{"as_of":"2026-08-16T17:40:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:ce409b673468374c51ea54d4b8e6d77fd6b9f19bec3232d9b6255ecc3c51bb1e","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":"2026-08-16T06:30:59.297886+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":"2026-08-15T23:29:17.179553Z","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":"2026-08-14T13:55:39.239467Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"1012.0287","last_updated":"2011-09-23T06:26:25Z","snapshot_observed_at":"2026-08-15T05:01:25.016481Z","submitted_at":"2010-12-01T20:26:47Z","title":"Chip-Firing and Riemann-Roch Theory for Directed Graphs","version":2},"cited_work":{"arxiv_id":"1012.0287","doi":null,"metadata_source":"pith","pith_arxiv_id":"1012.0287","snapshot_observed_at":"2026-08-14T13:55:39.239467Z","title":"Chip-Firing and Riemann-Roch Theory for Directed Graphs","venue":"math.CO","work_id":"7dc0f39c-c27b-4f7d-a169-3d82dabfc207","year":2010},"citing_paper":{"arxiv_id":"1908.04395","last_updated":"2019-08-12T21:07:32Z","snapshot_observed_at":"2026-08-16T15:35:23.622869Z","submitted_at":"2019-08-12T21:07:32Z","title":"Chip-Firing Games and Critical Groups","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-14T13:55:38.737773Z"},"links":{"cited_paper":"/paper/1012.0287","citing_paper":"/paper/1908.04395"},"observation_digest":"sha256:0c57cb2da8080500b365fc79c4cf3e1db7bfe68a7946a3b6c95d4dec0a9d3da4","observation_id":"e48c2663-2e19-4ef5-a6e4-c7858d2ff1b6","resolution":{"observed_at":"2026-08-14T13:55:39.244084Z","resolver_source":"local_arxiv","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":"1012.0287","last_updated":"2011-09-23T06:26:25Z","snapshot_observed_at":"2026-08-15T05:01:25.016481Z","submitted_at":"2010-12-01T20:26:47Z","title":"Chip-Firing and Riemann-Roch Theory for Directed Graphs","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1012.0287","snapshot_observed_at":"2026-08-15T23:29:17.179553Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.05392","last_updated":"2025-07-03T17:29:44Z","snapshot_observed_at":"2026-08-15T23:02:43.628492Z","submitted_at":"2025-05-08T16:27:32Z","title":"Generalized chip firing and critical groups of arithmetical structures on trees","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-15T23:29:17.179553Z"},"links":{"cited_paper":"/paper/1012.0287","citing_paper":"/paper/2505.05392"},"observation_digest":"sha256:d458c53316447d91ebff7a40efc58f71a508c99b6cebe8bfbe4ca8f32678ba1c","observation_id":"d8fd1c9f-2c5e-4243-b467-ce26768db5d3","resolution":{"observed_at":"2026-08-15T23:29:17.179553Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/1012.0287/citation-record","integrity":"/paper/1012.0287/integrity","json":"/paper/1012.0287/citation-record.json","paper":"/paper/1012.0287"},"outbound":[],"paper":{"arxiv_id":"1012.0287","last_updated":"2011-09-23T06:26:25Z","latest_version":2,"primary_category":"math.CO","snapshot_observed_at":"2026-08-15T05:01:25.016481Z","submitted_at":"2010-12-01T20:26:47Z","title":"Chip-Firing and Riemann-Roch Theory for Directed Graphs"},"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 2 inbound Pith citation observations for arXiv:1012.0287."}