{"as_of":"2026-08-15T12:41:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:08819cc7f4c84be0796e82c9e77cf5c0377db6e028f0f3a8389bee748710044e","coverage":[{"denominator":84,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":84,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-11T21:05:00.977609Z","state":"measured"},{"denominator":84,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":84,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-15T06:32:42.880941+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2412.05354/citation-record","integrity":"/paper/2412.05354/integrity","json":"/paper/2412.05354/citation-record.json","paper":"/paper/2412.05354"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T21:05:00.743527Z","title":"Aida, Diﬀerential calculus on path and loop spaces","venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.743527Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:2fdb611855427e986687598fc655e6efb33986e38788696ac1cc40ae7207d51d","observation_id":"1fec9e1f-ff98-4ab6-b95e-901be3c6fa76","resolution":{"observed_at":"2026-08-11T21:05:00.743527Z","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":"2026-08-11T21:05:00.746715Z","title":"Aida, On the irreducibility of Dirichlet forms on domains in inﬁni te-dimensional spaces , Osaka Journal of Mathematics 37 (2000), no","venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.746715Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:0e7a1a43eae721f3cb0f52281226a32638bda5d9d427b96cd8f5a6abf846744c","observation_id":"14dd4af8-9903-4cbb-bf56-eca772f629d0","resolution":{"observed_at":"2026-08-11T21:05:00.746715Z","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":"2026-08-11T21:05:00.749738Z","title":"Aizenman, Geometric analysis of ϕ4 ﬁelds and Ising models","venue":null,"work_id":null,"year":1982},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.749738Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:83f395deec0713525b45fca83e90ed66b25e3632f064e686c0c990437c3e3582","observation_id":"eff146ce-b835-44e0-b278-2f86633ccdbc","resolution":{"observed_at":"2026-08-11T21:05:00.749738Z","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":"2026-08-11T21:05:00.752136Z","title":"Aizenman and H","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.752136Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:d806f29156e275b71cfdb9815dbe96d73750437fd824dcbb8c3ac04bde07b1a2","observation_id":"cc9d3ab8-97ae-49f5-b08c-27273612c9ea","resolution":{"observed_at":"2026-08-11T21:05:00.752136Z","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":"2026-08-11T21:05:01.837206Z","title":"Aizenman, S","venue":null,"work_id":"049868cf-ae59-4479-a1e4-adaef28952cb","year":1977},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.754222Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:a3d5bca3d91f8dc6a7466ff10264e76a657cd699a0cff05f59bcc5479123d249","observation_id":"08dfcf3c-9f53-4e3f-845b-6b0219fd8216","resolution":{"observed_at":"2026-08-11T21:05:01.839208Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2405.04055","last_updated":"2024-05-07T06:56:11Z","snapshot_observed_at":"2026-08-15T02:37:03.869207Z","submitted_at":"2024-05-07T06:56:11Z","title":"Expansion of the Many-body Quantum Gibbs State of the Bose-Hubbard Model on a Finite Graph","version":1},"cited_work":{"arxiv_id":"2405.04055","doi":null,"metadata_source":"pith","pith_arxiv_id":"2405.04055","snapshot_observed_at":"2026-08-11T21:05:01.274402Z","title":"Expansion of the Many-body Quantum Gibbs State of the Bose-Hubbard Model on a Finite Graph","venue":"math-ph","work_id":"4293d64e-9515-40d9-b00d-70a0d82cb6c8","year":2024},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.756367Z"},"links":{"cited_paper":"/paper/2405.04055","citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:75b9d0df9ffff9acb8446c3eef7d603f09dbcd1003f268838017df3004f849ab","observation_id":"36c1d8fe-6902-4b81-8b56-294e46872b48","resolution":{"observed_at":"2026-08-11T21:05:01.277050Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-11T21:05:01.830869Z","title":"Ammari, S","venue":null,"work_id":"b0da48e3-52e4-48d1-8919-bea8bbf99b12","year":2024},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.758888Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:b9dbd5677ffa750664f5ff62579dead226183f3e1d7d92724806a7be2e224f50","observation_id":"87aea6f6-617b-4de0-9498-dde9c0ee273a","resolution":{"observed_at":"2026-08-11T21:05:01.833244Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-11T21:05:01.824248Z","title":"Ammari, S","venue":null,"work_id":"2af58cb6-23f8-46b3-ae9e-22466ab3b9db","year":2023},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.761260Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:5546b8365a29ed8ccd65d6bd6e03f1ea43c83b4b24e19d5fe38423220207edb4","observation_id":"c79d08ae-dc64-474d-974a-f213714605b5","resolution":{"observed_at":"2026-08-11T21:05:01.826382Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-11T21:05:01.816943Z","title":"Ammari, Q","venue":null,"work_id":"3a1315cf-8f9e-4311-9dee-4643fb7326f8","year":2018},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.763679Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:5f37f9d1e84c39486ad088c3207415891b1400f9fea77b848b5f94f972d90637","observation_id":"b9c37d56-94d1-4602-813b-647768377109","resolution":{"observed_at":"2026-08-11T21:05:01.819768Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-11T21:05:01.809160Z","title":"Ammari, A","venue":null,"work_id":"1c47600e-b3b8-45ac-8b85-22fd2f88016f","year":2021},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.766994Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:9e69437fb4be384a862ea94a11f20172834712c43a4758cce8671ce239924c4f","observation_id":"b27146f8-460b-4bd0-bd54-b663b8720f5d","resolution":{"observed_at":"2026-08-11T21:05:01.812228Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-11T21:05:01.800108Z","title":"Ammari, V","venue":null,"work_id":"10cf6c43-8af9-4352-a215-4100ae760c12","year":2023},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.769547Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:a61d773bc962a4dd35050dca3a2abaf64057d432952dff64e1ce4bdcde1ce451","observation_id":"f806cfdb-9e58-4438-9a6a-0333304ac2b5","resolution":{"observed_at":"2026-08-11T21:05:01.803016Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-11T21:05:01.790812Z","title":"Arsen’ev, Invariant