{"as_of":"2026-08-18T09:43:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:8910bd66d47974625221eac18754ffb28ecc36d20583b608889d779b6e6ae041","coverage":[{"denominator":54,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":54,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-11T14:41:45.332971Z","state":"measured"},{"denominator":58,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":58,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-18T06:34:40.430872+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":"2026-08-15T22:49:27.058271Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-05-11T21:01:12.577423Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2412.11845","last_updated":"2025-02-12T15:29:43Z","snapshot_observed_at":"2026-08-18T05:20:12.991711Z","submitted_at":"2024-12-16T15:08:31Z","title":"Infinite dimensional invariant tori for nonlinear Schr\\\"odinger equations","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2412.11845","snapshot_observed_at":"2026-08-11T23:26:46.022710Z","title":"Bernier, B","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2412.02648","last_updated":"2025-01-25T15:41:32Z","snapshot_observed_at":"2026-08-14T07:49:11.259581Z","submitted_at":"2024-12-03T18:22:55Z","title":"Asymptotically full measure sets of almost-periodic solutions for the NLS equation","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-11T23:26:46.022710Z"},"links":{"cited_paper":"/paper/2412.11845","citing_paper":"/paper/2412.02648"},"observation_digest":"sha256:7703b7de917d3fee4af562365ed49852eb3a706adea5ce725175aa769ad7182b","observation_id":"0967815d-323c-49cd-b16a-c48e6f905f2c","resolution":{"observed_at":"2026-08-11T23:26:46.022710Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2412.11845","last_updated":"2025-02-12T15:29:43Z","snapshot_observed_at":"2026-08-18T05:20:12.991711Z","submitted_at":"2024-12-16T15:08:31Z","title":"Infinite dimensional invariant tori for nonlinear Schr\\\"odinger equations","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2412.11845","snapshot_observed_at":"2026-08-15T22:49:27.058271Z","title":"Bernier, B","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.06526","last_updated":"2025-05-10T06:13:26Z","snapshot_observed_at":"2026-08-15T22:37:44.256825Z","submitted_at":"2025-05-10T06:13:26Z","title":"The Existence of Full-Dimensional KAM tori for one-dimensional nonlinear Klein-Gordon equation","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-15T22:49:27.058271Z"},"links":{"cited_paper":"/paper/2412.11845","citing_paper":"/paper/2505.06526"},"observation_digest":"sha256:22f1a9ad12884bb66d42c98e78f603aa6eff674deb76a7493b0b314066a6c692","observation_id":"1820b89e-e1e3-4506-b65c-1b656b45ea27","resolution":{"observed_at":"2026-08-15T22:49:27.058271Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2412.11845","last_updated":"2025-02-12T15:29:43Z","snapshot_observed_at":"2026-08-18T05:20:12.991711Z","submitted_at":"2024-12-16T15:08:31Z","title":"Infinite dimensional invariant tori for nonlinear Schr\\\"odinger equations","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2412.11845","snapshot_observed_at":"2026-08-15T21:27:17.760230Z","title":"Bernier, B","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.10051","last_updated":"2025-05-15T07:54:59Z","snapshot_observed_at":"2026-08-15T21:15:22.783480Z","submitted_at":"2025-05-15T07:54:59Z","title":"On almost periodic solutions to NLS without external parameters","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-15T21:27:17.760230Z"},"links":{"cited_paper":"/paper/2412.11845","citing_paper":"/paper/2505.10051"},"observation_digest":"sha256:ebee7915db5e4441629845f7611d4cdc9fd26e40ad942e2eb09271d033236d04","observation_id":"944ff3b3-2be3-45c4-bb37-8e2d90176623","resolution":{"observed_at":"2026-08-15T21:27:17.760230Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2412.11845","last_updated":"2025-02-12T15:29:43Z","snapshot_observed_at":"2026-08-18T05:20:12.991711Z","submitted_at":"2024-12-16T15:08:31Z","title":"Infinite dimensional invariant tori for nonlinear Schr\\\"odinger equations","version":2},"cited_work":{"arxiv_id":"2412.11845","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2412.11845","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Bernier, B","venue":null,"work_id":"63ef36e5-066c-4c1b-82bd-d72b3f0b9d57","year":2024},"citing_paper":{"arxiv_id":"2604.23202","last_updated":"2026-04-25T08:25:31Z","snapshot_observed_at":"2026-08-14T15:37:14.204210Z","submitted_at":"2026-04-25T08:25:31Z","title":"On the construction of almost periodic solutions for the derivative nonlinear Schr\\\"odinger equation","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-05-08T07:21:54.159245Z"},"links":{"cited_paper":"/paper/2412.11845","citing_paper":"/paper/2604.23202"},"observation_digest":"sha256:5b43efcbfcec45c8652a66dfc7e112492f1d341de45a6a56476318465d73e339","observation_id":"04c987ff-9621-4bdb-9118-7cf8d4c7f0da","resolution":{"observed_at":"2026-05-11T21:01:12.587482Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2412.11845/citation-record","integrity":"/paper/2412.11845/integrity","json":"/paper/2412.11845/citation-record.json","paper":"/paper/2412.11845"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s00222-018-0812-2","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T14:41:45.903252Z","title":"Baldi, M","venue":null,"work_id":"0472a2e9-16db-4bf8-97fb-99873796521a","year":2018},"citing_paper":{"arxiv_id":"2412.11845","last_updated":"2025-02-12T15:29:43Z","snapshot_observed_at":"2026-08-18T05:20:12.991711Z","submitted_at":"2024-12-16T15:08:31Z","title":"Infinite dimensional invariant tori for nonlinear Schr\\\"odinger equations","version":2},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-11T14:41:45.094719Z"},"links":{"citing_paper":"/paper/2412.11845"},"observation_digest":"sha256:76c43bcd4a3a29b5b02e49fddee3347af415fdf19ce56185e1384b8b090c1fb8","observation_id":"5eaae3ff-7cee-474c-b368-b7bd8c108c91","resolution":{"observed_at":"2026-08-11T14:41:45.908002Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2402.04122","last_updated":"2025-06-24T09:17:22Z","snapshot_observed_at":"2026-08-16T16:18:10.286234Z","submitted_at":"2024-02-06T16:19:57Z","title":"Long time stability for cubic nonlinear Schr\\\"odinger equations on non-rectangular flat tori","version":2},"cited_work":{"arxiv_id":"2402.04122","doi":null,"metadata_source":"pith","pith_arxiv_id":"2402.04122","snapshot_observed_at":"2026-08-11T14:41:46.079809Z","title":"Long time stability for cubic nonlinear Schr\\\"odinger equations on non-rectangular flat