{"as_of":"2026-08-10T04:51:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:fa272f838c7c8f4fa15a3897baf656148c26998e4d1d89d11066ad2773cfbffa","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":"2026-08-07T12:57:31.819288Z","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":"2026-08-07T12:57:35.754253Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"1603.07787","last_updated":"2018-12-06T00:58:27Z","snapshot_observed_at":"2026-07-06T04:50:40.527815Z","submitted_at":"2016-03-25T00:34:49Z","title":"Limit formulas for the normalized fundamental matrix of the northwest-corner truncation of Markov chains: Matrix-infinite-product-form solutions of block-Hessenberg Markov chains","version":7},"cited_work":{"arxiv_id":"1603.07787","doi":null,"metadata_source":"pith","pith_arxiv_id":"1603.07787","snapshot_observed_at":"2026-08-07T12:57:35.754253Z","title":"Limit formulas for the normalized fundamental matrix of the northwest-corner truncation of Markov chains: Matrix-infinite-product-form solutions of block-Hessenberg Markov chains","venue":"math.PR","work_id":"df62c5dc-86e4-41af-95a7-d0af82ff1472","year":2016},"citing_paper":{"arxiv_id":"2505.23264","last_updated":"2025-05-29T09:13:36Z","snapshot_observed_at":"2026-08-07T12:46:53.749201Z","submitted_at":"2025-05-29T09:13:36Z","title":"Efficiently Access Diffusion Fisher: Within the Outer Product Span Space","version":1},"reference_index":35,"source":"arxiv_source","source_observed_at":"2026-08-07T12:57:31.819288Z"},"links":{"cited_paper":"/paper/1603.07787","citing_paper":"/paper/2505.23264"},"observation_digest":"sha256:307df3d4aee8c64c2c371aab2cf15c56932373c0379c9616e60732f5e90f4e79","observation_id":"fd7e42b8-5614-47ee-ac96-36dfe093ede3","resolution":{"observed_at":"2026-08-07T12:57:35.923340Z","resolver_source":"local_arxiv","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/1603.07787/citation-record","integrity":"/paper/1603.07787/integrity","json":"/paper/1603.07787/citation-record.json","paper":"/paper/1603.07787"},"outbound":[],"paper":{"arxiv_id":"1603.07787","last_updated":"2018-12-06T00:58:27Z","latest_version":7,"primary_category":"math.PR","snapshot_observed_at":"2026-07-06T04:50:40.527815Z","submitted_at":"2016-03-25T00:34:49Z","title":"Limit formulas for the normalized fundamental matrix of the northwest-corner truncation of Markov chains: Matrix-infinite-product-form solutions of block-Hessenberg Markov chains"},"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 10 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 1 inbound Pith citation observation for arXiv:1603.07787."}