{"as_of":"2026-08-16T18:50:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:b9b5989e3143c3ecb8af2a943db0385bd8d695c2b08340d602ab3bb2592c09ff","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":3,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":3,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-16T06:30:59.297886+00:00","state":"measured"},{"denominator":3,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":3,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-15T17:13:32.539473Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":1,"source":"arxiv_reference","source_observed_at":"2026-08-05T02:28:24.338817Z","state":"measured"}],"external_citation_measurements":[{"count":0,"observed_at":"2026-08-05T02:28:24.338817Z","source":"arxiv_reference"}],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2407.10905","last_updated":"2025-07-28T08:11:07Z","snapshot_observed_at":"2026-08-16T13:34:04.170279Z","submitted_at":"2024-07-15T16:59:18Z","title":"Noncommutative topological boundaries and amenable invariant random intermediate subalgebras","version":4},"cited_work":{"arxiv_id":"2407.10905","doi":"10.48550/arxiv.2407.10905","metadata_source":"arxiv_reference","pith_arxiv_id":"2407.10905","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Noncommutative topological boundaries and amenable invariant random intermediate subalgebras","venue":"arXiv (Cornell University)","work_id":"3f7899b5-09de-463b-8ba7-98312b02d0f8","year":2024},"citing_paper":{"arxiv_id":"2405.01806","last_updated":"2025-11-09T15:04:10Z","snapshot_observed_at":"2026-07-06T18:09:08.963593Z","submitted_at":"2024-05-03T01:34:44Z","title":"On dense orbits in the space of subequivalence relations","version":3},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-05-24T01:26:34.170487Z"},"links":{"cited_paper":"/paper/2407.10905","citing_paper":"/paper/2405.01806"},"observation_digest":"sha256:cda44db53a86680f147cba8308b5bce22a678737f045b7cdc212d7df635ccb12","observation_id":"3eaf52cf-c239-4430-b9d5-79884da07216","resolution":{"observed_at":"2026-05-24T01:28:42.433709Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2407.10905","last_updated":"2025-07-28T08:11:07Z","snapshot_observed_at":"2026-08-16T13:34:04.170279Z","submitted_at":"2024-07-15T16:59:18Z","title":"Noncommutative topological boundaries and amenable invariant random intermediate subalgebras","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2407.10905","snapshot_observed_at":"2026-08-15T17:13:32.539473Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2508.18978","last_updated":"2025-08-26T12:25:49Z","snapshot_observed_at":"2026-08-15T16:51:41.026476Z","submitted_at":"2025-08-26T12:25:49Z","title":"Non-commutative Intermediate Factor theorem associated with $W^*$-dynamics of product groups","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-15T17:13:32.539473Z"},"links":{"cited_paper":"/paper/2407.10905","citing_paper":"/paper/2508.18978"},"observation_digest":"sha256:feeb8d7e98bfed8672d9f7086f663e4752527be0e9d0373bbe3e7f9fb4ed7f77","observation_id":"6a97ce98-52f3-47df-b77d-a3e6983a6622","resolution":{"observed_at":"2026-08-15T17:13:32.539473Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2407.10905","last_updated":"2025-07-28T08:11:07Z","snapshot_observed_at":"2026-08-16T13:34:04.170279Z","submitted_at":"2024-07-15T16:59:18Z","title":"Noncommutative topological boundaries and amenable invariant random intermediate subalgebras","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2407.10905","snapshot_observed_at":"2026-08-02T02:35:09.730892Z","title":"doi:10.48550/arXiv.2407.10905 , archiveprefix =","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.14358","last_updated":"2026-07-15T20:45:28Z","snapshot_observed_at":"2026-08-06T14:05:57.017903Z","submitted_at":"2026-07-15T20:45:28Z","title":"Spaces of UCP maps and subalgebras of von Neumann algebras","version":1},"reference_index":70,"source":"arxiv_source","source_observed_at":"2026-08-02T02:35:09.730892Z"},"links":{"cited_paper":"/paper/2407.10905","citing_paper":"/paper/2607.14358"},"observation_digest":"sha256:f75af4dc1d2bcc33aac18416aa45abd7e033a1aeff985d2b3cf7262b1460cd4c","observation_id":"3eb5de54-3f29-43c0-b250-37565964a716","resolution":{"observed_at":"2026-08-02T02:35:09.730892Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2407.10905/citation-record","integrity":"/paper/2407.10905/integrity","json":"/paper/2407.10905/citation-record.json","paper":"/paper/2407.10905"},"outbound":[],"paper":{"arxiv_id":"2407.10905","last_updated":"2025-07-28T08:11:07Z","latest_version":4,"primary_category":"math.OA","snapshot_observed_at":"2026-08-16T13:34:04.170279Z","submitted_at":"2024-07-15T16:59:18Z","title":"Noncommutative topological boundaries and amenable invariant random intermediate subalgebras"},"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":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"thesis":"As of 16 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 3 inbound Pith citation observations for arXiv:2407.10905."}