measures for classical dynamical systems with in ﬁnite phase space , Mat","venue":null,"work_id":"79cb7623-cefb-4275-b0ae-aebc16dc2672","year":1983},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.772594Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:c2d42b3b6d7abaaad3caf48aa6595f7195eba670dcacfd693883b83c5f1df580","observation_id":"fb30a194-2f3c-4d79-a767-8ff9eb6d3f72","resolution":{"observed_at":"2026-08-11T21:05:01.794125Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-11T21:05:00.775290Z","title":"Barashkov, M","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.775290Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:dfdecb3bdb23dc0056fd8c62cc608c0586a0c49a617718c4b613c76dc8364d1d","observation_id":"740fdffb-9af1-4ce2-90e1-e760f9d58433","resolution":{"observed_at":"2026-08-11T21:05:00.775290Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2211.16111","last_updated":"2026-01-13T09:07:10Z","snapshot_observed_at":"2026-08-13T13:32:38.068091Z","submitted_at":"2022-11-29T11:34:49Z","title":"Invariance of $\\phi^4$ measure under nonlinear wave and Schr\\\"odinger equations on the plane","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2211.16111","snapshot_observed_at":"2026-08-11T21:05:00.778628Z","title":"Barashkov, P","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.778628Z"},"links":{"cited_paper":"/paper/2211.16111","citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:bd68dfcfd61dd106bce8dffb88993c662f13e6adfac42286c3f7bf93083b7398","observation_id":"88a4b717-f512-42f4-a30f-8af85f30cac5","resolution":{"observed_at":"2026-08-11T21:05:00.778628Z","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":"2026-08-11T21:05:01.776911Z","title":"Bogachev, Gaussian measures, Mathematical Surveys and Monographs 62, American Mathema t- ical Society, Providence, RI, 1998","venue":null,"work_id":"c88e5995-d842-4e91-bada-cb5b06fe015e","year":1998},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.781445Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:1bda92fb8a9c5e84ba4647008af8886527816471d27f39e348042607b2eb1cd2","observation_id":"b13f890b-5ec5-499b-841c-58078562e0d0","resolution":{"observed_at":"2026-08-11T21:05:01.779934Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-11T21:05:01.768552Z","title":"Boucheron, G","venue":null,"work_id":"c01bb858-5af4-43ef-82fd-85a3ece8b6ca","year":2013},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.783799Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:d55f11791e746a425491ad028fdaa9e4e9b081bf16ad0e6ae5e3f10b1cf3338f","observation_id":"d6560e2c-f260-4ce1-9fbd-8898933c7b6b","resolution":{"observed_at":"2026-08-11T21:05:01.771431Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-11T21:05:00.786139Z","title":"Bourgain, Periodic nonlinear Schr¨ odinger equation and invariant me asures, Comm","venue":null,"work_id":null,"year":1994},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.786139Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:d89366b2adbe460c46cfbb8982d7fe64f80feda4a69bf9f965b7253a3e542ce4","observation_id":"3ffcf42e-1b17-4304-9772-6e205bca866a","resolution":{"observed_at":"2026-08-11T21:05:00.786139Z","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":"2026-08-11T21:05:01.757611Z","title":"Bourgain, Invariant measures for the 2D-defocusing nonlinear Schr¨ odinger equation, Comm","venue":null,"work_id":"8bd4f26e-1560-45da-8903-7a2640f6a6ae","year":1996},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.788543Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:5d43057cab0e6427f949f23b58cfbfc7e91256c0449a14a0fc362e6d7b6d348f","observation_id":"1e1e9156-c8ea-4ec1-975c-c655b1736e10","resolution":{"observed_at":"2026-08-11T21:05:01.760456Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-11T21:05:01.750616Z","title":"Bourgain, Invariant measures for the Gross-Pitaevskii equation , J","venue":null,"work_id":"9537619e-8a62-47e9-bf6d-cb023e8d6bb1","year":1997},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.791191Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:3f25d2a9fd3c949fbc505035b4e3364df074470fb654d49797d9a2075c572531","observation_id":"425bd6ed-cb56-4ca3-99ec-199b1ccd9377","resolution":{"observed_at":"2026-08-11T21:05:01.753525Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-11T21:05:01.743727Z","title":"Bourgain, Global Solutions of Nonlinear Schr¨ odinger Equations, AMS Colloquium Publications, Vol","venue":null,"work_id":"bf4ccdec-0646-4e59-bce7-de046f9d0b76","year":1999},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.793542Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:a72eccc2d33353746d5844477f81721a03cf20ece6164663a9d48cc61d20de3d","observation_id":"b07534d5-8cc4-4633-ae22-4072a9de8521","resolution":{"observed_at":"2026-08-11T21:05:01.746519Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-11T21:05:01.736812Z","title":"Bourgain, Invariant meausures for NLS in inﬁnite volume , Comm","venue":null,"work_id":"7853306c-a031-4f9d-8451-5516ad555133","year":2000},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.797290Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:bfc96a835223a20572859c43e38677619b88b10622aeaad51c1cf9032a95af26","observation_id":"5f3c1199-debc-4472-a82b-c4e79113b93c","resolution":{"observed_at":"2026-08-11T21:05:01.739648Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-11T21:05:01.730046Z","title":"Bratelli, D.W","venue":null,"work_id":"c52ba50b-cdc5-47b2-bc79-9013c7892c18","year":1997},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.800419Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:095d3cec43ef57144268e59af6e3d9e3e9a1ab0eb5df956475979b9f79330a62","observation_id":"1fc42b0f-b3a9-4d5b-9f76-5d6460ec6f6c","resolution":{"observed_at":"2026-08-11T21:05:01.732319Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-11T21:05:01.724487Z","title":"Brydges, J","venue":null,"work_id":"b510c71d-869f-478d-b7a2-daa6175e347d","year":1983},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.802860Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:b830b69f4f303824025e65e0dcfbf29cd3a1a758f48d1aeac501eb284cd06647","observation_id":"41b6abf5-4950-496b-af05-57495e9b7a90","resolution":{"observed_at":"2026-08-11T21:05:01.726519Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-11T21:05:01.718922Z","title":"Brydges, G","venue":null,"work_id":"77378ecf-1f24-4b84-ada1-d4a485e1cd6a","year":1996},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.805566Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:334ba0b4bda06e602ee0c6f776bf22525f600ce26cc65efa38ab9314613b160a","observation_id":"38b5361a-f843-419e-b2f1-bbb306fdad68","resolution":{"observed_at":"2026-08-11T21:05:01.720989Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-11T21:05:01.711693Z","title":null,"venue":null,"work_id":"dd402e56-54e3-4ac0-9bf4-48f5659a7dc5","year":2013},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.807924Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:09fe340072a692bda5d6856e8246e816ff2f5409d39c1c4fea54728aaa0f2e48","observation_id":"161ae41d-e06c-4653-b285-5901959a67a6","resolution":{"observed_at":"2026-08-11T21:05:01.714428Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-11T21:05:01.703768Z","title":null,"venue":null,"work_id":"69d119af-e99d-47f0-a389-331637a55114","year":2018},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.810213Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:02b53c74a540a07a40ea790683d65a784547471fbd6fff2f30ec775071a7ed4d","observation_id":"18d81778-deaa-4900-a746-e0cd94d11824","resolution":{"observed_at":"2026-08-11T21:05:01.706671Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-11T21:05:01.694855Z","title":"Cacciafesta, A.-S","venue":null,"work_id":"cd554d4f-bec1-462b-853f-83671dd563b3","year":2015},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.812766Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:246de2f25e0d87902b68a43ae0677686eba8517cb983f40482679aac5ae1ef26","observation_id":"81612094-29d2-402c-bc67-0e72e77b1c3d","resolution":{"observed_at":"2026-08-11T21:05:01.698402Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-11T21:05:01.686797Z","title":"Cacciafesta, A.-S","venue":null,"work_id":"77d37ad8-1190-4454-9f83-6e331aff697a","year":2020},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.815338Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:8beebf72794481191ccda64bd37711e605c9341a0a8f09445c2f110fc5c9c1e2","observation_id":"eba8c032-11bb-48bf-baf2-3eadb7ccfb3f","resolution":{"observed_at":"2026-08-11T21:05:01.689839Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-11T21:05:01.679307Z","title":"Carlen, J","venue":null,"work_id":"001ebceb-42e1-4e1e-93b2-b77edfe6fcc4","year":2016},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.817663Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:9efa70a8b2369eb74946257620a1f16b4a249210998855039f62d13e065de5ad","observation_id":"bd3fa5a7-8c95-4f9b-9f32-df4ec86d4fa7","resolution":{"observed_at":"2026-08-11T21:05:01.682279Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-11T21:05:01.669643Z","title":"Chueshov, Equilibrium statistical solutions for dynamical systems w ith an inﬁnite number of degrees of freedom, Mat","venue":null,"work_id":"ca9f39b0-8d6e-45fe-b126-43cd650f46b8","year":1986},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.820008Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:fb00febbb901d7ef2cab7b9cd5032f51d5464fbf18d6f6ecf5559a5e603975e1","observation_id":"09e6be7b-2055-4581-a0d4-bca1064f0b2c","resolution":{"observed_at":"2026-08-11T21:05:01.672830Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-11T21:05:01.661661Z","title":"Deng, Two dimensional nonlinear Schr¨ odinger equation with rand om initial data , ANAL PDE 5 (2012), 913–960","venue":null,"work_id":"9635bf06-9f5c-4754-9d54-feaa33adbbb8","year":2012},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.822612Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:ab01ddde5092880796a77e994c8f70c68587632f54816efbeec4e98b1ad2da2e","observation_id":"342eb4ee-6347-4d21-81ee-a9c362dd1e91","resolution":{"observed_at":"2026-08-11T21:05:01.664893Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2301.02544","last_updated":"2023-02-06T15:32:45Z","snapshot_observed_at":"2026-08-13T13:08:47.224887Z","submitted_at":"2023-01-06T14:55:47Z","title":"Invariant Gibbs measures for 1D NLS in a trap","version":2},"cited_work":{"arxiv_id":"2301.02544","doi":null,"metadata_source":"pith","pith_arxiv_id":"2301.02544","snapshot_observed_at":"2026-08-11T21:05:01.253289Z","title":"Invariant Gibbs measures for 1D NLS in a trap","venue":"math.AP","work_id":"81b91330-5eb6-4cec-bc34-e1802529c400","year":2023},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.826298Z"},"links":{"cited_paper":"/paper/2301.02544","citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:cd7eba1d138d4f47c00b66dae30c1c9af1e2e9360b40d7d80516767a8627c8a8","observation_id":"d49346ad-ed8b-4f11-afd3-6d398d4f0adb","resolution":{"observed_at":"2026-08-11T21:05:01.256318Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-11T21:05:00.829802Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.829802Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:976abe71bac4a9b4975e70febd8055b0e75ae769fa4b6455d4d035065278a3d4","observation_id":"b251163b-3e48-4ae4-853e-62670db75360","resolution":{"observed_at":"2026-08-11T21:05:00.829802Z","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":"2026-08-11T21:05:01.654307Z","title":"Fannes, J.V","venue":null,"work_id":"1c3b76b3-cdb8-49e2-951c-c7a589c533e0","year":1977},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.832298Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:5e426e272af1956a518503f1fddcd18d414ad188400a0fabebc4607a805d982e","observation_id":"3094ecb4-845e-46ce-b60c-8630a302a889","resolution":{"observed_at":"2026-08-11T21:05:01.657063Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2401.04292","last_updated":"2024-01-09T00:13:30Z","snapshot_observed_at":"2026-08-13T18:41:52.488132Z","submitted_at":"2024-01-09T00:13:30Z","title":"Invariant