tori","venue":"math.AP","work_id":"541a1e1c-450b-4e28-b055-9963359c1147","year":2024},"citing_paper":{"arxiv_id":"2412.11845","last_updated":"2025-02-12T15:29:43Z","snapshot_observed_at":"2026-08-18T05:20:12.991711Z","submitted_at":"2024-12-16T15:08:31Z","title":"Infinite dimensional invariant tori for nonlinear Schr\\\"odinger equations","version":2},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-11T14:41:45.100110Z"},"links":{"cited_paper":"/paper/2402.04122","citing_paper":"/paper/2412.11845"},"observation_digest":"sha256:7742b2812db20f52b320c6988f30fd76bf6fdbafd5f7c60f4ed47d4bf6b1b2c9","observation_id":"eb1c9d3e-9e5e-4545-9456-c752d8302e41","resolution":{"observed_at":"2026-08-11T14:41:46.084597Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T14:41:45.104950Z","title":"Bernier, E","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2412.11845","last_updated":"2025-02-12T15:29:43Z","snapshot_observed_at":"2026-08-18T05:20:12.991711Z","submitted_at":"2024-12-16T15:08:31Z","title":"Infinite dimensional invariant tori for nonlinear Schr\\\"odinger equations","version":2},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-11T14:41:45.104950Z"},"links":{"citing_paper":"/paper/2412.11845"},"observation_digest":"sha256:a120ffad4a4853fef5d8a44b9975f78e4d9359517da9883b4828f1ad46aaca95","observation_id":"b257ec47-7d9c-4489-a2e6-a8365a174e9d","resolution":{"observed_at":"2026-08-11T14:41:45.104950Z","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":"2026-08-11T14:41:45.109919Z","title":"Bernier, B","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2412.11845","last_updated":"2025-02-12T15:29:43Z","snapshot_observed_at":"2026-08-18T05:20:12.991711Z","submitted_at":"2024-12-16T15:08:31Z","title":"Infinite dimensional invariant tori for nonlinear Schr\\\"odinger equations","version":2},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-11T14:41:45.109919Z"},"links":{"citing_paper":"/paper/2412.11845"},"observation_digest":"sha256:6c04e1c90355328729c1db996862ebe786c67d3f7d3b48a75930fe64e3ad1cab","observation_id":"d81050e7-061a-494c-a1cd-5dff08c0e6c7","resolution":{"observed_at":"2026-08-11T14:41:45.109919Z","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":"10.5802/jep.193","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T14:41:45.870150Z","title":"Bernier, B","venue":null,"work_id":"1c735dc1-a479-4975-be72-1c0a8a47df79","year":2022},"citing_paper":{"arxiv_id":"2412.11845","last_updated":"2025-02-12T15:29:43Z","snapshot_observed_at":"2026-08-18T05:20:12.991711Z","submitted_at":"2024-12-16T15:08:31Z","title":"Infinite dimensional invariant tori for nonlinear Schr\\\"odinger equations","version":2},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-11T14:41:45.114859Z"},"links":{"citing_paper":"/paper/2412.11845"},"observation_digest":"sha256:f6475500cb4b007f8ef5145b7d8be20c53ce59ad845ef15d4a4c56a49536a1cc","observation_id":"842a70d1-fc55-43b0-b3e8-174b211177cc","resolution":{"observed_at":"2026-08-11T14:41:45.874696Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2305.05236","last_updated":"2024-12-17T10:33:20Z","snapshot_observed_at":"2026-08-18T00:08:05.921724Z","submitted_at":"2023-05-09T07:55:19Z","title":"Dynamics of quintic nonlinear Schr{\\\"o}dinger equations in $H^{2/5+}(\\mathbb{T})$","version":3},"cited_work":{"arxiv_id":"2305.05236","doi":null,"metadata_source":"pith","pith_arxiv_id":"2305.05236","snapshot_observed_at":"2026-08-11T14:41:46.061128Z","title":"Dynamics of quintic nonlinear Schr{\\\"o}dinger equations in $H^{2/5+}(\\mathbb{T})$","venue":"math.AP","work_id":"9f867a0a-ea6d-476f-8955-10876c220a4f","year":2023},"citing_paper":{"arxiv_id":"2412.11845","last_updated":"2025-02-12T15:29:43Z","snapshot_observed_at":"2026-08-18T05:20:12.991711Z","submitted_at":"2024-12-16T15:08:31Z","title":"Infinite dimensional invariant tori for nonlinear Schr\\\"odinger equations","version":2},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-11T14:41:45.119741Z"},"links":{"cited_paper":"/paper/2305.05236","citing_paper":"/paper/2412.11845"},"observation_digest":"sha256:278f6791bd65060fcc1fccbc057260f3aa1c99d66708b1b85d7a20b5925e5919","observation_id":"0e59c9e2-2894-4018-b513-51fe1fa9857d","resolution":{"observed_at":"2026-08-11T14:41:46.066138Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.4171/jems/361","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T14:41:45.856308Z","title":"Berti, P","venue":null,"work_id":"4e8b5f9b-1ec4-4aa3-83a7-96708d1b8168","year":2013},"citing_paper":{"arxiv_id":"2412.11845","last_updated":"2025-02-12T15:29:43Z","snapshot_observed_at":"2026-08-18T05:20:12.991711Z","submitted_at":"2024-12-16T15:08:31Z","title":"Infinite dimensional invariant tori for nonlinear Schr\\\"odinger equations","version":2},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-11T14:41:45.125253Z"},"links":{"citing_paper":"/paper/2412.11845"},"observation_digest":"sha256:1ae07ef5665114c1b03feb7df0c8b926c617ba47ce5b2289774dfd0033a010ff","observation_id":"3208cdc8-adb7-40af-a791-73b6c43caace","resolution":{"observed_at":"2026-08-11T14:41:45.860843Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s00222-023-01195-4","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T14:41:45.841685Z","title":"Berti, Z","venue":null,"work_id":"98bee09d-026e-4926-b247-538c5685b4db","year":2023},"citing_paper":{"arxiv_id":"2412.11845","last_updated":"2025-02-12T15:29:43Z","snapshot_observed_at":"2026-08-18T05:20:12.991711Z","submitted_at":"2024-12-16T15:08:31Z","title":"Infinite dimensional invariant tori for nonlinear Schr\\\"odinger equations","version":2},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-11T14:41:45.129806Z"},"links":{"citing_paper":"/paper/2412.11845"},"observation_digest":"sha256:ac0c6d9dd6d7f7b4104fa5f6b7e880573d37b00adab389522e37fc71449038be","observation_id":"9ae2deaa-f1bc-4a1a-ba24-0fb84f468145","resolution":{"observed_at":"2026-08-11T14:41:45.846422Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.24033/ast.1053","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T14:41:45.827999Z","title":"Berti, T","venue":null,"work_id":"3c921189-0faa-47cf-ad8c-734eadb20874","year":2018},"citing_paper":{"arxiv_id":"2412.11845","last_updated":"2025-02-12T15:29:43Z","snapshot_observed_at":"2026-08-18T05:20:12.991711Z","submitted_at":"2024-12-16T15:08:31Z","title":"Infinite dimensional invariant tori for nonlinear Schr\\\"odinger