{"as_of":"2026-08-12T11:27:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:6051db34c38b176122276738b555d50026afefc62e759e8f823c006e6f8b8de0","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":4,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":4,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-12T06:34:41.77262+00:00","state":"measured"},{"denominator":4,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":4,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-11T21:14:32.521996Z","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":"2026-05-18T13:11:24.239347Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2207.11591","last_updated":"2024-07-09T14:24:39Z","snapshot_observed_at":"2026-07-06T13:34:33.453082Z","submitted_at":"2022-07-23T20:04:11Z","title":"The Generalized Rank Invariant: M\\\"obius invertibility, Discriminating Power, and Connection to Other Invariants","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2207.11591","snapshot_observed_at":"2026-08-11T21:14:32.521996Z","title":"The Generalized Rank invariant: Möbius invertibility, Discriminating power, and Connection to Other Invariants.arXiv preprint arXiv:2207.11591v5, 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2412.04995","last_updated":"2026-06-27T06:45:33Z","snapshot_observed_at":"2026-08-11T20:58:07.306949Z","submitted_at":"2024-12-06T12:44:03Z","title":"Barcoding Invariants and Their Comparison","version":3},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-11T21:14:32.521996Z"},"links":{"cited_paper":"/paper/2207.11591","citing_paper":"/paper/2412.04995"},"observation_digest":"sha256:2f64831f9a5690f759d0daf81f16ae818feb6f1d306423b097da99a96af89ec0","observation_id":"1a0b441b-cf57-45fe-9f0e-e656097e55a8","resolution":{"observed_at":"2026-08-11T21:14:32.521996Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2207.11591","last_updated":"2024-07-09T14:24:39Z","snapshot_observed_at":"2026-07-06T13:34:33.453082Z","submitted_at":"2022-07-23T20:04:11Z","title":"The Generalized Rank Invariant: M\\\"obius invertibility, Discriminating Power, and Connection to Other Invariants","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2207.11591","snapshot_observed_at":"2026-08-11T20:19:00.935486Z","title":"The generalized rank invariant: M \\\"obius invertibility, discriminating power, and connection to other invariants","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2412.05900","last_updated":"2025-04-04T08:21:22Z","snapshot_observed_at":"2026-08-11T20:11:21.448103Z","submitted_at":"2024-12-08T11:36:53Z","title":"Sparsification of the Generalized Persistence Diagrams for Scalability through Gradient Descent","version":2},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-11T20:19:00.935486Z"},"links":{"cited_paper":"/paper/2207.11591","citing_paper":"/paper/2412.05900"},"observation_digest":"sha256:4a320674b360bde0b7cef7eb60766cf91d8c865fae6c50d35d5be32874ee84af","observation_id":"e01e754f-a187-435c-a9b4-b46edbbe81d2","resolution":{"observed_at":"2026-08-11T20:19:00.935486Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2207.11591","last_updated":"2024-07-09T14:24:39Z","snapshot_observed_at":"2026-07-06T13:34:33.453082Z","submitted_at":"2022-07-23T20:04:11Z","title":"The Generalized Rank Invariant: M\\\"obius invertibility, Discriminating Power, and Connection to Other Invariants","version":5},"cited_work":{"arxiv_id":"2207.11591","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2207.11591","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"The Generalized Rank Invariant: M ¨obius invertibility, Discriminating power, and Connection to Other Invariants","venue":null,"work_id":"a840b87d-35d4-4782-8967-643f95b8060e","year":2024},"citing_paper":{"arxiv_id":"2509.24233","last_updated":"2026-04-21T14:08:06Z","snapshot_observed_at":"2026-08-11T19:12:21.761303Z","submitted_at":"2025-09-29T03:18:34Z","title":"Interleaving Distance as a Galois-Edit Distance","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-05-18T13:08:36.574856Z"},"links":{"cited_paper":"/paper/2207.11591","citing_paper":"/paper/2509.24233"},"observation_digest":"sha256:fa3fbf6198040a128712213141d2ad1aeb85590b7cf67e320f60a825a42ec268","observation_id":"21ce2035-3408-4def-9ee5-d983246b6364","resolution":{"observed_at":"2026-05-18T13:11:24.242082Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2207.11591","last_updated":"2024-07-09T14:24:39Z","snapshot_observed_at":"2026-07-06T13:34:33.453082Z","submitted_at":"2022-07-23T20:04:11Z","title":"The Generalized Rank Invariant: M\\\"obius invertibility, Discriminating Power, and Connection to Other Invariants","version":5},"cited_work":{"arxiv_id":"2207.11591","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2207.11591","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"The Generalized Rank Invariant: M ¨obius invertibility, Discriminating power, and Connection to Other Invariants","venue":null,"work_id":"a840b87d-35d4-4782-8967-643f95b8060e","year":2024},"citing_paper":{"arxiv_id":"2604.07022","last_updated":"2026-06-10T20:32:46Z","snapshot_observed_at":"2026-08-02T08:46:22.062564Z","submitted_at":"2026-04-08T12:40:09Z","title":"An Algebraic Introduction to Persistence","version":1},"reference_index":74,"source":"arxiv_source","source_observed_at":"2026-05-10T17:58:09.021250Z"},"links":{"cited_paper":"/paper/2207.11591","citing_paper":"/paper/2604.07022"},"observation_digest":"sha256:63b3abd4fdcff61192a94bb8e589c366d3cacac269c4d7793974cf4ccd73c4a2","observation_id":"ed4f1533-9efc-46d7-bc96-9863d59d9d2f","resolution":{"observed_at":"2026-05-11T05:45:57.310668Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2207.11591/citation-record","integrity":"/paper/2207.11591/integrity","json":"/paper/2207.11591/citation-record.json","paper":"/paper/2207.11591"},"outbound":[],"paper":{"arxiv_id":"2207.11591","last_updated":"2024-07-09T14:24:39Z","latest_version":5,"primary_category":"math.AT","snapshot_observed_at":"2026-07-06T13:34:33.453082Z","submitted_at":"2022-07-23T20:04:11Z","title":"The Generalized Rank Invariant: M\\\"obius invertibility, Discriminating Power, and Connection to Other Invariants"},"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":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"thesis":"As of 12 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 4 inbound Pith citation observations for arXiv:2207.11591."}