measures for mKdV and KdV in infinite volume","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2401.04292","snapshot_observed_at":"2026-08-11T21:05:00.835325Z","title":"Forlano, R","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.835325Z"},"links":{"cited_paper":"/paper/2401.04292","citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:0ef1c79303cdf81ec2335b21efd41517f9804a7869415eaa6d1c8dd341934034","observation_id":"220cee67-5b7a-40f0-9f85-9e4473da9b76","resolution":{"observed_at":"2026-08-11T21:05:00.835325Z","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":"2026-08-11T21:05:01.646454Z","title":null,"venue":null,"work_id":"a2c5c274-b97e-4cbf-8301-fe7cc510356c","year":2020},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.838068Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:b7dd18fd4ada586e345e26b87bb6546db397d6490f84a1c909594ac98af7ff13","observation_id":"51bb2548-d4a0-4449-a934-cdf6b40348ef","resolution":{"observed_at":"2026-08-11T21:05:01.649604Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-11T21:05:01.637339Z","title":"Fr¨ ohlich,On the triviality of λφ4 d theories and the approach to the critical point in d > (−) 4 dimensions, Nucl","venue":null,"work_id":"8c6414e0-59e3-4e1f-be29-8eec81d0d04c","year":1982},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.839950Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:6f04d732f0627cb73e366e18deb93a3f26ef3833e311e7fcb85031e7335680c8","observation_id":"112c05ed-d27e-45d2-bace-9d27aed173b7","resolution":{"observed_at":"2026-08-11T21:05:01.640626Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-11T21:05:01.614472Z","title":"Fr¨ ohlich, A","venue":null,"work_id":"eb68d273-e410-4159-9bc7-f1d79bb515f9","year":2017},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.841956Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:a9f903d6731aa7fa812680adf02fad785133dc5e9e55cfabcc3106c1ee5884df","observation_id":"04ff290a-92d6-4039-abd1-abc49e078e50","resolution":{"observed_at":"2026-08-11T21:05:01.632225Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-11T21:05:01.576589Z","title":"Fr¨ ohlich, A","venue":null,"work_id":"54ae78ca-156c-40eb-8fdc-766bbe2349ed","year":2019},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.844745Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:6fbaee5f1cb78b977877b00c8723157f5f5e6b3c863ba64cee2149b2e6c4afc6","observation_id":"1068f892-7dc1-4537-b97c-61dee321eace","resolution":{"observed_at":"2026-08-11T21:05:01.591404Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-11T21:05:01.550283Z","title":"Fr¨ ohlich, A","venue":null,"work_id":"6aaf3a83-be8e-4a51-8c58-3435eededc9e","year":2022},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.847362Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:dda1ecc88f026e86c2f0d58f98a14590b1a8d3ff9feb07dfff0161e65e24c386","observation_id":"e66d97a6-7493-4833-943a-eaf218921866","resolution":{"observed_at":"2026-08-11T21:05:01.557326Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-11T21:05:01.540508Z","title":"Fr¨ ohlich, A","venue":null,"work_id":"b907b894-b817-4ab0-a4c5-a12dc6184b41","year":2020},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.849415Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:595b213cd169054b30e66d5b6e0f3cf946a2d9c7f7a3ffae6e53dc05ad62a47e","observation_id":"8cc9da4f-d581-4b2d-b807-982c310f9f72","resolution":{"observed_at":"2026-08-11T21:05:01.542826Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-11T21:05:01.532164Z","title":"Fr¨ ohlich, A","venue":null,"work_id":"1a9e12f0-dc91-49b0-a55a-4768e3297cc3","year":2023},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.851620Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:781ae4482db4c2b19d1419e562cf45a7abb669ee24c196f51f5df82a809894d4","observation_id":"03b943c9-22d3-4603-923a-02278a0b68ce","resolution":{"observed_at":"2026-08-11T21:05:01.536060Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2201.07632","last_updated":"2023-01-09T18:29:32Z","snapshot_observed_at":"2026-08-13T04:57:55.920452Z","submitted_at":"2022-01-19T14:53:11Z","title":"The Euclidean $\\phi^4_2$ theory as a limit of an interacting Bose gas","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2201.07632","snapshot_observed_at":"2026-08-11T21:05:00.853886Z","title":"Fr¨ ohlich, A","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.853886Z"},"links":{"cited_paper":"/paper/2201.07632","citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:69092f17ae9d7a1d49bbcfb8aeb7df348ae496fcf1bf4d8172fa0249d8ac2a49","observation_id":"8a402859-7739-4dc3-aead-f55a49d910a2","resolution":{"observed_at":"2026-08-11T21:05:00.853886Z","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":"2026-08-11T21:05:01.524293Z","title":"Gallavotti, E.J","venue":null,"work_id":"7dfde0a3-c159-4d42-aa77-78120f79107c","year":1975},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.856501Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:2fd75a2c1f899ae069a7c94a4b76f02476c4c7869bc484b46427dc9093d82f3d","observation_id":"8e1f8a5d-5b77-4a4b-b6dd-41dd2f3a3420","resolution":{"observed_at":"2026-08-11T21:05:01.526946Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-11T21:05:01.517712Z","title":"Glimm, A","venue":null,"work_id":"f7afe2e2-a172-4e6b-80a7-f73d7967b7ff","year":1987},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