equations","version":2},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-11T14:41:45.134272Z"},"links":{"citing_paper":"/paper/2412.11845"},"observation_digest":"sha256:22daf1c0dbfa6a4b7c8b9101de5ba21ce460ed62e847a9bc63db5598fed62942","observation_id":"3bead78e-6553-4107-bf90-22921eb2c702","resolution":{"observed_at":"2026-08-11T14:41:45.832330Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2412.02648","last_updated":"2025-01-25T15:41:32Z","snapshot_observed_at":"2026-08-14T07:49:11.259581Z","submitted_at":"2024-12-03T18:22:55Z","title":"Asymptotically full measure sets of almost-periodic solutions for the NLS equation","version":2},"cited_work":{"arxiv_id":"2412.02648","doi":null,"metadata_source":"pith","pith_arxiv_id":"2412.02648","snapshot_observed_at":"2026-08-11T14:41:46.041305Z","title":"Asymptotically full measure sets of almost-periodic solutions for the NLS equation","venue":"math.AP","work_id":"7af3c99b-fda2-4f1c-ac63-5d3f18b84807","year":2024},"citing_paper":{"arxiv_id":"2412.11845","last_updated":"2025-02-12T15:29:43Z","snapshot_observed_at":"2026-08-18T05:20:12.991711Z","submitted_at":"2024-12-16T15:08:31Z","title":"Infinite dimensional invariant tori for nonlinear Schr\\\"odinger equations","version":2},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-11T14:41:45.138552Z"},"links":{"cited_paper":"/paper/2412.02648","citing_paper":"/paper/2412.11845"},"observation_digest":"sha256:e4e3ec33e048814b982884836e570f81b99a314bd61e8e9462426f0821e2039b","observation_id":"56fee972-2df0-416c-a33a-296e51cf0c54","resolution":{"observed_at":"2026-08-11T14:41:46.046331Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.anihpc.2020.09.003","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T14:41:45.813918Z","title":"Biasco, J.E","venue":null,"work_id":"0d70dd0e-c71d-404b-a362-f7bd347213d5","year":2020},"citing_paper":{"arxiv_id":"2412.11845","last_updated":"2025-02-12T15:29:43Z","snapshot_observed_at":"2026-08-18T05:20:12.991711Z","submitted_at":"2024-12-16T15:08:31Z","title":"Infinite dimensional invariant tori for nonlinear Schr\\\"odinger equations","version":2},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-11T14:41:45.143650Z"},"links":{"citing_paper":"/paper/2412.11845"},"observation_digest":"sha256:d50d2447b31ec984b8f2f20a0595cdbe5913aaee8b219e315f57debafc332976","observation_id":"3e4f4f00-632c-42ec-b797-925ba5d8b027","resolution":{"observed_at":"2026-08-11T14:41:45.818433Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T14:41:45.148202Z","title":"Biasco, J.E","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2412.11845","last_updated":"2025-02-12T15:29:43Z","snapshot_observed_at":"2026-08-18T05:20:12.991711Z","submitted_at":"2024-12-16T15:08:31Z","title":"Infinite dimensional invariant tori for nonlinear Schr\\\"odinger equations","version":2},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-11T14:41:45.148202Z"},"links":{"citing_paper":"/paper/2412.11845"},"observation_digest":"sha256:e7e0a720f31708026849eb4eb9c78440146661061e64e2e94d7be5c5cbb829de","observation_id":"8ff6c484-bfc0-4ac0-8e96-b5bcd0e34382","resolution":{"observed_at":"2026-08-11T14:41:45.148202Z","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":"2026-08-11T14:41:46.121805Z","title":"Bohr , Almost Periodic Functions, Chelsea Publishing Co., New York, 1947","venue":null,"work_id":"468b9cf4-efd7-4229-aac3-25981416953c","year":1947},"citing_paper":{"arxiv_id":"2412.11845","last_updated":"2025-02-12T15:29:43Z","snapshot_observed_at":"2026-08-18T05:20:12.991711Z","submitted_at":"2024-12-16T15:08:31Z","title":"Infinite dimensional invariant tori for nonlinear Schr\\\"odinger equations","version":2},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-11T14:41:45.152490Z"},"links":{"citing_paper":"/paper/2412.11845"},"observation_digest":"sha256:4a1e46815fb337eeb75df8585d1743777f34ea62994ddf753687811fcbf8385a","observation_id":"988f331f-574f-48f2-a998-559eac73cf2a","resolution":{"observed_at":"2026-08-11T14:41:46.126584Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1155/s1073792894000516","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T14:41:45.791050Z","title":"Bourgain , Construction of quasi-periodic solutions for Hamiltonian perturbations of linear equations and applications to nonlinear PDE, Internat","venue":null,"work_id":"ef993677-cc7c-48ca-b82a-a74ef05a007f","year":1994},"citing_paper":{"arxiv_id":"2412.11845","last_updated":"2025-02-12T15:29:43Z","snapshot_observed_at":"2026-08-18T05:20:12.991711Z","submitted_at":"2024-12-16T15:08:31Z","title":"Infinite dimensional invariant tori for nonlinear Schr\\\"odinger equations","version":2},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-11T14:41:45.156809Z"},"links":{"citing_paper":"/paper/2412.11845"},"observation_digest":"sha256:a78c81ad791897e22e2d0c5e54d372434007081ca55a5ae1a75ef4b904ab2828","observation_id":"d5a781ce-3f44-4d10-ad1f-c7ac2fb099b7","resolution":{"observed_at":"2026-08-11T14:41:45.795659Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T14:41:46.108400Z","title":"Bourgain, Invariant measures for the 2D-defocusing nonlinear Schr\\\"odinger equation, Comm","venue":null,"work_id":"f65d0d9e-947f-40d5-83d7-cf89f85b57b5","year":1996},"citing_paper":{"arxiv_id":"2412.11845","last_updated":"2025-02-12T15:29:43Z","snapshot_observed_at":"2026-08-18T05:20:12.991711Z","submitted_at":"2024-12-16T15:08:31Z","title":"Infinite dimensional invariant tori for nonlinear Schr\\\"odinger equations","version":2},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-11T14:41:45.160992Z"},"links":{"citing_paper":"/paper/2412.11845"},"observation_digest":"sha256:6c8fefb0f598d3580b613597de0084dff318925c9e9f68c02010b211c78d8460","observation_id":"0ced7e56-f6ae-4541-b5db-c8cfb7d66438","resolution":{"observed_at":"2026-08-11T14:41:46.112904Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T14:41:45.167059Z","title":null,"venue":null,"work_id":null,"year":1996},"citing_paper":{"arxiv_id":"2412.11845","last_updated":"2025-02-12T15:29:43Z","snapshot_observed_at":"2026-08-18T05:20:12.991711Z","submitted_at":"2024-12-16T15:08:31Z","title":"Infinite dimensional invariant tori for nonlinear Schr\\\"odinger equations","version":2},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-11T14:41:45.167059Z"},"links":{"citing_paper":"/paper/2412.11845"},"observation_digest":"sha256:34ce0d28bfc2e9efc7de75dfb561aa3fbf813a473863743cae52e716418c0aa0","observation_id":"5b152214-3376-49b2-869b-022d28197834","resolution":{"observed_at":"2026-08-11T14:41:45.167059Z","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":"2026-08-11T14:41:45.171281Z","title":"Bourgain , Quasi-periodic solutions of H amiltonian perturbations of 2 D linear S chr\\\"odinger equations , Ann","venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2412.11845","last_updated":"2025-02-12T15:29:43Z","snapshot_observed_at":"2026-08-18T05:20:12.991711Z","submitted_at":"2024-12-16T15:08:31Z","title":"Infinite