{"as_of":"2026-08-11T20:11:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:8f75d014885c44e7cc905a241f7d8d2b5bc8fccfdc7943261957a87f5f1aef86","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":"2026-08-11T06:34:44.6726+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":"2026-08-03T14:58:17.570772Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2112.05227","last_updated":"2021-12-09T21:54:34Z","snapshot_observed_at":"2026-08-03T16:21:08.901678Z","submitted_at":"2021-12-09T21:54:34Z","title":"Fake Mu's","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2112.05227","snapshot_observed_at":"2026-08-03T14:58:17.570772Z","title":"Martin, M","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2512.18936","last_updated":"2026-06-05T00:03:04Z","snapshot_observed_at":"2026-08-03T14:58:15.966067Z","submitted_at":"2025-12-22T01:13:04Z","title":"Unimodular Fake Mobius Functions","version":3},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-03T14:58:17.570772Z"},"links":{"cited_paper":"/paper/2112.05227","citing_paper":"/paper/2512.18936"},"observation_digest":"sha256:8e3d21ea80bb81080c731835c58f276b44c9aced2f8f59e734f72329297d7c7c","observation_id":"a8681b46-0a94-4373-bfd3-104e6a89c08d","resolution":{"observed_at":"2026-08-03T14:58:17.570772Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2112.05227/citation-record","integrity":"/paper/2112.05227/integrity","json":"/paper/2112.05227/citation-record.json","paper":"/paper/2112.05227"},"outbound":[],"paper":{"arxiv_id":"2112.05227","last_updated":"2021-12-09T21:54:34Z","latest_version":1,"primary_category":"math.NT","snapshot_observed_at":"2026-08-03T16:21:08.901678Z","submitted_at":"2021-12-09T21:54:34Z","title":"Fake Mu's"},"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":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"thesis":"As of 11 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 1 inbound Pith citation observation for arXiv:2112.05227."}