{"as_of":"2026-08-18T19:49:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:aa8b0763a11d84138dcbbfffa4ab69f3ee39c63e70e716632c92c0b7c432ca7a","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":"2026-08-18T06:34:40.430872+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":"2026-05-14T23:53:36.959089Z","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":"2026-05-14T23:58:19.083658Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2205.05647","last_updated":"2024-01-17T02:05:49Z","snapshot_observed_at":"2026-08-16T17:00:59.617069Z","submitted_at":"2022-05-11T17:23:54Z","title":"Minimal Representations of Tropical Rational Functions","version":4},"cited_work":{"arxiv_id":"2205.05647","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2205.05647","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"e0589ab3-97c3-4aa5-b713-64d9109c611c","year":null},"citing_paper":{"arxiv_id":"2603.25953","last_updated":"2026-04-30T21:08:21Z","snapshot_observed_at":"2026-07-06T22:50:41.736941Z","submitted_at":"2026-03-26T22:46:43Z","title":"Geometric classification of primes modulo a (bend) congruence","version":2},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-05-14T23:53:36.959089Z"},"links":{"cited_paper":"/paper/2205.05647","citing_paper":"/paper/2603.25953"},"observation_digest":"sha256:39fc30374109d2955483a1f9dcd6bef8c59d9d8d4078d176da885ca07e65e064","observation_id":"011cc169-c624-42fe-b629-23229227403a","resolution":{"observed_at":"2026-05-14T23:58:19.085043Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2205.05647/citation-record","integrity":"/paper/2205.05647/integrity","json":"/paper/2205.05647/citation-record.json","paper":"/paper/2205.05647"},"outbound":[],"paper":{"arxiv_id":"2205.05647","last_updated":"2024-01-17T02:05:49Z","latest_version":4,"primary_category":"math.CO","snapshot_observed_at":"2026-08-16T17:00:59.617069Z","submitted_at":"2022-05-11T17:23:54Z","title":"Minimal Representations of Tropical Rational Functions"},"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":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"thesis":"As of 18 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 1 inbound Pith citation observation for arXiv:2205.05647."}