{"as_of":"2026-08-14T12:50:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:e4a9b0e8d144704f7ea08c5706db66ebeec8e1907619dc155ce4e21f4ec17e9a","coverage":[{"denominator":11,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":11,"source":"paper_references, paper_reference_links","source_observed_at":"2026-07-14T13:06:09.824175Z","state":"measured"},{"denominator":11,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":11,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-14T06:32:32.682623+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/2607.10259/citation-record","integrity":"/paper/2607.10259/integrity","json":"/paper/2607.10259/citation-record.json","paper":"/paper/2607.10259"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T13:06:09.824175Z","title":"Bourgain","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2607.10259","last_updated":"2026-07-11T11:07:29Z","snapshot_observed_at":"2026-08-07T13:18:58.696029Z","submitted_at":"2026-07-11T11:07:29Z","title":"The existence of full dimensional KAM tori for infinite dimensional Hamiltonian systems with long range interactions","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-07-14T13:06:09.824175Z"},"links":{"citing_paper":"/paper/2607.10259"},"observation_digest":"sha256:6f9acf6905097eff39b845da7da1752186ad9464665f179bef98a9df5f432834","observation_id":"578f3975-0342-4a7c-88a0-bd617bda0ed7","resolution":{"observed_at":"2026-07-14T13:06:09.824175Z","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":"2026-07-14T13:06:09.824175Z","title":"Cong, J.J","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.10259","last_updated":"2026-07-11T11:07:29Z","snapshot_observed_at":"2026-08-07T13:18:58.696029Z","submitted_at":"2026-07-11T11:07:29Z","title":"The existence of full dimensional KAM tori for infinite dimensional Hamiltonian systems with long range interactions","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-07-14T13:06:09.824175Z"},"links":{"citing_paper":"/paper/2607.10259"},"observation_digest":"sha256:f37852c83472de3b7550d370bc9a3b19de8a2ed24a18a245f754b23e885c62e8","observation_id":"77849f74-f83d-4391-91c3-74b089eac0f7","resolution":{"observed_at":"2026-07-14T13:06:09.824175Z","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":"2026-07-14T13:06:09.824175Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.10259","last_updated":"2026-07-11T11:07:29Z","snapshot_observed_at":"2026-08-07T13:18:58.696029Z","submitted_at":"2026-07-11T11:07:29Z","title":"The existence of full dimensional KAM tori for infinite dimensional Hamiltonian systems with long range interactions","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-07-14T13:06:09.824175Z"},"links":{"citing_paper":"/paper/2607.10259"},"observation_digest":"sha256:1a04c2be4e2e8f647098050ac1acbfe300c97154e76ab20c39cc7b1364745ace","observation_id":"0eee7632-bfdb-496e-a2f3-f3ef56993b18","resolution":{"observed_at":"2026-07-14T13:06:09.824175Z","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":"2026-07-14T13:06:09.824175Z","title":"Dolgopyat, B","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.10259","last_updated":"2026-07-11T11:07:29Z","snapshot_observed_at":"2026-08-07T13:18:58.696029Z","submitted_at":"2026-07-11T11:07:29Z","title":"The existence of full dimensional KAM tori for infinite dimensional Hamiltonian systems with long range interactions","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-07-14T13:06:09.824175Z"},"links":{"citing_paper":"/paper/2607.10259"},"observation_digest":"sha256:b21857426d10f9f359f14dd994c564cab502a19aa03fbacb0175c5b33a10ca02","observation_id":"69b0741d-a4ff-40a5-9eb2-e4aeba8f3d4e","resolution":{"observed_at":"2026-07-14T13:06:09.824175Z","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":"2026-07-14T13:06:09.824175Z","title":"Fröhlich, T","venue":null,"work_id":null,"year":1986},"citing_paper":{"arxiv_id":"2607.10259","last_updated":"2026-07-11T11:07:29Z","snapshot_observed_at":"2026-08-07T13:18:58.696029Z","submitted_at":"2026-07-11T11:07:29Z","title":"The existence of full dimensional KAM tori for infinite dimensional Hamiltonian systems with long range interactions","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-07-14T13:06:09.824175Z"},"links":{"citing_paper":"/paper/2607.10259"},"observation_digest":"sha256:6271c3fd8e51f0bcdfc33a3dd116a9db3967a018db46b5f048b88db64bb9c25f","observation_id":"97a5a373-8c4b-44f7-a2ae-5b0073f0508d","resolution":{"observed_at":"2026-07-14T13:06:09.824175Z","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":"2026-07-14T13:06:09.824175Z","title":null,"venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2607.10259","last_updated":"2026-07-11T11:07:29Z","snapshot_observed_at":"2026-08-07T13:18:58.696029Z","submitted_at":"2026-07-11T11:07:29Z","title":"The existence of full dimensional KAM tori for infinite dimensional Hamiltonian systems with long range