{"as_of":"2026-08-20T17:13:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:f46f7ed39515a367e246a1dfc81b501b8bac7c0aa605dda98812df7291da2e71","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":5,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":5,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-20T06:33:59.587034+00:00","state":"measured"},{"denominator":5,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":5,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T15:43:10.306226Z","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":"2026-05-22T12:11:31.232417Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2403.19987","last_updated":"2025-03-11T14:57:06Z","snapshot_observed_at":"2026-08-16T14:05:17.473644Z","submitted_at":"2024-03-29T05:41:27Z","title":"Fractional Laplace operator on finite graphs","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2403.19987","snapshot_observed_at":"2026-08-07T15:43:10.306226Z","title":"Fractional laplace operator on finite graphs","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.14799","last_updated":"2025-05-20T18:09:41Z","snapshot_observed_at":"2026-08-09T21:00:41.323153Z","submitted_at":"2025-05-20T18:09:41Z","title":"Existence theory for elliptic equations of general exponential nonlinearity on finite graphs","version":1},"reference_index":47,"source":"arxiv_source","source_observed_at":"2026-08-07T15:43:10.306226Z"},"links":{"cited_paper":"/paper/2403.19987","citing_paper":"/paper/2505.14799"},"observation_digest":"sha256:18998ba18ecbe6dac26cfa3db1828f9466accefc02cdedbdeeb680ad371f1a6a","observation_id":"c1884165-514b-4bda-a170-cf4daf6d1da3","resolution":{"observed_at":"2026-08-07T15:43:10.306226Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2403.19987","last_updated":"2025-03-11T14:57:06Z","snapshot_observed_at":"2026-08-16T14:05:17.473644Z","submitted_at":"2024-03-29T05:41:27Z","title":"Fractional Laplace operator on finite graphs","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2403.19987","snapshot_observed_at":"2026-08-06T19:32:12.817991Z","title":"Fractional laplace operator on finite graphs","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.05936","last_updated":"2025-07-27T09:06:35Z","snapshot_observed_at":"2026-08-18T19:39:46.558906Z","submitted_at":"2025-07-08T12:37:29Z","title":"The Logarithmic Laplacian on General Graphs","version":2},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-06T19:32:12.817991Z"},"links":{"cited_paper":"/paper/2403.19987","citing_paper":"/paper/2507.05936"},"observation_digest":"sha256:53f924f4ea6ba35b6eb8c8f9da6768e57e9c194f3f804a9a9a629b1e79acaa94","observation_id":"517e8482-902a-4f10-af75-7c24eb1aa220","resolution":{"observed_at":"2026-08-06T19:32:12.817991Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2403.19987","last_updated":"2025-03-11T14:57:06Z","snapshot_observed_at":"2026-08-16T14:05:17.473644Z","submitted_at":"2024-03-29T05:41:27Z","title":"Fractional Laplace operator on finite graphs","version":3},"cited_work":{"arxiv_id":"2403.19987","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2403.19987","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Fractional laplace operator on finite graphs","venue":null,"work_id":"7e0abcbd-763e-4829-b856-310c1b374261","year":2024},"citing_paper":{"arxiv_id":"2509.01155","last_updated":"2026-07-31T22:53:13Z","snapshot_observed_at":"2026-08-06T23:10:35.644193Z","submitted_at":"2025-09-01T06:24:11Z","title":"On finite-energy solutions of Kazan-Warner equations on the lattice graph","version":2},"reference_index":57,"source":"arxiv_source","source_observed_at":"2026-05-22T12:07:45.229486Z"},"links":{"cited_paper":"/paper/2403.19987","citing_paper":"/paper/2509.01155"},"observation_digest":"sha256:b51c65a8ccb090a1e98016412e573340abe45f727396632719f0da9023e1a408","observation_id":"8860ff2f-0dce-4d38-a6af-0e32fb982d32","resolution":{"observed_at":"2026-05-22T12:11:31.234901Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2403.19987","last_updated":"2025-03-11T14:57:06Z","snapshot_observed_at":"2026-08-16T14:05:17.473644Z","submitted_at":"2024-03-29T05:41:27Z","title":"Fractional Laplace operator on finite graphs","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2403.19987","snapshot_observed_at":"2026-08-05T13:04:10.790079Z","title":"Fractional laplace operator on finite graphs","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2509.01155","last_updated":"2026-07-31T22:53:13Z","snapshot_observed_at":"2026-08-06T23:10:35.644193Z","submitted_at":"2025-09-01T06:24:11Z","title":"On finite-energy solutions of Kazan-Warner equations on the lattice graph","version":3},"reference_index":57,"source":"arxiv_source","source_observed_at":"2026-08-05T13:04:10.790079Z"},"links":{"cited_paper":"/paper/2403.19987","citing_paper":"/paper/2509.01155"},"observation_digest":"sha256:4145413d0b456eb3212d60064b2f9f0753765fd121ac5e95cc295507504bad1e","observation_id":"48db8cde-242b-4e8a-8489-d6dee50784cd","resolution":{"observed_at":"2026-08-05T13:04:10.790079Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2403.19987","last_updated":"2025-03-11T14:57:06Z","snapshot_observed_at":"2026-08-16T14:05:17.473644Z","submitted_at":"2024-03-29T05:41:27Z","title":"Fractional Laplace operator on finite graphs","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2403.19987","snapshot_observed_at":"2026-07-13T12:43:29.044156Z","title":"Fractional L aplace operator on finite graphs","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2604.03638","last_updated":"2026-04-04T08:28:53Z","snapshot_observed_at":"2026-08-14T13:23:03.653725Z","submitted_at":"2026-04-04T08:28:53Z","title":"Extension theorems for logarithmic Schr\\\"odinger and discrete Laplacian operators","version":1},"reference_index":40,"source":"arxiv_source","source_observed_at":"2026-07-13T12:43:29.044156Z"},"links":{"cited_paper":"/paper/2403.19987","citing_paper":"/paper/2604.03638"},"observation_digest":"sha256:fca2dd75db321a3f18910500f99a7cc5cb81c414b5557eba49ab3002a6d255ed","observation_id":"ef928571-057e-4982-8f71-46d1ac66a224","resolution":{"observed_at":"2026-07-13T12:43:29.044156Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2403.19987/citation-record","integrity":"/paper/2403.19987/integrity","json":"/paper/2403.19987/citation-record.json","paper":"/paper/2403.19987"},"outbound":[],"paper":{"arxiv_id":"2403.19987","last_updated":"2025-03-11T14:57:06Z","latest_version":3,"primary_category":"math.AP","snapshot_observed_at":"2026-08-16T14:05:17.473644Z","submitted_at":"2024-03-29T05:41:27Z","title":"Fractional Laplace operator on finite graphs"},"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":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"thesis":"As of 20 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 5 inbound Pith citation observations for arXiv:2403.19987."}