dimensional invariant tori for nonlinear Schr\\\"odinger equations","version":2},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-11T14:41:45.171281Z"},"links":{"citing_paper":"/paper/2412.11845"},"observation_digest":"sha256:e465895bb037aeba81b64b0ae34f199ee9b68bbbcfa9121dbb21d3bf30774509","observation_id":"8fee6926-0697-4de5-ac01-25aee0da1070","resolution":{"observed_at":"2026-08-11T14:41:45.171281Z","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":"2026-08-11T14:41:45.175452Z","title":"Bourgain , On diffusion in high-dimensional Hamiltonian systems and PDE, J","venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2412.11845","last_updated":"2025-02-12T15:29:43Z","snapshot_observed_at":"2026-08-18T05:20:12.991711Z","submitted_at":"2024-12-16T15:08:31Z","title":"Infinite dimensional invariant tori for nonlinear Schr\\\"odinger equations","version":2},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-11T14:41:45.175452Z"},"links":{"citing_paper":"/paper/2412.11845"},"observation_digest":"sha256:cfac6fa7604d82a6ef867a827f2635f15c344ae19e16355bd2c9bd0f66613e66","observation_id":"57cdef68-dc5b-44cb-99eb-54681ac34c96","resolution":{"observed_at":"2026-08-11T14:41:45.175452Z","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":"2026-08-11T14:41:45.179597Z","title":"Bourgain , On invariant tori of full dimension for 1 D periodic NLS , J","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2412.11845","last_updated":"2025-02-12T15:29:43Z","snapshot_observed_at":"2026-08-18T05:20:12.991711Z","submitted_at":"2024-12-16T15:08:31Z","title":"Infinite dimensional invariant tori for nonlinear Schr\\\"odinger equations","version":2},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-11T14:41:45.179597Z"},"links":{"citing_paper":"/paper/2412.11845"},"observation_digest":"sha256:66ebb15a064f460a79b877f6aaaf2879884f7bbf5f5ab8c34920687998a6a04a","observation_id":"9a3a1f0b-1d4e-43ed-8f0d-09c15a6c43e3","resolution":{"observed_at":"2026-08-11T14:41:45.179597Z","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":"10.4064/sm-39-1-59-76","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T14:41:45.742005Z","title":"Bochnak, J","venue":null,"work_id":"efbec2bc-3bd8-40a6-9322-7571bcd7644c","year":1971},"citing_paper":{"arxiv_id":"2412.11845","last_updated":"2025-02-12T15:29:43Z","snapshot_observed_at":"2026-08-18T05:20:12.991711Z","submitted_at":"2024-12-16T15:08:31Z","title":"Infinite dimensional invariant tori for nonlinear Schr\\\"odinger equations","version":2},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-11T14:41:45.183912Z"},"links":{"citing_paper":"/paper/2412.11845"},"observation_digest":"sha256:f8e226b33df8207707511bf95e1b55583c94d5b0db32f7a4d4dfa887e81c2786","observation_id":"c4760880-0830-4909-8229-b8e8b1112783","resolution":{"observed_at":"2026-08-11T14:41:45.746538Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"1995.1033","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T14:41:46.019101Z","title":"Chierchia, P","venue":null,"work_id":"088fb990-fc3a-4344-8eaf-00376875aedd","year":1995},"citing_paper":{"arxiv_id":"2412.11845","last_updated":"2025-02-12T15:29:43Z","snapshot_observed_at":"2026-08-18T05:20:12.991711Z","submitted_at":"2024-12-16T15:08:31Z","title":"Infinite dimensional invariant tori for nonlinear Schr\\\"odinger equations","version":2},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-11T14:41:45.188013Z"},"links":{"citing_paper":"/paper/2412.11845"},"observation_digest":"sha256:7defaef82b2d1a22339e2b06a7f4050c85a6bcb834486bdc1710280b1f4af534","observation_id":"bc57733f-a1c6-4d2b-a3ff-0da06bcaea83","resolution":{"observed_at":"2026-08-11T14:41:46.026376Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T14:41:45.192105Z","title":"Cong , The existence of full dimensional KAM tori for nonlinear Schr\\\"odinger equation, Math","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2412.11845","last_updated":"2025-02-12T15:29:43Z","snapshot_observed_at":"2026-08-18T05:20:12.991711Z","submitted_at":"2024-12-16T15:08:31Z","title":"Infinite dimensional invariant tori for nonlinear Schr\\\"odinger equations","version":2},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-11T14:41:45.192105Z"},"links":{"citing_paper":"/paper/2412.11845"},"observation_digest":"sha256:fb321c0867756ae5c5ff3f1ef8305f77a0a1e5ce4b6eb0d6e49bf716b58fa0a2","observation_id":"dd3cbbb8-e716-4f13-b099-6ffe452565d3","resolution":{"observed_at":"2026-08-11T14:41:45.192105Z","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":"10.1016/j.jde.2017.12.013","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T14:41:45.717312Z","title":null,"venue":null,"work_id":"b6ba64eb-e5d2-47c7-9716-620c16c9a441","year":2018},"citing_paper":{"arxiv_id":"2412.11845","last_updated":"2025-02-12T15:29:43Z","snapshot_observed_at":"2026-08-18T05:20:12.991711Z","submitted_at":"2024-12-16T15:08:31Z","title":"Infinite dimensional invariant tori for nonlinear Schr\\\"odinger equations","version":2},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-11T14:41:45.196364Z"},"links":{"citing_paper":"/paper/2412.11845"},"observation_digest":"sha256:10476c5e7331288d23a19849cb105bb97892a4d4e7d68612cc59094699edf348","observation_id":"8db63d57-7d3b-4c2c-9b57-e66cba06deb9","resolution":{"observed_at":"2026-08-11T14:41:45.722005Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.anihpc.2020.09.006","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T14:41:45.703382Z","title":null,"venue":null,"work_id":"2706065e-4f74-4cc9-bf16-7cb52ad49a64","year":2021},"citing_paper":{"arxiv_id":"2412.11845","last_updated":"2025-02-12T15:29:43Z","snapshot_observed_at":"2026-08-18T05:20:12.991711Z","submitted_at":"2024-12-16T15:08:31Z","title":"Infinite dimensional invariant tori for nonlinear Schr\\\"odinger equations","version":2},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-08-11T14:41:45.200493Z"},"links":{"citing_paper":"/paper/2412.11845"},"observation_digest":"sha256:448ab67e3833f21d73c066b02171901886832ee5e71f4ca39d37e52e2ccc3f78","observation_id":"047af598-ae4e-4773-8da0-2c0e9943107c","resolution":{"observed_at":"2026-08-11T14:41:45.707900Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2309.14276","last_updated":"2023-09-25T16:39:38Z","snapshot_observed_at":"2026-08-16T14:57:47.598773Z","submitted_at":"2023-09-25T16:39:38Z","title":"Almost-periodic solutions to the NLS equation with smooth convolution potentials","version":1},"cited_work":{"arxiv_id":"2309.14276","doi":null,"metadata_source":"pith","pith_arxiv_id":"2309.14276","snapshot_observed_at":"2026-08-11T14:41:45.936036Z","title":"Almost-periodic