.858777Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:9cc1a5c175791d3cf6536f863597dcbc92cce59c5e645936980b121f31e0e876","observation_id":"bc22e6be-3174-480d-b75e-bed76a586507","resolution":{"observed_at":"2026-08-11T21:05:01.520116Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-11T21:05:01.510029Z","title":"Gubinelli, M","venue":null,"work_id":"c54d24e5-9290-4a09-9af0-e81b149a1022","year":2021},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.861633Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:c9bda5b327a2071b6940ff4fd694faded30cb34aa2c79a36b3ee2ccfe04efa8f","observation_id":"116cd08b-d752-4ecd-a6ad-1d3fa85bd422","resolution":{"observed_at":"2026-08-11T21:05:01.513038Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-11T21:05:01.503136Z","title":"Gubinelli, N","venue":null,"work_id":"af7459be-9e2e-4fb4-8ab4-98e738c76468","year":2018},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.864536Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:ad9f3487cf60e475ffe0334992e8ad9558a710220f68dd7e142a44455a24d75e","observation_id":"12fe19fa-4588-4023-bc04-25338325ebad","resolution":{"observed_at":"2026-08-11T21:05:01.505951Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-11T21:05:01.493414Z","title":"Haag, N.M","venue":null,"work_id":"bf1cfed1-d9fb-4a82-b4ba-66aeead1c078","year":1967},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.867990Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:449a68bed555d9c3cf072c9314129e88ccbe88cd2144a8ecc82c67bf137a3a44","observation_id":"5d74e37a-185a-4f07-8ef9-585eac986ec9","resolution":{"observed_at":"2026-08-11T21:05:01.497373Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-11T21:05:01.485286Z","title":"Kusuoka, Analysis on Wiener spaces","venue":null,"work_id":"72d6f960-5a49-4142-ac66-e85c25144cf4","year":1991},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.871428Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:c8c2586a4e50dceaadc01b6a63ddb5bda7e15d08d9c0e7373f79616ca61368c8","observation_id":"19fc3940-c707-4b1a-8c13-cc8085d54c15","resolution":{"observed_at":"2026-08-11T21:05:01.488288Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-11T21:05:01.479207Z","title":"Kusuoka, Analysis on Wiener spaces","venue":null,"work_id":"456fee60-f8be-4839-9825-6c685ad0e65b","year":1992},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.874055Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:af2ef4210e6044baa6eda5f8d6f354c71b04b29b587632330f7d17703bc0d381","observation_id":"8bae1f68-b7d2-4299-990b-a1eadacc0299","resolution":{"observed_at":"2026-08-11T21:05:01.481313Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-11T21:05:01.471595Z","title":"Lebowitz, H","venue":null,"work_id":"9f1a89e4-0aa8-4abf-ad18-e4318e81febf","year":1988},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.877842Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:db7e56ba652225b30a9c351b9328e1bf7cea681393e18701f2353a87a188a18e","observation_id":"6cb72a5f-a6cc-4135-8d8b-19635a1af550","resolution":{"observed_at":"2026-08-11T21:05:01.474229Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-11T21:05:01.465197Z","title":"Lewin, P.-T","venue":null,"work_id":"f71991c5-cbb9-47b8-8394-3f6ec74a64ed","year":2015},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.880987Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:8c99299503861bff827115597107e46c95b045d5cce9e1de81bcb1ad05cf74b6","observation_id":"163ebeb3-6b46-4ef3-a5f7-f7ada8dab2ea","resolution":{"observed_at":"2026-08-11T21:05:01.467589Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-11T21:05:01.458627Z","title":"Lewin, P.-T","venue":null,"work_id":"7f90f000-c0c4-4607-b845-b54469d1c6bd","year":2018},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.883780Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:1c0b92055c02169f444100bfbccdaee236555403e91083b67c6a9b5bd43002be","observation_id":"e2abb27e-7a34-4085-bb32-8401c7bdb105","resolution":{"observed_at":"2026-08-11T21:05:01.460891Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1810.08370","last_updated":"2020-10-13T12:14:17Z","snapshot_observed_at":"2026-08-15T03:02:54.490397Z","submitted_at":"2018-10-19T07:00:27Z","title":"Classical field theory limit of many-body quantum Gibbs states in 2D and 3D","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1810.08370","snapshot_observed_at":"2026-08-11T21:05:00.886752Z","title":"Lewin, P.-T","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.886752Z"},"links":{"cited_paper":"/paper/1810.08370","citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:6cb5ace07b97c4c9da1fb19ac18f9f8941c6ad177bc191f1f60c71dad7f3f704","observation_id":"1416a3e9-3e15-4b8f-a2ab-7af1e866a6f3","resolution":{"observed_at":"2026-08-11T21:05:00.886752Z","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":"2026-08-11T21:05:01.450267Z","title":"Lewin, P.-T","venue":null,"work_id":"845df89b-2c03-4ec8-a3cf-895cf4538dc4","year":2019},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.890193Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:ec9832ba16dc72c97bb398e4b69692fdbcac5d7b3089d92edf4ee107627db383","observation_id":"e1aa0ba3-1d19-4406-8a2e-28c211a9b8e6","resolution":{"observed_at":"2026-08-11T21:05:01.453480Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-11T21:05:01.442128Z","title":"Lewin, P.