{"as_of":"2026-08-15T16:29:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:733af617e9f33ac06094b5d93115a745a19888f19a3d87c5caacaa2ca813fbe1","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":3,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":3,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-15T06:32:42.880941+00:00","state":"measured"},{"denominator":3,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":3,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-12T10:27:27.295644Z","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":"2026-07-04T18:20:04.973712Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"1808.05159","last_updated":"2018-08-15T15:53:28Z","snapshot_observed_at":"2026-08-14T18:40:48.539375Z","submitted_at":"2018-08-15T15:53:28Z","title":"User's guide to the fractional Laplacian and the method of semigroups","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1808.05159","snapshot_observed_at":"2026-08-12T10:27:27.295644Z","title":null,"venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2411.19312","last_updated":"2024-11-28T18:35:09Z","snapshot_observed_at":"2026-08-15T12:36:50.864698Z","submitted_at":"2024-11-28T18:35:09Z","title":"Smooth Perturbations to R\\'enyi Entropy","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-12T10:27:27.295644Z"},"links":{"cited_paper":"/paper/1808.05159","citing_paper":"/paper/2411.19312"},"observation_digest":"sha256:3d2adb6b08416839bdf197b9e1cc54feeeb6d624d9839d784439dba8b8d62aa3","observation_id":"c560cb10-1a34-4100-ae50-742dd9fa7da3","resolution":{"observed_at":"2026-08-12T10:27:27.295644Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1808.05159","last_updated":"2018-08-15T15:53:28Z","snapshot_observed_at":"2026-08-14T18:40:48.539375Z","submitted_at":"2018-08-15T15:53:28Z","title":"User's guide to the fractional Laplacian and the method of semigroups","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1808.05159","snapshot_observed_at":"2026-08-05T14:31:54.231566Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2508.21269","last_updated":"2025-08-29T00:04:24Z","snapshot_observed_at":"2026-08-05T14:31:50.569923Z","submitted_at":"2025-08-29T00:04:24Z","title":"Fractional Heat Semigroup Characterization of Distances from Functions in Lipschitz Spaces to Their Subspaces","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-05T14:31:54.231566Z"},"links":{"cited_paper":"/paper/1808.05159","citing_paper":"/paper/2508.21269"},"observation_digest":"sha256:d5a83be4ea4706e5df044105fbcc269ec9dbfa6872b23e6d64bc444070f74587","observation_id":"602298d4-6d55-44e4-9077-0775389578fd","resolution":{"observed_at":"2026-08-05T14:31:54.231566Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1808.05159","last_updated":"2018-08-15T15:53:28Z","snapshot_observed_at":"2026-08-14T18:40:48.539375Z","submitted_at":"2018-08-15T15:53:28Z","title":"User's guide to the fractional Laplacian and the method of semigroups","version":1},"cited_work":{"arxiv_id":"1808.05159","doi":null,"metadata_source":"pith","pith_arxiv_id":"1808.05159","snapshot_observed_at":"2026-07-04T18:20:04.973712Z","title":"User's guide to the fractional Laplacian and the method of semigroups","venue":"math.AP","work_id":"96b067c8-90a2-4262-b62e-a799645d2635","year":2018},"citing_paper":{"arxiv_id":"2606.24749","last_updated":"2026-06-23T16:11:14Z","snapshot_observed_at":"2026-08-02T15:35:14.080915Z","submitted_at":"2026-06-23T16:11:14Z","title":"The Fractional Dunkl Laplacian: Extension Problem and Fundamental Solution","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-06-25T22:54:39.583448Z"},"links":{"cited_paper":"/paper/1808.05159","citing_paper":"/paper/2606.24749"},"observation_digest":"sha256:89f5b3d06cc8513384dec314ede930639640242430027def2504aa3e71a736ea","observation_id":"9ada1f10-96b3-4112-816e-bfb09ad53ed5","resolution":{"observed_at":"2026-07-04T18:20:04.975492Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/1808.05159/citation-record","integrity":"/paper/1808.05159/integrity","json":"/paper/1808.05159/citation-record.json","paper":"/paper/1808.05159"},"outbound":[],"paper":{"arxiv_id":"1808.05159","last_updated":"2018-08-15T15:53:28Z","latest_version":1,"primary_category":"math.AP","snapshot_observed_at":"2026-08-14T18:40:48.539375Z","submitted_at":"2018-08-15T15:53:28Z","title":"User's guide to the fractional Laplacian and the method of semigroups"},"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":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"thesis":"As of 15 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 3 inbound Pith citation observations for arXiv:1808.05159."}