solutions to the NLS equation with smooth convolution potentials","venue":"math.AP","work_id":"ad3296a8-4d27-407c-bb2d-78d1490484b6","year":2023},"citing_paper":{"arxiv_id":"2412.11845","last_updated":"2025-02-12T15:29:43Z","snapshot_observed_at":"2026-08-18T05:20:12.991711Z","submitted_at":"2024-12-16T15:08:31Z","title":"Infinite dimensional invariant tori for nonlinear Schr\\\"odinger equations","version":2},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-08-11T14:41:45.204749Z"},"links":{"cited_paper":"/paper/2309.14276","citing_paper":"/paper/2412.11845"},"observation_digest":"sha256:369647c1073a6e89afea63c0e4c6baa3eb25587298465d56c3f4ae732e7f7f2e","observation_id":"5e5e5cb0-f3ed-4ae7-93eb-6496963d4d21","resolution":{"observed_at":"2026-08-11T14:41:45.941258Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T14:41:45.209380Z","title":"Craig, C.E","venue":null,"work_id":null,"year":1993},"citing_paper":{"arxiv_id":"2412.11845","last_updated":"2025-02-12T15:29:43Z","snapshot_observed_at":"2026-08-18T05:20:12.991711Z","submitted_at":"2024-12-16T15:08:31Z","title":"Infinite dimensional invariant tori for nonlinear Schr\\\"odinger equations","version":2},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-08-11T14:41:45.209380Z"},"links":{"citing_paper":"/paper/2412.11845"},"observation_digest":"sha256:0d56424aeb3c5eaf7d27b9c812a9808731814d7922b694d124df50e717471fc0","observation_id":"25a65c9e-d9d6-47ed-afe6-06595cf15412","resolution":{"observed_at":"2026-08-11T14:41:45.209380Z","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":"2026-08-11T14:41:45.213649Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2412.11845","last_updated":"2025-02-12T15:29:43Z","snapshot_observed_at":"2026-08-18T05:20:12.991711Z","submitted_at":"2024-12-16T15:08:31Z","title":"Infinite dimensional invariant tori for nonlinear Schr\\\"odinger equations","version":2},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-08-11T14:41:45.213649Z"},"links":{"citing_paper":"/paper/2412.11845"},"observation_digest":"sha256:e315a398394f94eda6c8fab4d1f2dfbb734d83903c4d0a8d521781a898c707d9","observation_id":"214b6fb8-f50c-4423-a8f8-1487c32561e0","resolution":{"observed_at":"2026-08-11T14:41:45.213649Z","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":"2026-08-11T14:41:45.218151Z","title":"Eliasson, S.B","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2412.11845","last_updated":"2025-02-12T15:29:43Z","snapshot_observed_at":"2026-08-18T05:20:12.991711Z","submitted_at":"2024-12-16T15:08:31Z","title":"Infinite dimensional invariant tori for nonlinear Schr\\\"odinger equations","version":2},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-08-11T14:41:45.218151Z"},"links":{"citing_paper":"/paper/2412.11845"},"observation_digest":"sha256:7efbfb914ad34a520afa23281e094cf7814356b156a036e9ebe991a78afbc8a8","observation_id":"fb6b73e4-dc95-4239-9069-9c0e72dffd28","resolution":{"observed_at":"2026-08-11T14:41:45.218151Z","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":"10.1007/s00039-016-0390-7","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T14:41:45.662328Z","title":"Eliasson, B","venue":null,"work_id":"c2565cbd-a9cb-446e-8127-1801e39e5d38","year":2016},"citing_paper":{"arxiv_id":"2412.11845","last_updated":"2025-02-12T15:29:43Z","snapshot_observed_at":"2026-08-18T05:20:12.991711Z","submitted_at":"2024-12-16T15:08:31Z","title":"Infinite dimensional invariant tori for nonlinear Schr\\\"odinger equations","version":2},"reference_index":29,"source":"arxiv_source","source_observed_at":"2026-08-11T14:41:45.222577Z"},"links":{"citing_paper":"/paper/2412.11845"},"observation_digest":"sha256:628dd1cef7166bf137d803b9f96b2a32498953899cee5e10b2da91129a501825","observation_id":"99eea4bd-173a-4c0c-8120-eb7b9ab8d462","resolution":{"observed_at":"2026-08-11T14:41:45.666981Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.4310/mrl.2013.v20.n6.a7","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T14:41:45.647451Z","title":"Erdo gan, N","venue":null,"work_id":"f51533a4-006f-4693-a11b-a346a0c9f500","year":2013},"citing_paper":{"arxiv_id":"2412.11845","last_updated":"2025-02-12T15:29:43Z","snapshot_observed_at":"2026-08-18T05:20:12.991711Z","submitted_at":"2024-12-16T15:08:31Z","title":"Infinite dimensional invariant tori for nonlinear Schr\\\"odinger equations","version":2},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-08-11T14:41:45.226737Z"},"links":{"citing_paper":"/paper/2412.11845"},"observation_digest":"sha256:1a9b0f8222f0b1dc9488a178abd3349990505805e04127baa204f380c9c6bc36","observation_id":"f22c4a4a-4a4e-4532-856e-346adc749019","resolution":{"observed_at":"2026-08-11T14:41:45.652287Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1093/imrn/rns189","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T14:41:45.632943Z","title":"Erdo gan, N","venue":null,"work_id":"bb56daf1-fe5f-4d30-90db-6379faf689f2","year":2013},"citing_paper":{"arxiv_id":"2412.11845","last_updated":"2025-02-12T15:29:43Z","snapshot_observed_at":"2026-08-18T05:20:12.991711Z","submitted_at":"2024-12-16T15:08:31Z","title":"Infinite dimensional invariant tori for nonlinear Schr\\\"odinger equations","version":2},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-08-11T14:41:45.231209Z"},"links":{"citing_paper":"/paper/2412.11845"},"observation_digest":"sha256:ba5d127602ff95f27ee3637eac689f4e2f934b1513ebb71310c113a68dd6978e","observation_id":"798a1de1-bd9d-43fe-a295-a49989a311da","resolution":{"observed_at":"2026-08-11T14:41:45.638199Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.2140/apde.2013.6.723","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T14:41:45.618290Z","title":"Erdo gan, N","venue":null,"work_id":"59b40595-ebad-4f3a-93d4-3e4d2a6c6c13","year":2013},"citing_paper":{"arxiv_id":"2412.11845","last_updated":"2025-02-12T15:29:43Z","snapshot_observed_at":"2026-08-18T05:20:12.991711Z","submitted_at":"2024-12-16T15:08:31Z","title":"Infinite dimensional invariant tori for nonlinear Schr\\\"odinger equations","version":2},"reference_index":32,"source":"arxiv_source","source_observed_at":"2026-08-11T14:41:45.235486Z"},"links":{"citing_paper":"/paper/2412.11845"},"observation_digest":"sha256:df651851eb7ac9b1ee124557f673262af796b9b665e1018966c13e31458f2c67","observation_id":"5685f72c-68ea-4eae-98bc-f99053af79ef","resolution":{"observed_at":"2026-08-11T14:41:45.623828Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1512/iumj.2019.68.7618","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T14:41:45.604066Z","title":"urel, N. Tzirakis, Smoothing for the fractional