{"as_of":"2026-08-16T23:25:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:83b55e688f821aa8ac679e3a6bf76f8b71595233fdf01c6f4e1820aab130df21","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":"2026-08-16T06:30:59.297886+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":"2026-08-14T13:03:14.931875Z","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":"2026-08-14T13:03:14.980444Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"1811.01706","last_updated":"2018-11-21T11:00:07Z","snapshot_observed_at":"2026-08-16T18:56:59.048531Z","submitted_at":"2018-11-05T14:22:06Z","title":"Estimates by gap potentials of free homotopy decompositions of critical Sobolev maps","version":2},"cited_work":{"arxiv_id":"1811.01706","doi":null,"metadata_source":"pith","pith_arxiv_id":"1811.01706","snapshot_observed_at":"2026-08-14T13:03:14.980444Z","title":"Estimates by gap potentials of free homotopy decompositions of critical Sobolev maps","venue":"math.FA","work_id":"9964f776-bd22-463b-9e8f-5028e62d6484","year":2018},"citing_paper":{"arxiv_id":"1908.06179","last_updated":"2019-08-16T21:16:59Z","snapshot_observed_at":"2026-08-14T12:51:32.783384Z","submitted_at":"2019-08-16T21:16:59Z","title":"Exponential integrability in the spirit of Moser-Trudinger's inequalities of functions with finite non-local, non-convex energy","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-14T13:03:14.931875Z"},"links":{"cited_paper":"/paper/1811.01706","citing_paper":"/paper/1908.06179"},"observation_digest":"sha256:445be9943b3564837ac9db4e06ead7c395b7e22eb647a3a201a1b6277bb8ddd7","observation_id":"fd59b686-1b4c-4d95-83e4-0357a823c52c","resolution":{"observed_at":"2026-08-14T13:03:14.987413Z","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"}}],"links":{"evidence":"/evidence","html":"/paper/1811.01706/citation-record","integrity":"/paper/1811.01706/integrity","json":"/paper/1811.01706/citation-record.json","paper":"/paper/1811.01706"},"outbound":[],"paper":{"arxiv_id":"1811.01706","last_updated":"2018-11-21T11:00:07Z","latest_version":2,"primary_category":"math.FA","snapshot_observed_at":"2026-08-16T18:56:59.048531Z","submitted_at":"2018-11-05T14:22:06Z","title":"Estimates by gap potentials of free homotopy decompositions of critical Sobolev maps"},"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 1 inbound Pith citation observation for arXiv:1811.01706."}