interactions","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-07-14T13:06:09.824175Z"},"links":{"citing_paper":"/paper/2607.10259"},"observation_digest":"sha256:7a0b628173ea5188cb19cbe1efc5235edf453bb475e62dccf3818fa459f11cc6","observation_id":"860410a2-bd0c-463c-8c4c-a265790631a9","resolution":{"observed_at":"2026-07-14T13:06:09.824175Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2606.29154","last_updated":"2026-06-28T02:23:01Z","snapshot_observed_at":"2026-08-08T17:45:12.012707Z","submitted_at":"2026-06-28T02:23:01Z","title":"Transfer Operators, Canonical Center Dynamics, and Spectral Applications for Long-Range Operators","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2606.29154","snapshot_observed_at":"2026-07-14T13:06:09.824175Z","title":null,"venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.10259","last_updated":"2026-07-11T11:07:29Z","snapshot_observed_at":"2026-08-07T13:18:58.696029Z","submitted_at":"2026-07-11T11:07:29Z","title":"The existence of full dimensional KAM tori for infinite dimensional Hamiltonian systems with long range interactions","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-07-14T13:06:09.824175Z"},"links":{"cited_paper":"/paper/2606.29154","citing_paper":"/paper/2607.10259"},"observation_digest":"sha256:db671b8a3282d6388c5536b0ae3df51d2eb5a094b61deeac58addf94ca85ea5f","observation_id":"bf351973-c1fd-4016-9b0e-1cd4711f7612","resolution":{"observed_at":"2026-07-14T13:06:09.824175Z","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":"2026-07-14T13:06:09.824175Z","title":"P \\\"o schel","venue":null,"work_id":null,"year":1990},"citing_paper":{"arxiv_id":"2607.10259","last_updated":"2026-07-11T11:07:29Z","snapshot_observed_at":"2026-08-07T13:18:58.696029Z","submitted_at":"2026-07-11T11:07:29Z","title":"The existence of full dimensional KAM tori for infinite dimensional Hamiltonian systems with long range interactions","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-07-14T13:06:09.824175Z"},"links":{"citing_paper":"/paper/2607.10259"},"observation_digest":"sha256:5d7383cf18d0589a564ac420ad29b883223d24018665cd578214187b8bc3298a","observation_id":"5d05d68e-da7a-4407-ab9f-5ad60fd323d1","resolution":{"observed_at":"2026-07-14T13:06:09.824175Z","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":"2026-07-14T13:06:09.824175Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.10259","last_updated":"2026-07-11T11:07:29Z","snapshot_observed_at":"2026-08-07T13:18:58.696029Z","submitted_at":"2026-07-11T11:07:29Z","title":"The existence of full dimensional KAM tori for infinite dimensional Hamiltonian systems with long range interactions","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-07-14T13:06:09.824175Z"},"links":{"citing_paper":"/paper/2607.10259"},"observation_digest":"sha256:986d3177dbcae4b6dc8e4dedb5d09fb53a7ed62b8c731b76c22db65229dcd7f0","observation_id":"3ebbac35-522e-4746-ac41-239c9ae9e1fe","resolution":{"observed_at":"2026-07-14T13:06:09.824175Z","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":"2026-07-14T13:06:09.824175Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.10259","last_updated":"2026-07-11T11:07:29Z","snapshot_observed_at":"2026-08-07T13:18:58.696029Z","submitted_at":"2026-07-11T11:07:29Z","title":"The existence of full dimensional KAM tori for infinite dimensional Hamiltonian systems with long range interactions","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-07-14T13:06:09.824175Z"},"links":{"citing_paper":"/paper/2607.10259"},"observation_digest":"sha256:73d35a814fe6613a417d1eec1408a6bcfc7c8b2856473e5e0e26795f6242c7ce","observation_id":"4858b933-a320-463b-a1ae-9aa77d5899aa","resolution":{"observed_at":"2026-07-14T13:06:09.824175Z","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":"2026-07-14T13:06:09.824175Z","title":"Shi and L","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.10259","last_updated":"2026-07-11T11:07:29Z","snapshot_observed_at":"2026-08-07T13:18:58.696029Z","submitted_at":"2026-07-11T11:07:29Z","title":"The existence of full dimensional KAM tori for infinite dimensional Hamiltonian systems with long range interactions","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-07-14T13:06:09.824175Z"},"links":{"citing_paper":"/paper/2607.10259"},"observation_digest":"sha256:d07ce9a5cb8f5360a171ba7f5d4fecac661b5ee6aed9972c47267ac33801b910","observation_id":"ea8a6b57-77ef-4880-9c85-2a0052621bb6","resolution":{"observed_at":"2026-07-14T13:06:09.824175Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.10259","last_updated":"2026-07-11T11:07:29Z","latest_version":1,"primary_category":"math-ph","snapshot_observed_at":"2026-08-07T13:18:58.696029Z","submitted_at":"2026-07-11T11:07:29Z","title":"The existence of full dimensional KAM tori for infinite dimensional Hamiltonian systems with long range interactions"},"reference_resolution":{"displayed":11,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":11,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":11},"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":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"thesis":"As of 14 August 2026, this Paper Citation Record lists 11 of 11 outbound references and 0 inbound Pith citation observations for arXiv:2607.10259."}