-T","venue":null,"work_id":"5041b51f-058f-4801-b105-fa01747dd503","year":2021},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.892443Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:33e1e96b0f1a814068729a4f98002a11ca31693a8d45fef829f6f0cc64414b19","observation_id":"3e4633ba-e5c2-46c0-bba5-e97c3ddbef08","resolution":{"observed_at":"2026-08-11T21:05:01.444968Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-11T21:05:01.435347Z","title":"Liang, Y","venue":null,"work_id":"84c10d10-bfad-43ac-a6db-70790f1adc64","year":2022},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.895080Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:23efdd77ea959ef9b90d739dc3fa0bfe9ba60c812e8288c53947038ca2d72983","observation_id":"237e0e56-1450-437f-b969-c175dfb79f08","resolution":{"observed_at":"2026-08-11T21:05:01.437796Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2310.08783","last_updated":"2025-09-01T17:51:59Z","snapshot_observed_at":"2026-08-13T05:50:12.072868Z","submitted_at":"2023-10-13T00:08:03Z","title":"Optimal divergence rate of the focusing Gibbs measures","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2310.08783","snapshot_observed_at":"2026-08-11T21:05:00.897465Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":58,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.897465Z"},"links":{"cited_paper":"/paper/2310.08783","citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:9c361251cb1b447f577997f637c6ea120b879427f29d650a15a83c4768c6549a","observation_id":"dc57a90b-0f4b-41d4-bcc3-4fb6641581e9","resolution":{"observed_at":"2026-08-11T21:05:00.897465Z","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":"2026-08-11T21:05:01.428866Z","title":"Malliavin, Stochastic analysis , Grundlehren der mathematischen Wissenschaften, textbf3 13, (1997) Springer-Verlag, Berlin","venue":null,"work_id":"e1d9cfb4-aed2-4851-902e-ac4551ca3f18","year":1997},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":59,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.900617Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:9f7bfbb84899d05b083a156e81793b41a3332fff4812ed36783d79ff4aa95c8e","observation_id":"4c9bf602-f067-4a35-a5d5-0e5195a16502","resolution":{"observed_at":"2026-08-11T21:05:01.431397Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-11T21:05:01.421285Z","title":null,"venue":null,"work_id":"78faea8e-360d-4b78-a056-8aed6a18ffc6","year":1997},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":60,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.902907Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:dd1e1d5035453f2ca511dcc441a428a59de599ba4d41283765681fa5fb270687","observation_id":"c97b84ac-a8c1-44cb-b97c-564df29dbde0","resolution":{"observed_at":"2026-08-11T21:05:01.423821Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-11T21:05:01.413456Z","title":null,"venue":null,"work_id":"4e08a1d5-8a64-46f3-b3aa-345483838275","year":1997},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":61,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.905705Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:c4222dcb61a7d2bd24ba6d6a064de416195dc45a0552a95ba73b17cfa9a205be","observation_id":"a5365583-7a3c-4934-885e-d26b87d99de7","resolution":{"observed_at":"2026-08-11T21:05:01.416560Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-11T21:05:01.406595Z","title":"Nahmod, G","venue":null,"work_id":"62b44d4b-9697-49de-b525-399f0f672262","year":2019},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":62,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.908013Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:5483de14af809efe6d30636f3164eeb82f5e18cbf6050fdcca0aa3b5c2909c21","observation_id":"46fb6276-07a7-4af0-93ac-76778d7b3c1f","resolution":{"observed_at":"2026-08-11T21:05:01.409494Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-11T21:05:01.397791Z","title":"Nelson The free Markoﬀ ﬁeld , J","venue":null,"work_id":"ab3f3171-ac3d-4b6a-89d2-1fbe4ac00d04","year":1973},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":63,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.910644Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:5900d103bffc0eea51e29f22ec80f5bb2a7056beb3a5e95e33fd9a190ab9b92b","observation_id":"6e409080-796f-4f22-83ba-85d7c7f1545e","resolution":{"observed_at":"2026-08-11T21:05:01.400598Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-11T21:05:01.391673Z","title":"Nelson, Probability theory and Euclidean ﬁeld theory , Constructive quantum ﬁeld theory, Springer, 1973, pp","venue":null,"work_id":"482d54d0-858c-4e66-bbd1-b1f6cf831424","year":1973},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":64,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.913353Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:ec87ad264e3bfebc5fa66af2ee343b13155bbdb5c9e846aca119dbc7ae0cea86","observation_id":"8d6eecd0-63cb-46b5-b5b7-658228849d9b","resolution":{"observed_at":"2026-08-11T21:05:01.394212Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-11T21:05:01.384764Z","title":"Nualart, The Malliavin calculus and related topics , Second edition, Probability and its Applications (New York), Springer-Verlag, Berlin, 2006","venue":null,"work_id":"e93cbae2-253c-4433-be4f-8ce9a874be84","year":2006},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":65,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.916688Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:2aac68fb380005a7ec11dbeadd6ee67738d446cc4360f4f93b12c28685696d06","observation_id":"1be6d620-4c4b-44b6-b410-1a2f4d592413","resolution":{"observed_at":"2026-08-11T21:05:01.387303Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2009.03251","last_updated":"2024-12-12T18:37:18Z","snapshot_observed_at":"2026-08-15T05:35:08.401955Z","submitted_at":"2020-09-07T17:24:14Z","title":"Focusing $\\Phi^4_3$-model with a Hartree-type nonlinearity","version":4},"cited_work":{"arxiv_id":"2009.03251","doi":null,"metadata_source":"pith","pith_arxiv_id":"2009.03251","snapshot_observed_at":"2026-08-11T21:05:01.148791Z","title":"Focusing $\\Phi^4_3$-model with a Hartree-type