{"as_of":"2026-08-08T20:05:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:ffd54d0642d3faaff0e2b836cd8615aa0c62d55cd1f78f2e8554aecc00482725","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":9,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":9,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-08T06:32:00.761636+00:00","state":"measured"},{"denominator":9,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":9,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T00:57:58.542666Z","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":"2026-05-16T07:02:28.912024Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2312.15689","last_updated":"2023-12-25T10:39:14Z","snapshot_observed_at":"2026-07-06T17:07:52.197869Z","submitted_at":"2023-12-25T10:39:14Z","title":"An extension problem for the logarithmic Laplacian","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2312.15689","snapshot_observed_at":"2026-08-07T00:57:58.542666Z","title":"An extension problem for the logarithmic Laplacian","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2506.12535","last_updated":"2025-07-03T04:22:57Z","snapshot_observed_at":"2026-08-07T00:44:22.151334Z","submitted_at":"2025-06-14T15:15:37Z","title":"Anisotropic Calder\\'{o}n problem of a nearly Laplace-Beltrami operator of order $2+$","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-07T00:57:58.542666Z"},"links":{"cited_paper":"/paper/2312.15689","citing_paper":"/paper/2506.12535"},"observation_digest":"sha256:35040594ff6fa420e6a131468ef9e25d14d7a539278215d37ec6528ab9a2d091","observation_id":"6f4dc301-755d-49a2-9190-3bc5ea6838df","resolution":{"observed_at":"2026-08-07T00:57:58.542666Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2312.15689","last_updated":"2023-12-25T10:39:14Z","snapshot_observed_at":"2026-07-06T17:07:52.197869Z","submitted_at":"2023-12-25T10:39:14Z","title":"An extension problem for the logarithmic Laplacian","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2312.15689","snapshot_observed_at":"2026-08-06T23:14:11.885782Z","title":"An extension problem for the loga- rithmic laplacian","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2506.19311","last_updated":"2025-06-24T04:57:54Z","snapshot_observed_at":"2026-08-08T06:21:02.572741Z","submitted_at":"2025-06-24T04:57:54Z","title":"Logarithmic Laplacian on General Riemannian Manifolds","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-06T23:14:11.885782Z"},"links":{"cited_paper":"/paper/2312.15689","citing_paper":"/paper/2506.19311"},"observation_digest":"sha256:6c7f5c4c89c216231c81df0aada0944d7ad478f3090ad2b0e238d0d0ecad777c","observation_id":"a1728fe1-635b-422a-8de3-1ee92c0daf17","resolution":{"observed_at":"2026-08-06T23:14:11.885782Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2312.15689","last_updated":"2023-12-25T10:39:14Z","snapshot_observed_at":"2026-07-06T17:07:52.197869Z","submitted_at":"2023-12-25T10:39:14Z","title":"An extension problem for the logarithmic Laplacian","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2312.15689","snapshot_observed_at":"2026-08-06T19:32:12.699558Z","title":"An extension problem for the loga- rithmic laplacian","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2507.05936","last_updated":"2025-07-27T09:06:35Z","snapshot_observed_at":"2026-08-06T19:12:21.106932Z","submitted_at":"2025-07-08T12:37:29Z","title":"The Logarithmic Laplacian on General Graphs","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-06T19:32:12.699558Z"},"links":{"cited_paper":"/paper/2312.15689","citing_paper":"/paper/2507.05936"},"observation_digest":"sha256:de65766cb5221e6510d7911e8d41f3597839973740d051a3a5f21f59e83a6dd1","observation_id":"47938c02-f4f5-4b4e-a825-774383534fba","resolution":{"observed_at":"2026-08-06T19:32:12.699558Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2312.15689","last_updated":"2023-12-25T10:39:14Z","snapshot_observed_at":"2026-07-06T17:07:52.197869Z","submitted_at":"2023-12-25T10:39:14Z","title":"An extension problem for the logarithmic Laplacian","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2312.15689","snapshot_observed_at":"2026-08-06T12:34:41.571078Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2507.21779","last_updated":"2025-08-27T17:04:32Z","snapshot_observed_at":"2026-08-06T12:34:39.052530Z","submitted_at":"2025-07-29T13:03:43Z","title":"The conformal logarithmic Laplacian on the sphere: Yamabe-type problems and Sobolev spaces","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-06T12:34:41.571078Z"},"links":{"cited_paper":"/paper/2312.15689","citing_paper":"/paper/2507.21779"},"observation_digest":"sha256:279d890e193638baef6107acf5c5c8c2d4164e4e21b5fd8e67eaa26b38792d2b","observation_id":"27008a04-9a08-42d3-bac2-d425dac2b9d8","resolution":{"observed_at":"2026-08-06T12:34:41.571078Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2312.15689","last_updated":"2023-12-25T10:39:14Z","snapshot_observed_at":"2026-07-06T17:07:52.197869Z","submitted_at":"2023-12-25T10:39:14Z","title":"An extension problem for the logarithmic Laplacian","version":1},"cited_work":{"arxiv_id":"2312.15689","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2312.15689","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"d8d28ceb-e576-43c4-b0c4-274ca3171f0b","year":2023},"citing_paper":{"arxiv_id":"2602.06581","last_updated":"2026-04-11T14:26:08Z","snapshot_observed_at":"2026-07-06T22:44:46.690576Z","submitted_at":"2026-02-06T10:20:54Z","title":"The