{"as_of":"2026-08-13T06:31:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:51852ef0409799af9912e88e9b1dc27b66a2f9266578ced6404c2671ecc14620","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":"2026-08-12T06:34:41.77262+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":"2026-05-18T21:50:01.091994Z","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":"2026-05-18T21:51:52.104791Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2303.12042","last_updated":"2025-08-19T10:08:41Z","snapshot_observed_at":"2026-08-05T18:10:08.624494Z","submitted_at":"2023-03-21T17:27:53Z","title":"Multifactorisations and Divisor Functions","version":2},"cited_work":{"arxiv_id":"2303.12042","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2303.12042","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Multifactorisations and Divisor Functions","venue":null,"work_id":"523d7370-b073-4739-ad7d-bf7d9f49f334","year":null},"citing_paper":{"arxiv_id":"2508.17285","last_updated":"2026-03-30T23:14:36Z","snapshot_observed_at":"2026-08-11T07:09:19.907702Z","submitted_at":"2025-08-24T10:19:14Z","title":"Additive systems for $\\mathbb{Z}$ are undecidable","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-05-18T21:50:01.091994Z"},"links":{"cited_paper":"/paper/2303.12042","citing_paper":"/paper/2508.17285"},"observation_digest":"sha256:8c0899b51aaf3cac3bf18940b76b084dcec41fbdeb55665a08cef0f846306575","observation_id":"697a1f78-19ff-4235-961d-a945ed4bba1b","resolution":{"observed_at":"2026-05-18T21:51:52.107767Z","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/2303.12042/citation-record","integrity":"/paper/2303.12042/integrity","json":"/paper/2303.12042/citation-record.json","paper":"/paper/2303.12042"},"outbound":[],"paper":{"arxiv_id":"2303.12042","last_updated":"2025-08-19T10:08:41Z","latest_version":2,"primary_category":"math.NT","snapshot_observed_at":"2026-08-05T18:10:08.624494Z","submitted_at":"2023-03-21T17:27:53Z","title":"Multifactorisations and Divisor 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":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"thesis":"As of 13 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 1 inbound Pith citation observation for arXiv:2303.12042."}