nonlinearity","venue":"math.PR","work_id":"a95c189a-6f85-47ca-889b-79bad437c33a","year":2020},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":66,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.919017Z"},"links":{"cited_paper":"/paper/2009.03251","citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:809e53115aaf7d34c88806539fafcb4af8fb140046e3877774d1027d5d0bd0db","observation_id":"0fea4db8-1814-4cfb-b5c2-fd8693a413d8","resolution":{"observed_at":"2026-08-11T21:05:01.152179Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-11T21:05:01.378814Z","title":null,"venue":null,"work_id":"92d024ec-7631-4ef1-b78f-82ccc66acb12","year":2022},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":67,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.922064Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:529177d05e13cde15ea2e31aa47fd9c9d6d1cc722378c4c34f8d13c687239086","observation_id":"2714b9ac-4421-42e7-be27-ac092f3a775f","resolution":{"observed_at":"2026-08-11T21:05:01.381021Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-11T21:05:01.371081Z","title":null,"venue":null,"work_id":"05bc259c-184a-4bec-bade-66697ff08f89","year":2018},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":68,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.925221Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:c687e461d53baab76385ab6787659f5a5d33bc930ee710d4c44c8d2a99318090","observation_id":"740e05fa-a0fc-4dce-a591-30f58076f8ba","resolution":{"observed_at":"2026-08-11T21:05:01.374745Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-11T21:05:01.363888Z","title":null,"venue":null,"work_id":"3336b483-1a95-4456-9055-20e7dc6cdcc3","year":2020},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":69,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.929010Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:95126977089d75df282a9f7311254d83dbb3cd0323477ecdb7364cdca138917a","observation_id":"f5f20cb2-dffa-4101-9565-e2c8c2f676ae","resolution":{"observed_at":"2026-08-11T21:05:01.366554Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-11T21:05:00.932103Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":70,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.932103Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:1468d82ba8fb5f549482c0c5a4acff2e9313a646f01716d3a0329c57cd6f2f98","observation_id":"0ed2f23e-e174-42cb-b216-732167454571","resolution":{"observed_at":"2026-08-11T21:05:00.932103Z","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":"2026-08-11T21:05:01.355877Z","title":"Peskov, The KMS state of a sine-Gordon system , Teoret","venue":null,"work_id":"c53983ad-86ae-4a30-b247-0f4e412aa73b","year":1985},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":71,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.934746Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:3b228f50c6b2d69281e5dc745912ce6c6140803f8b33f1be49faf084b12a715d","observation_id":"be54d0de-86c1-47f9-8ec0-bfc88014d33c","resolution":{"observed_at":"2026-08-11T21:05:01.358639Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-11T21:05:01.348098Z","title":"Pulvirenti, G","venue":null,"work_id":"8c217817-8718-46c1-b194-38a4ea832a13","year":1977},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":72,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.937667Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:21204a2cee50ef394cf573614fc3f17022e814795e458c2a98b7a0ccefa84b90","observation_id":"1b61268a-6fec-4836-9d5c-96989152ed82","resolution":{"observed_at":"2026-08-11T21:05:01.350786Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-11T21:05:01.339302Z","title":"Rider, On the ∞-volume limit of the focusing cubic Schr¨ odinger equation, Comm","venue":null,"work_id":"5d2bdfdd-6571-4271-b2ce-5c15252f97b9","year":2002},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":73,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.941209Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:0ee25f32c0e79058afbda97a862199147d522f8ed2519b29979c2b56036c79e2","observation_id":"6655a77e-b071-41f0-a3a9-2397a2bb7fdc","resolution":{"observed_at":"2026-08-11T21:05:01.342285Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2212.11386","last_updated":"2022-12-21T22:08:50Z","snapshot_observed_at":"2026-08-13T13:16:55.295975Z","submitted_at":"2022-12-21T22:08:50Z","title":"Focusing Gibbs measures with harmonic potential","version":1},"cited_work":{"arxiv_id":"2212.11386","doi":null,"metadata_source":"pith","pith_arxiv_id":"2212.11386","snapshot_observed_at":"2026-08-11T21:05:01.081067Z","title":"Focusing Gibbs measures with harmonic potential","venue":"math.PR","work_id":"fa0d3388-5f53-443d-8763-7616d98624d8","year":2022},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":74,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.943854Z"},"links":{"cited_paper":"/paper/2212.11386","citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:7cc21bc305fd72baa608f6623cf64ea7b994392e61d615f7061964aff5dd1e27","observation_id":"f1340b09-d2e4-4e69-99c1-8c5c4e19602e","resolution":{"observed_at":"2026-08-11T21:05:01.084114Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-11T21:05:01.331970Z","title":null,"venue":null,"work_id":"79a142c6-1456-4100-acd4-fee8997f6592","year":2023},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":75,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.947665Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:e5b16371a53d4e8d2736c2b3365637a30013b8fd6d759c37efd8d69b409547f9","observation_id":"ec1e948a-4954-46b2-a494-6c48a5304355","resolution":{"observed_at":"2026-08-11T21:05:01.334812Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2308.06569","last_updated":"2024-01-11T11:47:06Z","snapshot_observed_at":"2026-08-15T06:45:54.626091Z","submitted_at":"2023-08-12T13:43:21Z","title":"A microscopic derivation of Gibbs measures for the 1D focusing quintic nonlinear Schr\\\"{o}dinger equation","version":2},"cited_work":{"arxiv_id":"2308.06569","doi":null,"metadata_source":"pith","pith_arxiv_id":"2308.06569","snapshot_observed_at":"2026-08-11T21:05:01.067838Z","title":"A microscopic derivation of Gibbs measures for the 1D focusing quintic nonlinear Schr\\\"{o}dinger