{"as_of":"2026-08-09T16:21:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:1d9ca1ea87cf9030d30452a6eb95bb8492244a4c790333625fdd371dad1ad77a","coverage":[{"denominator":0,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":1,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-09T06:31:02.800959+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-06-28T11:52:58.472085Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-07-02T01:36:24.886446Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2209.06801","last_updated":"2023-01-30T13:02:38Z","snapshot_observed_at":"2026-07-06T13:52:16.762474Z","submitted_at":"2022-09-14T17:33:02Z","title":"Donati representation theorem for periodic functions in relation to homogenization theory","version":2},"cited_work":{"arxiv_id":"2209.06801","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2209.06801","snapshot_observed_at":"2026-07-02T01:36:24.886446Z","title":"arXiv preprint arXiv:2209.06801 , year=","venue":null,"work_id":"850ad0a4-f4bf-495e-ab74-a04dc10bdd8f","year":null},"citing_paper":{"arxiv_id":"2606.02089","last_updated":"2026-06-01T11:17:52Z","snapshot_observed_at":"2026-08-03T15:32:29.917772Z","submitted_at":"2026-06-01T11:17:52Z","title":"Sequential Subspace Mode Adaptation for the Reduced-Order Homogenization of Dissipative Microstructures using E3C Hyper-Reduction","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-06-28T11:52:58.472085Z"},"links":{"cited_paper":"/paper/2209.06801","citing_paper":"/paper/2606.02089"},"observation_digest":"sha256:c63cdf547c66e9270a6e239489fb0a9446bad51fa5df9eeaa4d68d75b442caa6","observation_id":"06b1e2eb-54b9-40ea-8b42-4710aaa33064","resolution":{"observed_at":"2026-07-02T01:36:24.889527Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2209.06801/citation-record","integrity":"/paper/2209.06801/integrity","json":"/paper/2209.06801/citation-record.json","paper":"/paper/2209.06801"},"outbound":[],"paper":{"arxiv_id":"2209.06801","last_updated":"2023-01-30T13:02:38Z","latest_version":2,"primary_category":"math.AP","snapshot_observed_at":"2026-07-06T13:52:16.762474Z","submitted_at":"2022-09-14T17:33:02Z","title":"Donati representation theorem for periodic functions in relation to homogenization theory"},"reference_resolution":{"displayed":0,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":0,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":0},"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":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"thesis":"As of 9 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 1 inbound Pith citation observation for arXiv:2209.06801."}