{"as_of":"2026-08-11T18:59:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:a00f93e20c64957d089c6ea49587d081abfb297b7f77606b47283ef3b6204d35","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":"2026-08-01T20:06:45.177887Z","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":"2026-08-11T06:34:44.6726+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/2607.16827/citation-record","integrity":"/paper/2607.16827/integrity","json":"/paper/2607.16827/citation-record.json","paper":"/paper/2607.16827"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T20:06:44.114625Z","title":"Azouani, E","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2607.16827","last_updated":"2026-07-18T14:02:50Z","snapshot_observed_at":"2026-08-07T06:51:02.321158Z","submitted_at":"2026-07-18T14:02:50Z","title":"Projectional continuous data assimilation on the torus: Resonant and kernel-free regimes","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-01T20:06:44.114625Z"},"links":{"citing_paper":"/paper/2607.16827"},"observation_digest":"sha256:3e35fd856536ac06f3895e1b65b4625e1626ac3984f37e9e3d614b0f2a415b52","observation_id":"e7da6418-9319-47a5-93e6-3b470b41fa81","resolution":{"observed_at":"2026-08-01T20:06:44.114625Z","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":"2026-08-01T20:06:44.192968Z","title":"Farhat, E","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2607.16827","last_updated":"2026-07-18T14:02:50Z","snapshot_observed_at":"2026-08-07T06:51:02.321158Z","submitted_at":"2026-07-18T14:02:50Z","title":"Projectional continuous data assimilation on the torus: Resonant and kernel-free regimes","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-01T20:06:44.192968Z"},"links":{"citing_paper":"/paper/2607.16827"},"observation_digest":"sha256:408f9e03fba441415cd0d9d660bb36474679eca07c6c8f326618618d1b455a3a","observation_id":"13bd913a-6284-4724-bfe7-bea3569d5a9b","resolution":{"observed_at":"2026-08-01T20:06:44.192968Z","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":"2026-08-01T20:06:44.364240Z","title":"Carlson, A","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.16827","last_updated":"2026-07-18T14:02:50Z","snapshot_observed_at":"2026-08-07T06:51:02.321158Z","submitted_at":"2026-07-18T14:02:50Z","title":"Projectional continuous data assimilation on the torus: Resonant and kernel-free regimes","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-01T20:06:44.364240Z"},"links":{"citing_paper":"/paper/2607.16827"},"observation_digest":"sha256:7929a7a750d05f2afadf233eec12185cfb12840c90fb660766cf9cea7642028f","observation_id":"6684218c-bbe6-459c-ba13-90e908cbde5c","resolution":{"observed_at":"2026-08-01T20:06:44.364240Z","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":"2026-08-01T20:06:44.489469Z","title":"Franz, A","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.16827","last_updated":"2026-07-18T14:02:50Z","snapshot_observed_at":"2026-08-07T06:51:02.321158Z","submitted_at":"2026-07-18T14:02:50Z","title":"Projectional continuous data assimilation on the torus: Resonant and kernel-free regimes","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-01T20:06:44.489469Z"},"links":{"citing_paper":"/paper/2607.16827"},"observation_digest":"sha256:c74f28b58079e603bbf45830dcf34de26874416715aba899c6c949242d0691b4","observation_id":"93b8a3f7-08d9-435f-b7fd-fbfff15e04f0","resolution":{"observed_at":"2026-08-01T20:06:44.489469Z","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":"2026-08-01T20:06:44.621571Z","title":"Biswas, Z","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.16827","last_updated":"2026-07-18T14:02:50Z","snapshot_observed_at":"2026-08-07T06:51:02.321158Z","submitted_at":"2026-07-18T14:02:50Z","title":"Projectional continuous data assimilation on the torus: Resonant and kernel-free regimes","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-01T20:06:44.621571Z"},"links":{"citing_paper":"/paper/2607.16827"},"observation_digest":"sha256:9ccae9e066890631a53161fc813b4da9faf9febba85c1bfac9105359f6276bd7","observation_id":"19f9dbd6-63ba-49b6-b626-1919c0dd2d2e","resolution":{"observed_at":"2026-08-01T20:06:44.621571Z","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":"2026-08-01T20:06:44.729890Z","title":"Farhat, A","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.16827","last_updated":"2026-07-18T14:02:50Z","snapshot_observed_at":"2026-08-07T06:51:02.321158Z","submitted_at":"2026-07-18T14:02:50Z","title":"Projectional continuous data assimilation on the torus: Resonant and kernel-free