equation","venue":"math-ph","work_id":"c83584d9-5548-4807-8544-a69bc3968d25","year":2023},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":76,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.950304Z"},"links":{"cited_paper":"/paper/2308.06569","citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:56445a610b2be55823068e627754db50a9dcd35bdb5314359a83ddb91c2701da","observation_id":"35b3b590-f560-487f-94b0-c769d5e5ee96","resolution":{"observed_at":"2026-08-11T21:05:01.074066Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-11T21:05:01.321064Z","title":"Rudelson, R","venue":null,"work_id":"d0693df9-6f0f-4502-ac34-e07ebf0114d8","year":2013},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":77,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.953476Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:23b643ff507dc0583c264557a759225b1401f0c963e2f41b90aa4faf8412922b","observation_id":"3989e01c-6b48-40e6-b636-898506d2b822","resolution":{"observed_at":"2026-08-11T21:05:01.325873Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-11T21:05:01.311724Z","title":"Simon, The P (Φ) 2 Euclidean (Quantum) Field Theory , Princeton Univ","venue":null,"work_id":"c65eb568-83e1-4b08-8e34-215663771d47","year":1974},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":78,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.957041Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:3655649448e8617bbf60eaddec19c8d8ab135cf97914e0f4812cbec04edf325e","observation_id":"f11c6f27-974b-4a94-8f0b-faa369d2b5ec","resolution":{"observed_at":"2026-08-11T21:05:01.314839Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-11T21:05:01.302747Z","title":"Sohinger, A microscopic derivation of Gibbs measures for nonlinear Sc hr¨ odinger equations with unbounded interaction potentials , Int","venue":null,"work_id":"9dd688ad-1f37-49e2-8ede-a7700785e846","year":2022},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":79,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.960222Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:7cfa3cbd1ca28a8f538ce21511f93214b833e19390b14e45b199450954157928","observation_id":"f48feeef-e1bb-4760-ae71-677e28e4d7f0","resolution":{"observed_at":"2026-08-11T21:05:01.305928Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-11T21:05:00.963979Z","title":"Tolomeo, H","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":80,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.963979Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:823a50cd5409e5f0d9f37915e68adfe4e3e58806db906855cdedfb9e3b649401","observation_id":"8afb0a90-0ee3-4071-90d1-905f4264e961","resolution":{"observed_at":"2026-08-11T21:05:00.963979Z","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":"2026-08-11T21:05:01.295216Z","title":"Vershynin, Introduction to the non-asymptotic analysis of random matr ices, In: Y.C","venue":null,"work_id":"27977413-854f-4be2-8daf-2e0bb48452e7","year":2012},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":81,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.967823Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:9f2769853b57a4ce51995be363dea29f2386c1555947ca30bcef1a1b1a47febd","observation_id":"f69d83a6-7047-4244-87d5-b9e7e699d529","resolution":{"observed_at":"2026-08-11T21:05:01.298137Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-11T21:05:01.288578Z","title":null,"venue":null,"work_id":"18e3a649-2f92-44bb-a569-51ba4d8d693f","year":1984},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":82,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.970652Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:ee2489f70f61b4f3553953198ee0bc00d28c17e54d5d1f41d3d444cae32be0c9","observation_id":"46c2a500-6e27-4836-8dbb-29f96fde1780","resolution":{"observed_at":"2026-08-11T21:05:01.290811Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2204.09561","last_updated":"2022-04-20T15:59:21Z","snapshot_observed_at":"2026-08-13T15:58:54.402688Z","submitted_at":"2022-04-20T15:59:21Z","title":"Optimal mass normalizability for Gibbs measure associated with NLS on the 2D disc","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2204.09561","snapshot_observed_at":"2026-08-11T21:05:00.973613Z","title":"Xian, Optimal mass normalizability for Gibbs measure associated with NLS on the 2D disc , Preprint arXiv: 2204.09561 (2022)","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":83,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.973613Z"},"links":{"cited_paper":"/paper/2204.09561","citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:43e28e70d6fd6630a5d2a2a56987021aa7375a481b319c661069b2a25a58991a","observation_id":"9566a549-6e31-458b-a22c-d1c3b10c599d","resolution":{"observed_at":"2026-08-11T21:05:00.973613Z","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":"2026-08-11T21:05:01.281277Z","title":"Zhidkov, An invariant measure for the nonlinear Schr¨ odinger equati on (Russian), Dokl","venue":null,"work_id":"56a29ae1-af20-46a9-a1ac-d656cf1de6c0","year":1991},"citing_paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations","version":1},"reference_index":84,"source":"pdf_text","source_observed_at":"2026-08-11T21:05:00.977609Z"},"links":{"citing_paper":"/paper/2412.05354"},"observation_digest":"sha256:9bc3a246b56d871de357de03d736b1750ee38868741d9ccd489b79262320d212","observation_id":"7918208e-28bc-4c73-a287-2ddc371c6844","resolution":{"observed_at":"2026-08-11T21:05:01.284314Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2412.05354","last_updated":"2024-12-06T18:55:18Z","latest_version":1,"primary_category":"math.AP","snapshot_observed_at":"2026-08-12T16:20:52.903505Z","submitted_at":"2024-12-06T18:55:18Z","title":"Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\\\"odinger equations"},"reference_resolution":{"displayed":84,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":25,"verified_exact":5,"verified_fuzzy":54},"total_outbound_references":84},"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":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"thesis":"As of 15 August 2026, this Paper Citation Record lists 84 of 84 outbound references and 0 inbound Pith citation observations for arXiv:2412.05354."}