null,"work_id":"d634bffb-0094-492b-b229-c243196cb252","year":2022},"citing_paper":{"arxiv_id":"2505.24271","last_updated":"2025-05-30T06:48:06Z","snapshot_observed_at":"2026-08-09T11:54:16.310893Z","submitted_at":"2025-05-30T06:48:06Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS","version":1},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-07T12:39:34.612474Z"},"links":{"citing_paper":"/paper/2505.24271"},"observation_digest":"sha256:526dae89cac8adeb61c9382ad4d3fdf96e5c5c716ba541093de1709a7f12b013","observation_id":"5a3f3dc3-4edb-40ed-a333-639107068b7f","resolution":{"observed_at":"2026-08-07T12:39:37.279152Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T12:39:37.033501Z","title":"Pocovnicu, Almost sure global well-posedness for the energy-critical defocusing nonlinear wave equation on Rd, d = 4 and 5, J","venue":null,"work_id":"d851f790-180c-454f-a58d-d8e753d78127","year":2017},"citing_paper":{"arxiv_id":"2505.24271","last_updated":"2025-05-30T06:48:06Z","snapshot_observed_at":"2026-08-09T11:54:16.310893Z","submitted_at":"2025-05-30T06:48:06Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS","version":1},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-08-07T12:39:34.722313Z"},"links":{"citing_paper":"/paper/2505.24271"},"observation_digest":"sha256:4dc8f0b4d0a7c5d06c10b86a2052ce19ea6908c8ad98ef98c13a5fc5d48a5ca9","observation_id":"02db9913-9f6e-4426-b56a-854ef1ee8c08","resolution":{"observed_at":"2026-08-07T12:39:37.102252Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T12:39:36.769031Z","title":"Ryan, Introduction to tensor products of Banach spaces, Springer Monographs in Mathematics","venue":null,"work_id":"41de11f0-a64a-48b2-849a-3a2dc72f3a98","year":2002},"citing_paper":{"arxiv_id":"2505.24271","last_updated":"2025-05-30T06:48:06Z","snapshot_observed_at":"2026-08-09T11:54:16.310893Z","submitted_at":"2025-05-30T06:48:06Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS","version":1},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-08-07T12:39:34.806964Z"},"links":{"citing_paper":"/paper/2505.24271"},"observation_digest":"sha256:e6d0bdaf4fbba9f5e5d308724e2489c55d8b63528f460b6a5abdfad4fe2cbfc9","observation_id":"ad904551-08f3-4a5e-ad72-38a679231702","resolution":{"observed_at":"2026-08-07T12:39:36.879358Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T12:39:34.895955Z","title":"Simon, The P (φ)2 Euclidean (quantum) field theory, Princeton Series in Physics","venue":null,"work_id":null,"year":1974},"citing_paper":{"arxiv_id":"2505.24271","last_updated":"2025-05-30T06:48:06Z","snapshot_observed_at":"2026-08-09T11:54:16.310893Z","submitted_at":"2025-05-30T06:48:06Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS","version":1},"reference_index":58,"source":"pdf_text","source_observed_at":"2026-08-07T12:39:34.895955Z"},"links":{"citing_paper":"/paper/2505.24271"},"observation_digest":"sha256:1d04845633d46c8d145420b5cd092584596b2ecb4104c1bf139f3a799a3468d4","observation_id":"7eff76c8-cd28-4370-a472-9465d19f95d8","resolution":{"observed_at":"2026-08-07T12:39:34.895955Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:39:35.024261Z","title":"Takaoka, N","venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2505.24271","last_updated":"2025-05-30T06:48:06Z","snapshot_observed_at":"2026-08-09T11:54:16.310893Z","submitted_at":"2025-05-30T06:48:06Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS","version":1},"reference_index":59,"source":"pdf_text","source_observed_at":"2026-08-07T12:39:35.024261Z"},"links":{"citing_paper":"/paper/2505.24271"},"observation_digest":"sha256:111b462cf50d53951f8b907251e92e99d06341148b6ef88c9865ca3621b5f4f5","observation_id":"0b982747-568d-43c0-8efd-b520d0d0ba45","resolution":{"observed_at":"2026-08-07T12:39:35.024261Z","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":"2026-08-07T12:39:36.532741Z","title":"Tao, Nonlinear dispersive