Fractional-Logarithmic Laplacian:Fundamental Properties and Eigenvalues","version":3},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-05-16T07:02:22.122426Z"},"links":{"cited_paper":"/paper/2312.15689","citing_paper":"/paper/2602.06581"},"observation_digest":"sha256:d734ebd2d15785eceac32ff3f83ae6ed11da4afdbae3b4406c2830c7f48fec27","observation_id":"a3140e4e-00fe-4545-bb9a-632b7d49f70b","resolution":{"observed_at":"2026-05-16T07:02:28.914905Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2312.15689","last_updated":"2023-12-25T10:39:14Z","snapshot_observed_at":"2026-07-06T17:07:52.197869Z","submitted_at":"2023-12-25T10:39:14Z","title":"An extension problem for the logarithmic Laplacian","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2312.15689","snapshot_observed_at":"2026-07-13T12:43:29.044156Z","title":"An extension problem for the logarithm L aplacian","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2604.03638","last_updated":"2026-04-04T08:28:53Z","snapshot_observed_at":"2026-08-07T06:04:17.814131Z","submitted_at":"2026-04-04T08:28:53Z","title":"Extension theorems for logarithmic Schr\\\"odinger and discrete Laplacian operators","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-07-13T12:43:29.044156Z"},"links":{"cited_paper":"/paper/2312.15689","citing_paper":"/paper/2604.03638"},"observation_digest":"sha256:aba224b1112a3dace2807618daeb67c8e5580b095094000811859f4a85505c09","observation_id":"01520bf6-0421-4c7f-9ff5-8aa6bbb10f3c","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"}},{"citation":{"cited_paper":{"arxiv_id":"2312.15689","last_updated":"2023-12-25T10:39:14Z","snapshot_observed_at":"2026-07-06T17:07:52.197869Z","submitted_at":"2023-12-25T10:39:14Z","title":"An extension problem for the logarithmic Laplacian","version":1},"cited_work":{"arxiv_id":"2312.15689","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2312.15689","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"d8d28ceb-e576-43c4-b0c4-274ca3171f0b","year":2023},"citing_paper":{"arxiv_id":"2605.06102","last_updated":"2026-05-07T12:17:08Z","snapshot_observed_at":"2026-07-06T23:18:36.537416Z","submitted_at":"2026-05-07T12:17:08Z","title":"$s$-harmonic functions in the small order limit","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-05-08T07:21:57.500531Z"},"links":{"cited_paper":"/paper/2312.15689","citing_paper":"/paper/2605.06102"},"observation_digest":"sha256:3c07ac4773847adcf8f2cc9a1f51fa5fa3453097d731aadba94a2dac7de2b8e4","observation_id":"2709fbd5-51e1-4dba-8e68-194ad87df662","resolution":{"observed_at":"2026-05-11T21:01:12.448713Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2312.15689","last_updated":"2023-12-25T10:39:14Z","snapshot_observed_at":"2026-07-06T17:07:52.197869Z","submitted_at":"2023-12-25T10:39:14Z","title":"An extension problem for the logarithmic Laplacian","version":1},"cited_work":{"arxiv_id":"2312.15689","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2312.15689","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"d8d28ceb-e576-43c4-b0c4-274ca3171f0b","year":2023},"citing_paper":{"arxiv_id":"2605.12050","last_updated":"2026-05-12T12:30:09Z","snapshot_observed_at":"2026-08-02T08:07:35.570399Z","submitted_at":"2026-05-12T12:30:09Z","title":"On the fractional logarithmic $p$-Laplacian","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-05-13T04:44:34.203908Z"},"links":{"cited_paper":"/paper/2312.15689","citing_paper":"/paper/2605.12050"},"observation_digest":"sha256:80cf5055e8e447fa92dc9844d02a53a426174d0a1ed4f2c4015d7cf496710e48","observation_id":"509891ea-8bac-47d7-83a7-8138d4b783d3","resolution":{"observed_at":"2026-05-13T04:57:17.841700Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2312.15689","last_updated":"2023-12-25T10:39:14Z","snapshot_observed_at":"2026-07-06T17:07:52.197869Z","submitted_at":"2023-12-25T10:39:14Z","title":"An extension problem for the logarithmic Laplacian","version":1},"cited_work":{"arxiv_id":"2312.15689","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2312.15689","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"d8d28ceb-e576-43c4-b0c4-274ca3171f0b","year":2023},"citing_paper":{"arxiv_id":"2605.13513","last_updated":"2026-05-13T13:31:57Z","snapshot_observed_at":"2026-07-06T23:25:07.022065Z","submitted_at":"2026-05-13T13:31:57Z","title":"Spectral Properties of the Logarithmic Laplacian with Indefinite Weights","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-05-14T18:05:21.472364Z"},"links":{"cited_paper":"/paper/2312.15689","citing_paper":"/paper/2605.13513"},"observation_digest":"sha256:cf56b1d4bc6cc8ba3560c7a3c8fb98585b6f871f4a6b2dfd843c266c7183a19b","observation_id":"3c0c38c6-7fdc-4164-b681-8358a4954a93","resolution":{"observed_at":"2026-05-14T18:07:33.713208Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2312.15689/citation-record","integrity":"/paper/2312.15689/integrity","json":"/paper/2312.15689/citation-record.json","paper":"/paper/2312.15689"},"outbound":[],"paper":{"arxiv_id":"2312.15689","last_updated":"2023-12-25T10:39:14Z","latest_version":1,"primary_category":"math.AP","snapshot_observed_at":"2026-07-06T17:07:52.197869Z","submitted_at":"2023-12-25T10:39:14Z","title":"An extension problem for the logarithmic Laplacian"},"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":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"thesis":"As of 8 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 9 inbound Pith citation observations for arXiv:2312.15689."}