regimes","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-01T20:06:44.729890Z"},"links":{"citing_paper":"/paper/2607.16827"},"observation_digest":"sha256:b31bc1183cbcd6c02c14ffafc73bbf91768749cb771c47632d608631e422d61a","observation_id":"288d0a90-7cba-433c-a91c-2283df353404","resolution":{"observed_at":"2026-08-01T20:06:44.729890Z","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":"2026-08-01T20:06:44.841289Z","title":"Biswas and V","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2607.16827","last_updated":"2026-07-18T14:02:50Z","snapshot_observed_at":"2026-08-07T06:51:02.321158Z","submitted_at":"2026-07-18T14:02:50Z","title":"Projectional continuous data assimilation on the torus: Resonant and kernel-free regimes","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-01T20:06:44.841289Z"},"links":{"citing_paper":"/paper/2607.16827"},"observation_digest":"sha256:0c0faf37bc6c2da56cf014b0dbe2d089c1f05a37a01be9cb904e3f09063314e4","observation_id":"0609fc5f-f5d6-4bbd-81a1-d1e2701293c6","resolution":{"observed_at":"2026-08-01T20:06:44.841289Z","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":"2026-08-01T20:06:44.949602Z","title":"Biswas, K","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.16827","last_updated":"2026-07-18T14:02:50Z","snapshot_observed_at":"2026-08-07T06:51:02.321158Z","submitted_at":"2026-07-18T14:02:50Z","title":"Projectional continuous data assimilation on the torus: Resonant and kernel-free regimes","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-01T20:06:44.949602Z"},"links":{"citing_paper":"/paper/2607.16827"},"observation_digest":"sha256:6196fc5ed8eba6ef3e977da5eca830ce10006ef30db97014e9bb5fda3896eeb6","observation_id":"cc69a3f7-8195-470d-8c89-626695b3e616","resolution":{"observed_at":"2026-08-01T20:06:44.949602Z","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":"2026-08-01T20:06:45.025134Z","title":"Foias, O","venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2607.16827","last_updated":"2026-07-18T14:02:50Z","snapshot_observed_at":"2026-08-07T06:51:02.321158Z","submitted_at":"2026-07-18T14:02:50Z","title":"Projectional continuous data assimilation on the torus: Resonant and kernel-free regimes","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-01T20:06:45.025134Z"},"links":{"citing_paper":"/paper/2607.16827"},"observation_digest":"sha256:cfe11e5a64b47297fdb4b9f3406c84c9459089efc6f95e21461960e6a6ffb8dc","observation_id":"c8626c00-0762-4391-aad7-226f8dd6a888","resolution":{"observed_at":"2026-08-01T20:06:45.025134Z","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":"2026-08-01T20:06:45.101478Z","title":"Temam,Navier–Stokes Equations: Theory and Numerical Analysis, AMS Chelsea Publishing, Providence, RI, 2001","venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2607.16827","last_updated":"2026-07-18T14:02:50Z","snapshot_observed_at":"2026-08-07T06:51:02.321158Z","submitted_at":"2026-07-18T14:02:50Z","title":"Projectional continuous data assimilation on the torus: Resonant and kernel-free regimes","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-01T20:06:45.101478Z"},"links":{"citing_paper":"/paper/2607.16827"},"observation_digest":"sha256:0431533b91f7a504cd2357526bd942421e195aa08caca12c3133add290111f2d","observation_id":"d908a72d-a8e2-4f73-b705-5d08a571364e","resolution":{"observed_at":"2026-08-01T20:06:45.101478Z","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":"2026-08-01T20:06:45.177887Z","title":"Simon,Compact sets in the spaceL p(0, T;B), Ann","venue":null,"work_id":null,"year":1986},"citing_paper":{"arxiv_id":"2607.16827","last_updated":"2026-07-18T14:02:50Z","snapshot_observed_at":"2026-08-07T06:51:02.321158Z","submitted_at":"2026-07-18T14:02:50Z","title":"Projectional continuous data assimilation on the torus: Resonant and kernel-free regimes","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-01T20:06:45.177887Z"},"links":{"citing_paper":"/paper/2607.16827"},"observation_digest":"sha256:ba94f258fcac808b932bbf75da8065d0f924ca9f2ebf86acf601c804cb35a6eb","observation_id":"cf99a040-db0a-4f58-bb50-df851df7c55a","resolution":{"observed_at":"2026-08-01T20:06:45.177887Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.16827","last_updated":"2026-07-18T14:02:50Z","latest_version":1,"primary_category":"math.AP","snapshot_observed_at":"2026-08-07T06:51:02.321158Z","submitted_at":"2026-07-18T14:02:50Z","title":"Projectional continuous data assimilation on the torus: Resonant and kernel-free regimes"},"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":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"thesis":"As of 11 August 2026, this Paper Citation Record lists 11 of 11 outbound references and 0 inbound Pith citation observations for arXiv:2607.16827."}