equations","venue":null,"work_id":"cdfb4f3e-7b60-4373-8ef1-ff0ed3f827b8","year":2006},"citing_paper":{"arxiv_id":"2505.24271","last_updated":"2025-05-30T06:48:06Z","snapshot_observed_at":"2026-08-09T11:54:16.310893Z","submitted_at":"2025-05-30T06:48:06Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS","version":1},"reference_index":60,"source":"pdf_text","source_observed_at":"2026-08-07T12:39:35.128988Z"},"links":{"citing_paper":"/paper/2505.24271"},"observation_digest":"sha256:9ea50f55d04ddcee9661a503887affab6e651ca71ea8b35165deb8223c10a174","observation_id":"4a50267c-1d41-4444-8d6e-6d9056f415d1","resolution":{"observed_at":"2026-08-07T12:39:36.656196Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T12:39:36.286162Z","title":"Tzvetkov, Construction of a Gibbs measure associated to the periodic Benjamin-Ono equation , Probab","venue":null,"work_id":"04b28c88-a281-43af-bad3-efbe6cceeba7","year":2010},"citing_paper":{"arxiv_id":"2505.24271","last_updated":"2025-05-30T06:48:06Z","snapshot_observed_at":"2026-08-09T11:54:16.310893Z","submitted_at":"2025-05-30T06:48:06Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS","version":1},"reference_index":61,"source":"pdf_text","source_observed_at":"2026-08-07T12:39:35.235382Z"},"links":{"citing_paper":"/paper/2505.24271"},"observation_digest":"sha256:a8df79da2d230f8767121638cc396fcca9658ff47c6c99d45c70aa6400078f5e","observation_id":"4ba0ebbd-f33b-44f3-b2e9-e2ea08d70c43","resolution":{"observed_at":"2026-08-07T12:39:36.418643Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-07T12:39:36.025017Z","title":"Tzvetkov, Random data wave equations , Singular random dynamics, 221–313, Lecture Notes in Math., 2253, Fond","venue":null,"work_id":"452dabee-e123-422a-b5fc-146c33fa9fc1","year":2019},"citing_paper":{"arxiv_id":"2505.24271","last_updated":"2025-05-30T06:48:06Z","snapshot_observed_at":"2026-08-09T11:54:16.310893Z","submitted_at":"2025-05-30T06:48:06Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS","version":1},"reference_index":62,"source":"pdf_text","source_observed_at":"2026-08-07T12:39:35.307295Z"},"links":{"citing_paper":"/paper/2505.24271"},"observation_digest":"sha256:285ffa458ff7f9692f1643d1077ffa0b7d012a7d6112e1a45ceb548e6ae52d21","observation_id":"5b61f48d-1908-4a8e-bd04-1cae882c82b1","resolution":{"observed_at":"2026-08-07T12:39:36.134028Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2212.00604","last_updated":"2022-12-01T15:58:14Z","snapshot_observed_at":"2026-08-04T19:05:00.604181Z","submitted_at":"2022-12-01T15:58:14Z","title":"On the inviscid limit of the singular stochastic complex Ginzburg-Landau equation at statistical equilibrium","version":1},"cited_work":{"arxiv_id":"2212.00604","doi":null,"metadata_source":"pith","pith_arxiv_id":"2212.00604","snapshot_observed_at":"2026-08-07T12:39:35.543028Z","title":"On the inviscid limit of the singular stochastic complex Ginzburg-Landau equation at statistical equilibrium","venue":"math.AP","work_id":"6545c698-6235-4350-9968-5c2d12a655a9","year":2022},"citing_paper":{"arxiv_id":"2505.24271","last_updated":"2025-05-30T06:48:06Z","snapshot_observed_at":"2026-08-09T11:54:16.310893Z","submitted_at":"2025-05-30T06:48:06Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS","version":1},"reference_index":63,"source":"pdf_text","source_observed_at":"2026-08-07T12:39:35.381953Z"},"links":{"cited_paper":"/paper/2212.00604","citing_paper":"/paper/2505.24271"},"observation_digest":"sha256:1d11d676b95d745b08c8800b9a71fdf85df1ef18e925ac22bc5a3ed2fd55143a","observation_id":"e66f1723-5118-4ee8-a456-8c4695fe1b0d","resolution":{"observed_at":"2026-08-07T12:39:35.639556Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2505.24271","last_updated":"2025-05-30T06:48:06Z","latest_version":1,"primary_category":"math.AP","snapshot_observed_at":"2026-08-09T11:54:16.310893Z","submitted_at":"2025-05-30T06:48:06Z","title":"Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS"},"reference_resolution":{"displayed":63,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":30,"verified_exact":2,"verified_fuzzy":31},"total_outbound_references":63},"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":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"thesis":"As of 10 August 2026, this Paper Citation Record lists 63 of 63 outbound references and 4 inbound Pith citation observations for arXiv:2505.24271."}