{"as_of":"2026-08-16T15:55:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:11c9729103a4d3a4fd327059bb27cccebad60e03ac86906a01848b243419ddb7","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":5,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":5,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-16T06:30:59.297886+00:00","state":"measured"},{"denominator":5,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":5,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-16T01:07:38.873432Z","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":"2026-06-30T22:05:06.059138Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2411.11883","last_updated":"2024-11-04T23:19:57Z","snapshot_observed_at":"2026-08-16T13:02:57.799387Z","submitted_at":"2024-11-04T23:19:57Z","title":"Operator Characterization via Projectors and Nilpotents","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2411.11883","snapshot_observed_at":"2026-08-10T19:07:02.257226Z","title":"Operator characterization via projectors and nilpotents,","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2501.10603","last_updated":"2025-01-17T23:34:17Z","snapshot_observed_at":"2026-08-10T18:59:48.568566Z","submitted_at":"2025-01-17T23:34:17Z","title":"Matrix Ordering through Spectral and Nilpotent Structures in Totally Ordered Complex Number Fields","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-10T19:07:02.257226Z"},"links":{"cited_paper":"/paper/2411.11883","citing_paper":"/paper/2501.10603"},"observation_digest":"sha256:a295a59dc47493524615bfbe638f461b2cad73cd4f137d55782d51b64d7fdaef","observation_id":"f9e4c913-68f7-4bc2-a417-2f1454b891ee","resolution":{"observed_at":"2026-08-10T19:07:02.257226Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2411.11883","last_updated":"2024-11-04T23:19:57Z","snapshot_observed_at":"2026-08-16T13:02:57.799387Z","submitted_at":"2024-11-04T23:19:57Z","title":"Operator Characterization via Projectors and Nilpotents","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2411.11883","snapshot_observed_at":"2026-08-16T01:07:38.873432Z","title":"Operator characterization via projectors and nilpotents,","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.02188","last_updated":"2025-05-04T17:07:55Z","snapshot_observed_at":"2026-08-16T00:56:17.675886Z","submitted_at":"2025-05-04T17:07:55Z","title":"Generalized Double Operator Integrals for Continuous Spectrum Operators","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-16T01:07:38.873432Z"},"links":{"cited_paper":"/paper/2411.11883","citing_paper":"/paper/2505.02188"},"observation_digest":"sha256:317c928456b4a679a9664af90659c9e2f036c829b98847a25abafeff4ba1a2b0","observation_id":"14dd0ae6-b36c-478e-a7be-2ebb85828e25","resolution":{"observed_at":"2026-08-16T01:07:38.873432Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2411.11883","last_updated":"2024-11-04T23:19:57Z","snapshot_observed_at":"2026-08-16T13:02:57.799387Z","submitted_at":"2024-11-04T23:19:57Z","title":"Operator Characterization via Projectors and Nilpotents","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2411.11883","snapshot_observed_at":"2026-08-15T18:31:55.257637Z","title":"Operator characterization via projectors and nilpotents,","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2506.19971","last_updated":"2025-06-24T19:40:05Z","snapshot_observed_at":"2026-08-15T20:13:46.469972Z","submitted_at":"2025-06-24T19:40:05Z","title":"Generalized Multiple Operator Integrals for Operators with Finite Dimensions","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-15T18:31:55.257637Z"},"links":{"cited_paper":"/paper/2411.11883","citing_paper":"/paper/2506.19971"},"observation_digest":"sha256:cf63ee2952bdabaf5f4c3898ba010037909952ea84aab2d6200d945f53f10021","observation_id":"ca00944c-1528-49de-a695-755661fd557d","resolution":{"observed_at":"2026-08-15T18:31:55.257637Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2411.11883","last_updated":"2024-11-04T23:19:57Z","snapshot_observed_at":"2026-08-16T13:02:57.799387Z","submitted_at":"2024-11-04T23:19:57Z","title":"Operator Characterization via Projectors and Nilpotents","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2411.11883","snapshot_observed_at":"2026-08-06T11:10:37.170256Z","title":"Operator characterization via projectors and nilpotents,","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.23049","last_updated":"2025-07-30T19:23:25Z","snapshot_observed_at":"2026-08-14T04:31:03.863012Z","submitted_at":"2025-07-30T19:23:25Z","title":"Generalized Multiple Operator Integrals and Perturbation Theory for Operators with Continuous Spectra","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-06T11:10:37.170256Z"},"links":{"cited_paper":"/paper/2411.11883","citing_paper":"/paper/2507.23049"},"observation_digest":"sha256:fb9d64a02b39ad7e42517aa8f6a23ea4d71f7731bb89a2a4866e78e56644a961","observation_id":"fab409ab-6440-4f2a-b478-be2060d3e856","resolution":{"observed_at":"2026-08-06T11:10:37.170256Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2411.11883","last_updated":"2024-11-04T23:19:57Z","snapshot_observed_at":"2026-08-16T13:02:57.799387Z","submitted_at":"2024-11-04T23:19:57Z","title":"Operator Characterization via Projectors and Nilpotents","version":1},"cited_work":{"arxiv_id":"2411.11883","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2411.11883","snapshot_observed_at":"2026-06-30T22:05:06.059138Z","title":"Operator characterization via projectors and nilpotents,","venue":null,"work_id":"04c9d501-4c0b-4ca6-90c2-5aac2e46c857","year":2024},"citing_paper":{"arxiv_id":"2605.12886","last_updated":"2026-05-13T02:01:43Z","snapshot_observed_at":"2026-08-14T09:59:57.515652Z","submitted_at":"2026-05-13T02:01:43Z","title":"Tensor-Lifted Multivariate Functional Calculus Beyond Commutativity and Boundedness","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-06-30T21:56:07.752541Z"},"links":{"cited_paper":"/paper/2411.11883","citing_paper":"/paper/2605.12886"},"observation_digest":"sha256:13990d018cf6668b40e7cc74711b0c06edf4db86f0196d0d04c1a18709504c12","observation_id":"e48ce93d-a328-4434-bbb1-77f8896bb619","resolution":{"observed_at":"2026-06-30T22:05:06.060470Z","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"}}],"links":{"evidence":"/evidence","html":"/paper/2411.11883/citation-record","integrity":"/paper/2411.11883/integrity","json":"/paper/2411.11883/citation-record.json","paper":"/paper/2411.11883"},"outbound":[],"paper":{"arxiv_id":"2411.11883","last_updated":"2024-11-04T23:19:57Z","latest_version":1,"primary_category":"math.FA","snapshot_observed_at":"2026-08-16T13:02:57.799387Z","submitted_at":"2024-11-04T23:19:57Z","title":"Operator Characterization via Projectors and Nilpotents"},"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 5 inbound Pith citation observations for arXiv:2411.11883."}