{"as_of":"2026-08-12T22:48:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:a849d72924c1e144c2f12ebae13f3698e3ca59d6e9ec28b2f3712d55d3bb7391","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":"2026-08-12T06:34:41.77262+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":"2026-08-11T00:54:50.578544Z","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":"2026-08-11T00:54:50.771800Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2412.07098","last_updated":"2024-12-28T00:15:01Z","snapshot_observed_at":"2026-08-11T19:05:20.822615Z","submitted_at":"2024-12-10T01:34:13Z","title":"Phase Transitions on 1d Long-Range Ising Models with Decaying Fields: A Direct Proof via Contours","version":2},"cited_work":{"arxiv_id":"2412.07098","doi":null,"metadata_source":"pith","pith_arxiv_id":"2412.07098","snapshot_observed_at":"2026-08-11T00:54:50.771800Z","title":"Phase Transitions on 1d Long-Range Ising Models with Decaying Fields: A Direct Proof via Contours","venue":"math-ph","work_id":"3c3cd69f-b902-4c9b-85fe-c868139ae0cd","year":2024},"citing_paper":{"arxiv_id":"2412.19281","last_updated":"2025-01-19T03:47:28Z","snapshot_observed_at":"2026-08-11T04:10:25.204347Z","submitted_at":"2024-12-26T16:56:04Z","title":"Phase transitions in low-dimensional long-range random field Ising models","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-11T00:54:50.578544Z"},"links":{"cited_paper":"/paper/2412.07098","citing_paper":"/paper/2412.19281"},"observation_digest":"sha256:563751f43ebd8408ed65d71e816dcd734199c133b232a483ecf2554ca74944bd","observation_id":"56285d1b-5da5-4d1f-8c75-26c55c26b29d","resolution":{"observed_at":"2026-08-11T00:54:50.779729Z","resolver_source":"local_arxiv","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":"2412.07098","last_updated":"2024-12-28T00:15:01Z","snapshot_observed_at":"2026-08-11T19:05:20.822615Z","submitted_at":"2024-12-10T01:34:13Z","title":"Phase Transitions on 1d Long-Range Ising Models with Decaying Fields: A Direct Proof via Contours","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2412.07098","snapshot_observed_at":"2026-08-02T23:55:49.755282Z","title":"Affonso, R","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2602.12447","last_updated":"2026-06-23T18:49:51Z","snapshot_observed_at":"2026-08-10T08:16:43.251908Z","submitted_at":"2026-02-12T22:11:52Z","title":"A Cluster Expansion and the Decay of Correlations of the 1D Long-Range Ising Model at Low Temperatures","version":3},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-02T23:55:49.755282Z"},"links":{"cited_paper":"/paper/2412.07098","citing_paper":"/paper/2602.12447"},"observation_digest":"sha256:965ec415063183316c5fa54bfd4a14f3d6d9c1b9919474cd30b4301a9dc28405","observation_id":"00aa8cb6-e5b2-4772-afc9-fd3e438a3e4c","resolution":{"observed_at":"2026-08-02T23:55:49.755282Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2412.07098/citation-record","integrity":"/paper/2412.07098/integrity","json":"/paper/2412.07098/citation-record.json","paper":"/paper/2412.07098"},"outbound":[],"paper":{"arxiv_id":"2412.07098","last_updated":"2024-12-28T00:15:01Z","latest_version":2,"primary_category":"math-ph","snapshot_observed_at":"2026-08-11T19:05:20.822615Z","submitted_at":"2024-12-10T01:34:13Z","title":"Phase Transitions on 1d Long-Range Ising Models with Decaying Fields: A Direct Proof via Contours"},"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 2 inbound Pith citation observations for arXiv:2412.07098."}