Schr\\","venue":null,"work_id":"1dbd532a-593b-45ae-87ba-9734278fd425","year":2019},"citing_paper":{"arxiv_id":"2412.11845","last_updated":"2025-02-12T15:29:43Z","snapshot_observed_at":"2026-08-18T05:20:12.991711Z","submitted_at":"2024-12-16T15:08:31Z","title":"Infinite dimensional invariant tori for nonlinear Schr\\\"odinger equations","version":2},"reference_index":33,"source":"arxiv_source","source_observed_at":"2026-08-11T14:41:45.239735Z"},"links":{"citing_paper":"/paper/2412.11845"},"observation_digest":"sha256:73130f9026754fd0ab5d1600ce94f660839d1e3b6bf3f29d8c93f03cfea0b383","observation_id":"6012806b-1653-4b73-b0d0-006c709d9900","resolution":{"observed_at":"2026-08-11T14:41:45.609269Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1090/memo/1471","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T14:41:45.589902Z","title":"Feola, F","venue":null,"work_id":"34f2abc2-f0ac-446d-a681-a2203b18bc4e","year":2024},"citing_paper":{"arxiv_id":"2412.11845","last_updated":"2025-02-12T15:29:43Z","snapshot_observed_at":"2026-08-18T05:20:12.991711Z","submitted_at":"2024-12-16T15:08:31Z","title":"Infinite dimensional invariant tori for nonlinear Schr\\\"odinger equations","version":2},"reference_index":34,"source":"arxiv_source","source_observed_at":"2026-08-11T14:41:45.244196Z"},"links":{"citing_paper":"/paper/2412.11845"},"observation_digest":"sha256:a04e4f6084108501481c6f6dcb007324d6da58537b36f8bb293cb297f949e300","observation_id":"d4d6ac83-4038-4a19-8ec4-65f92929387a","resolution":{"observed_at":"2026-08-11T14:41:45.594258Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T14:41:45.248470Z","title":"Fr\\\"olich, T","venue":null,"work_id":null,"year":1986},"citing_paper":{"arxiv_id":"2412.11845","last_updated":"2025-02-12T15:29:43Z","snapshot_observed_at":"2026-08-18T05:20:12.991711Z","submitted_at":"2024-12-16T15:08:31Z","title":"Infinite dimensional invariant tori for nonlinear Schr\\\"odinger equations","version":2},"reference_index":35,"source":"arxiv_source","source_observed_at":"2026-08-11T14:41:45.248470Z"},"links":{"citing_paper":"/paper/2412.11845"},"observation_digest":"sha256:18d6306c051ef3e38fc016cb98b08f3738ecbe8cc6072c420bef1ed3e69dc4d0","observation_id":"f53392e4-0d05-4748-b267-684bdb49eb1d","resolution":{"observed_at":"2026-08-11T14:41:45.248470Z","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":"10.1007/s00220-005-1497-0","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T14:41:45.566226Z","title":null,"venue":null,"work_id":"648fc363-b4db-492c-9075-3b05038c19df","year":2006},"citing_paper":{"arxiv_id":"2412.11845","last_updated":"2025-02-12T15:29:43Z","snapshot_observed_at":"2026-08-18T05:20:12.991711Z","submitted_at":"2024-12-16T15:08:31Z","title":"Infinite dimensional invariant tori for nonlinear Schr\\\"odinger equations","version":2},"reference_index":36,"source":"arxiv_source","source_observed_at":"2026-08-11T14:41:45.252945Z"},"links":{"citing_paper":"/paper/2412.11845"},"observation_digest":"sha256:55f68edae59849bb5f68897e5df061d8a8519acef93d16c497e28d9f5e713ff5","observation_id":"34bce49a-a2cf-4702-ba1e-1972454ced22","resolution":{"observed_at":"2026-08-11T14:41:45.570751Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s10884-013-9302-9","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T14:41:45.552290Z","title":null,"venue":null,"work_id":"3e8a4553-925c-4275-9f13-0752e914f073","year":2013},"citing_paper":{"arxiv_id":"2412.11845","last_updated":"2025-02-12T15:29:43Z","snapshot_observed_at":"2026-08-18T05:20:12.991711Z","submitted_at":"2024-12-16T15:08:31Z","title":"Infinite dimensional invariant tori for nonlinear Schr\\\"odinger equations","version":2},"reference_index":37,"source":"arxiv_source","source_observed_at":"2026-08-11T14:41:45.257190Z"},"links":{"citing_paper":"/paper/2412.11845"},"observation_digest":"sha256:8858f25af3c74bf75a782e71336a090bfaf1323d610ac99a109ed301d304ff71","observation_id":"cad3e67f-0957-44af-b87d-2f24091b638d","resolution":{"observed_at":"2026-08-11T14:41:45.556869Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1002/cpa.21896","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T11:03:20.376878Z","title":"G\\'erard, T","venue":"Communications on Pure and Applied Mathematics","work_id":"97a5142e-9da2-43db-8232-d26763857285","year":2021},"citing_paper":{"arxiv_id":"2412.11845","last_updated":"2025-02-12T15:29:43Z","snapshot_observed_at":"2026-08-18T05:20:12.991711Z","submitted_at":"2024-12-16T15:08:31Z","title":"Infinite dimensional invariant tori for nonlinear Schr\\\"odinger equations","version":2},"reference_index":38,"source":"arxiv_source","source_observed_at":"2026-08-11T14:41:45.261370Z"},"links":{"citing_paper":"/paper/2412.11845"},"observation_digest":"sha256:f35162d89d33a73246d565bc9836f0e3c9f0782daf4ff3d5171b6cc5061c4330","observation_id":"67cb6d4a-2d36-4f17-b5bc-ef9ac2ce7b5d","resolution":{"observed_at":"2026-08-11T14:41:45.542610Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.4171/131","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T14:41:45.524474Z","title":"Gr\\'ebert, T","venue":null,"work_id":"0ae9c86f-4fff-473e-aba9-d2266eecfde8","year":2014},"citing_paper":{"arxiv_id":"2412.11845","last_updated":"2025-02-12T15:29:43Z","snapshot_observed_at":"2026-08-18T05:20:12.991711Z","submitted_at":"2024-12-16T15:08:31Z","title":"Infinite dimensional invariant tori for nonlinear Schr\\\"odinger equations","version":2},"reference_index":39,"source":"arxiv_source","source_observed_at":"2026-08-11T14:41:45.265459Z"},"links":{"citing_paper":"/paper/2412.11845"},"observation_digest":"sha256:a8b749e431846257e704ab2b4154b228279f10fe0537edd22e93ca8b4fa95d51","observation_id":"aea108ad-a5dd-492e-9f15-6b5740ba421a","resolution":{"observed_at":"2026-08-11T14:41:45.529100Z","resolver_source":"doi_truncated","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s40574-016-0072-2","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T14:41:45.510422Z","title":"Gr\\'ebert, E","venue":null,"work_id":"34e03a20-5b4f-49cb-8b97-e5fc7319f403","year":2016},"citing_paper":{"arxiv_id":"2412.11845","last_updated":"2025-02-12T15:29:43Z","snapshot_observed_at":"2026-08-18T05:20:12.991711Z","submitted_at":"2024-12-16T15:08:31Z","title":"Infinite dimensional invariant tori for nonlinear Schr\\\"odinger equations","version":2},"reference_index":40,"source":"arxiv_source","source_observed_at":"2026-08-11T14:41:45.269794Z"},"links":{"citing_paper":"/paper/2412.11845"},"observation_digest":"sha256:ff8f1cba58ebed462420e8dd947ec97612ee47a7919ddf331a1074abd4e2dbf1","observation_id":"6f0b92f9-6787-463b-9d9b-94edcd92d571","resolution":{"observed_at":"2026-08-11T14:41:45.515212Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T14:41:45.274256Z","title":null,"venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2412.11845","last_updated":"2025-02-12T15:29:43Z","snapshot_observed_at":"2026-08-18T05:20:12.991711Z","submitted_at":"2024-12-16T15:08:31Z","title":"Infinite