{"as_of":"2026-08-08T10:11:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:22251f661736e7b1022fac78b9f2104c005cea936891062dc35ff788c5784d39","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":2,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":2,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-08T06:32:00.761636+00:00","state":"measured"},{"denominator":2,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":2,"source":"paper_references, paper_reference_links","source_observed_at":"2026-07-12T14:18:11.354143Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"pith","source_observed_at":"2026-07-03T13:38:19.679891Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2606.06241","last_updated":"2026-07-03T14:23:38Z","snapshot_observed_at":"2026-08-02T05:09:15.040718Z","submitted_at":"2026-06-04T14:47:21Z","title":"Decomposition Theorem for Perfectoid Rings along General Ideals","version":2},"cited_work":{"arxiv_id":"2606.06241","doi":null,"metadata_source":"pith","pith_arxiv_id":"2606.06241","snapshot_observed_at":"2026-07-03T13:38:19.679891Z","title":"Decomposition Theorem for Perfectoid Rings along General Ideals","venue":"math.AC","work_id":"d8b988f7-0b92-4937-83e7-6fcb9e313485","year":2026},"citing_paper":{"arxiv_id":"2606.12229","last_updated":"2026-07-03T14:30:59Z","snapshot_observed_at":"2026-07-12T14:18:06.427458Z","submitted_at":"2026-06-10T15:38:08Z","title":"On Perfectoidizaiton of Finite Algebras over a Perfectoid Ring","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-06-27T07:38:07.874076Z"},"links":{"cited_paper":"/paper/2606.06241","citing_paper":"/paper/2606.12229"},"observation_digest":"sha256:a0292c06cca80259dc739c80cefb20b59c102f7ae2de8bb087e85de67457ad64","observation_id":"7b804087-dda9-4fe9-a6ef-78b70f6ee5d5","resolution":{"observed_at":"2026-07-03T13:38:19.681072Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2606.06241","last_updated":"2026-07-03T14:23:38Z","snapshot_observed_at":"2026-08-02T05:09:15.040718Z","submitted_at":"2026-06-04T14:47:21Z","title":"Decomposition Theorem for Perfectoid Rings along General Ideals","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2606.06241","snapshot_observed_at":"2026-07-12T14:18:11.354143Z","title":"Ishizuka and L","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2606.12229","last_updated":"2026-07-03T14:30:59Z","snapshot_observed_at":"2026-07-12T14:18:06.427458Z","submitted_at":"2026-06-10T15:38:08Z","title":"On Perfectoidizaiton of Finite Algebras over a Perfectoid Ring","version":2},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-07-12T14:18:11.354143Z"},"links":{"cited_paper":"/paper/2606.06241","citing_paper":"/paper/2606.12229"},"observation_digest":"sha256:62f175354b400c9c0f55cd72dceee12545a7702e8c6c69935b9c4f34f1419406","observation_id":"0a02d9fa-c616-47da-a441-9fb5491df931","resolution":{"observed_at":"2026-07-12T14:18:11.354143Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2606.06241/citation-record","integrity":"/paper/2606.06241/integrity","json":"/paper/2606.06241/citation-record.json","paper":"/paper/2606.06241"},"outbound":[],"paper":{"arxiv_id":"2606.06241","last_updated":"2026-07-03T14:23:38Z","latest_version":2,"primary_category":"math.AC","snapshot_observed_at":"2026-08-02T05:09:15.040718Z","submitted_at":"2026-06-04T14:47:21Z","title":"Decomposition Theorem for Perfectoid Rings along General Ideals"},"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":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"thesis":"As of 8 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 2 inbound Pith citation observations for arXiv:2606.06241."}