dimensional invariant tori for nonlinear Schr\\\"odinger equations","version":2},"reference_index":41,"source":"arxiv_source","source_observed_at":"2026-08-11T14:41:45.274256Z"},"links":{"citing_paper":"/paper/2412.11845"},"observation_digest":"sha256:11c92b983420192745faad2dd8dbbf76f67b4709ba90672b594f921c8c319363","observation_id":"a80ae2e7-9f89-45f1-b061-9aeb3ea3ed80","resolution":{"observed_at":"2026-08-11T14:41:45.274256Z","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":"10.1007/978-3-662-08054-2","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-13T11:03:48.094449Z","title":"Kappeler, J","venue":null,"work_id":"fe45ff3e-995a-42ec-af51-e52d0f8715fb","year":2003},"citing_paper":{"arxiv_id":"2412.11845","last_updated":"2025-02-12T15:29:43Z","snapshot_observed_at":"2026-08-18T05:20:12.991711Z","submitted_at":"2024-12-16T15:08:31Z","title":"Infinite dimensional invariant tori for nonlinear Schr\\\"odinger equations","version":2},"reference_index":42,"source":"arxiv_source","source_observed_at":"2026-08-11T14:41:45.278578Z"},"links":{"citing_paper":"/paper/2412.11845"},"observation_digest":"sha256:13771f6e7b0344e77cf97ad2c77562c0dd017b342e75edbcb74b5a2f6122cb45","observation_id":"ab672c8d-8b2e-45fe-ae0c-af9bb177a8de","resolution":{"observed_at":"2026-08-11T14:41:45.492224Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1911.04349","last_updated":"2021-07-19T15:34:02Z","snapshot_observed_at":"2026-08-15T22:37:04.020507Z","submitted_at":"2019-11-11T15:46:45Z","title":"Unconditional uniqueness of solutions for nonlinear dispersive equations","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1911.04349","snapshot_observed_at":"2026-08-11T14:41:45.282985Z","title":"Kishimoto, Unconditional uniqueness of solutions for nonlinear dispersive equations, arXiv:1911.04349 https://arxiv.org/abs/1911.04349 (2019)","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2412.11845","last_updated":"2025-02-12T15:29:43Z","snapshot_observed_at":"2026-08-18T05:20:12.991711Z","submitted_at":"2024-12-16T15:08:31Z","title":"Infinite dimensional invariant tori for nonlinear Schr\\\"odinger equations","version":2},"reference_index":43,"source":"arxiv_source","source_observed_at":"2026-08-11T14:41:45.282985Z"},"links":{"cited_paper":"/paper/1911.04349","citing_paper":"/paper/2412.11845"},"observation_digest":"sha256:fb60ff9a7ab246f7f8b8480490c582a56e5ee07d0f7ca0bf1b669ce0eccb4f69","observation_id":"97308391-5ce4-4d76-905e-3ab2efc1f025","resolution":{"observed_at":"2026-08-11T14:41:45.282985Z","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":"10.4310/mrl.2017.v24.n3.a9","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T14:41:45.473745Z","title":"Kappeler, B","venue":null,"work_id":"c83cb0b9-d8e7-464c-bd92-1fbc2835a023","year":2017},"citing_paper":{"arxiv_id":"2412.11845","last_updated":"2025-02-12T15:29:43Z","snapshot_observed_at":"2026-08-18T05:20:12.991711Z","submitted_at":"2024-12-16T15:08:31Z","title":"Infinite dimensional invariant tori for nonlinear Schr\\\"odinger equations","version":2},"reference_index":44,"source":"arxiv_source","source_observed_at":"2026-08-11T14:41:45.287706Z"},"links":{"citing_paper":"/paper/2412.11845"},"observation_digest":"sha256:b79fa11e8aa5cc46ae8aea6a4ee0ae4c6452a7cbf0f8afac576f8c25683acb0e","observation_id":"cdd889e7-6d7a-409b-a4e0-4fe31c146739","resolution":{"observed_at":"2026-08-11T14:41:45.478242Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T14:41:45.291795Z","title":"Kuksin , Hamiltonian perturbations of infinite-dimensional linear systems with imaginary spectrum, Funktsional","venue":null,"work_id":null,"year":1987},"citing_paper":{"arxiv_id":"2412.11845","last_updated":"2025-02-12T15:29:43Z","snapshot_observed_at":"2026-08-18T05:20:12.991711Z","submitted_at":"2024-12-16T15:08:31Z","title":"Infinite dimensional invariant tori for nonlinear Schr\\\"odinger equations","version":2},"reference_index":45,"source":"arxiv_source","source_observed_at":"2026-08-11T14:41:45.291795Z"},"links":{"citing_paper":"/paper/2412.11845"},"observation_digest":"sha256:58b5bb826eb90fc2f8d535e697475c6fdd73538ecae0d96ae9ebb9a0b3a0aad2","observation_id":"c7cbce36-0392-43dd-9d29-66b538da0d97","resolution":{"observed_at":"2026-08-11T14:41:45.291795Z","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":"2026-08-11T14:41:45.296026Z","title":"o schel , Invariant C antor manifolds of quasi-periodic oscillations for a nonlinear S chr \\","venue":null,"work_id":null,"year":1996},"citing_paper":{"arxiv_id":"2412.11845","last_updated":"2025-02-12T15:29:43Z","snapshot_observed_at":"2026-08-18T05:20:12.991711Z","submitted_at":"2024-12-16T15:08:31Z","title":"Infinite dimensional invariant tori for nonlinear Schr\\\"odinger equations","version":2},"reference_index":46,"source":"arxiv_source","source_observed_at":"2026-08-11T14:41:45.296026Z"},"links":{"citing_paper":"/paper/2412.11845"},"observation_digest":"sha256:21b0a4d5b6f5278437153beea435ce458e6e47b8e7cf6fc9a55eeb1a1bf2d5ce","observation_id":"490fbccd-9e6b-402b-9d7b-ef80b0e68eb2","resolution":{"observed_at":"2026-08-11T14:41:45.296026Z","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":"2026-08-11T14:41:45.300150Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2412.11845","last_updated":"2025-02-12T15:29:43Z","snapshot_observed_at":"2026-08-18T05:20:12.991711Z","submitted_at":"2024-12-16T15:08:31Z","title":"Infinite dimensional invariant tori for nonlinear Schr\\\"odinger equations","version":2},"reference_index":47,"source":"arxiv_source","source_observed_at":"2026-08-11T14:41:45.300150Z"},"links":{"citing_paper":"/paper/2412.11845"},"observation_digest":"sha256:36a011416dffc02977e03cc4e3445026254b4c5e6da6c0aeca1fba8b639fa956","observation_id":"2c46cfea-5341-4ed9-9fb0-470dde28fdd8","resolution":{"observed_at":"2026-08-11T14:41:45.300150Z","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":"10.1016/j.jde.2022.09.017","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T14:41:45.432598Z","title":"McConnell , Nonlinear smoothing for the periodic generalized nonlinear Schr\\\"odinger equation, J","venue":null,"work_id":"419a5e7b-ecc7-4be8-8c43-5814ace4b177","year":2022},"citing_paper":{"arxiv_id":"2412.11845","last_updated":"2025-02-12T15:29:43Z","snapshot_observed_at":"2026-08-18T05:20:12.991711Z","submitted_at":"2024-12-16T15:08:31Z","title":"Infinite dimensional invariant tori for nonlinear Schr\\\"odinger equations","version":2},"reference_index":48,"source":"arxiv_source","source_observed_at":"2026-08-11T14:41:45.304589Z"},"links":{"citing_paper":"/paper/2412.11845"},"observation_digest":"sha256:9230541ebdfad66558ad4af2ddd26c51c490de4e750e328c28cef38c766ff592","observation_id":"d2918dcd-95d8-45a3-b3f4-78a3f174195f","resolution":{"observed_at":"2026-08-11T14:41:45.437427Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T14:41:46.093718Z","title":"P\\\"oschel , A KAM theorem for some nonlinear PDEs, Ann","venue":null,"work_id":"740fd697-13d5-4456-880e-ed9986c16068","year":1996},"citing_paper":{"arxiv_id":"2412.11845","last_updated":"2025-02-12T15:29:43Z","snapshot_observed_at":"2026-08-18T05:20:12.991711Z","submitted_at":"2024-12-16T15:08:31Z","title":"Infinite dimensional invariant tori for nonlinear Schr\\\"odinger equations","version":2},"reference_index":49,"source":"arxiv_source","source_observed_at":"2026-08-11T14:41:45.309290Z"},"links":{"citing_paper":"/paper/2412.11845"},"observation_digest":"sha256:f5d3665088e789dd4c1f5f56f7a5852602a4266794fa5542dbf174ca5d85a2a8","observation_id":"598340b0-8c14-4fc1-89ae-d9334f92e1a2","resolution":{"observed_at":"2026-08-11T14:41:46.098662Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/bf02096763","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T11:08:50.044864Z","title":"P\\\"oschel , Small divisors with spatial structure in infinite dimensional Hamiltonian systems, Comm","venue":"Communications in Mathematical Physics","work_id":"97ee76e7-9009-4b90-9683-4d9c164a292c","year":1990},"citing_paper":{"arxiv_id":"2412.11845","last_updated":"2025-02-12T15:29:43Z","snapshot_observed_at":"2026-08-18T05:20:12.991711Z","submitted_at":"2024-12-16T15:08:31Z","title":"Infinite dimensional invariant tori for nonlinear Schr\\\"odinger equations","version":2},"reference_index":50,"source":"arxiv_source","source_observed_at":"2026-08-11T14:41:45.314291Z"},"links":{"citing_paper":"/paper/2412.11845"},"observation_digest":"sha256:474daadc0c15226f5c877d07e0240e5a34cb29d29fe4c9b54b2edff3cadbbece","observation_id":"a95ae0dc-82f9-4d09-842b-86eb4e612d99","resolution":{"observed_at":"2026-08-11T14:41:45.422747Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T14:41:45.319027Z","title":"o schel , On the construction of almost-periodic solutions for a nonlinear Schr \\","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2412.11845","last_updated":"2025-02-12T15:29:43Z","snapshot_observed_at":"2026-08-18T05:20:12.991711Z","submitted_at":"2024-12-16T15:08:31Z","title":"Infinite dimensional invariant tori for nonlinear Schr\\\"odinger equations","version":2},"reference_index":51,"source":"arxiv_source","source_observed_at":"2026-08-11T14:41:45.319027Z"},"links":{"citing_paper":"/paper/2412.11845"},"observation_digest":"sha256:81206cd5e6b28da4d302d8e5f1cf1bcb6e2c36294ba9658ea6517ebf98217fe4","observation_id":"1a724d09-0db3-41d8-b588-4f5d3f250f49","resolution":{"observed_at":"2026-08-11T14:41:45.319027Z","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":"10.1016/j.aim.2014.12.004","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T14:41:45.393295Z","title":"Procesi, M","venue":null,"work_id":"bfd2cc65-d5d7-417c-8918-ffda556f8d6a","year":2015},"citing_paper":{"arxiv_id":"2412.11845","last_updated":"2025-02-12T15:29:43Z","snapshot_observed_at":"2026-08-18T05:20:12.991711Z","submitted_at":"2024-12-16T15:08:31Z","title":"Infinite dimensional invariant tori for nonlinear Schr\\\"odinger equations","version":2},"reference_index":52,"source":"arxiv_source","source_observed_at":"2026-08-11T14:41:45.324312Z"},"links":{"citing_paper":"/paper/2412.11845"},"observation_digest":"sha256:41398ae22f59d7f9630a8c0bdfb1e657382e48ceb26fe40db84721ad9b759dbb","observation_id":"386b739b-5b4f-4045-bc72-8e8cbd0ee120","resolution":{"observed_at":"2026-08-11T14:41:45.397902Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1002/cpa.3160480604","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T11:03:20.376878Z","title":"Safonov , The Abstract Cauchy-Kovalevskaya Theorem in a Weighted Banach Space, Comm","venue":"Communications on Pure and Applied Mathematics","work_id":"6aad33fa-cc3a-48e9-a5fe-2c22b0bc2d22","year":1995},"citing_paper":{"arxiv_id":"2412.11845","last_updated":"2025-02-12T15:29:43Z","snapshot_observed_at":"2026-08-18T05:20:12.991711Z","submitted_at":"2024-12-16T15:08:31Z","title":"Infinite dimensional invariant tori for nonlinear Schr\\\"odinger equations","version":2},"reference_index":53,"source":"arxiv_source","source_observed_at":"2026-08-11T14:41:45.328671Z"},"links":{"citing_paper":"/paper/2412.11845"},"observation_digest":"sha256:ebb664fff0b70b444b74c55b98e5d01e8d3489367fcc96f4acb43eb2aae019e6","observation_id":"aabae9db-a450-4426-b6b1-053cc850472f","resolution":{"observed_at":"2026-08-11T14:41:45.383802Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/bf02104499","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T11:08:50.044864Z","title":"Wayne , Periodic and quasi-periodic solutions of nonlinear wave equations via KAM theory, Comm","venue":"Communications in Mathematical Physics","work_id":"a08df543-c535-4c20-8b99-b2bad322f7f0","year":1990},"citing_paper":{"arxiv_id":"2412.11845","last_updated":"2025-02-12T15:29:43Z","snapshot_observed_at":"2026-08-18T05:20:12.991711Z","submitted_at":"2024-12-16T15:08:31Z","title":"Infinite dimensional invariant tori for nonlinear Schr\\\"odinger equations","version":2},"reference_index":54,"source":"arxiv_source","source_observed_at":"2026-08-11T14:41:45.332971Z"},"links":{"citing_paper":"/paper/2412.11845"},"observation_digest":"sha256:6407cd0c108ebf9bcf88594e4fac1f0ef553485cc0b51a4d9898053602a3ffb9","observation_id":"6a14edb5-bd3b-4afe-986a-ad6b6b4b62f8","resolution":{"observed_at":"2026-08-11T14:41:45.369629Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2412.11845","last_updated":"2025-02-12T15:29:43Z","latest_version":2,"primary_category":"math.AP","snapshot_observed_at":"2026-08-18T05:20:12.991711Z","submitted_at":"2024-12-16T15:08:31Z","title":"Infinite dimensional invariant tori for nonlinear Schr\\\"odinger equations"},"reference_resolution":{"displayed":54,"state_counts":{"malformed_identifier":1,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":18,"verified_exact":32,"verified_fuzzy":3},"total_outbound_references":54},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"thesis":"As of 18 August 2026, this Paper Citation Record lists 54 of 54 outbound references and 4 inbound Pith citation observations for arXiv:2412.11845."}