{"as_of":"2026-08-22T11:54:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:14be7996278dfc3ff3f76c55ce2d140a36af1272348871506599ab43d3495696","coverage":[{"denominator":20,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":20,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-15T18:31:11.084857Z","state":"measured"},{"denominator":22,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":22,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-22T06:32:14.747728+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":"2026-07-13T12:43:29.044156Z","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":"2026-07-04T06:49:38.091484Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2506.20121","last_updated":"2025-06-25T04:21:31Z","snapshot_observed_at":"2026-08-21T17:33:28.885820Z","submitted_at":"2025-06-25T04:21:31Z","title":"Fundamental Solutions of the Logarithmic Laplacian: An Approach via the Division Problem","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2506.20121","snapshot_observed_at":"2026-07-13T12:43:29.044156Z","title":"Fundamental solutions of the logarithmic L aplacian: an approach via the division problem","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2604.03638","last_updated":"2026-04-04T08:28:53Z","snapshot_observed_at":"2026-08-21T11:29:30.873769Z","submitted_at":"2026-04-04T08:28:53Z","title":"Extension theorems for logarithmic Schr\\\"odinger and discrete Laplacian operators","version":1},"reference_index":35,"source":"arxiv_source","source_observed_at":"2026-07-13T12:43:29.044156Z"},"links":{"cited_paper":"/paper/2506.20121","citing_paper":"/paper/2604.03638"},"observation_digest":"sha256:93f67dfd6d8f3dec306cdcccc677170b10b32eb6879d95a41ae6e21d8be193e9","observation_id":"7e653917-24de-42c2-9dc7-1255c414e8a7","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":"2506.20121","last_updated":"2025-06-25T04:21:31Z","snapshot_observed_at":"2026-08-21T17:33:28.885820Z","submitted_at":"2025-06-25T04:21:31Z","title":"Fundamental Solutions of the Logarithmic Laplacian: An Approach via the Division Problem","version":1},"cited_work":{"arxiv_id":"2506.20121","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2506.20121","snapshot_observed_at":"2026-07-04T06:49:38.091484Z","title":"Fundamental solutions of the logarithmic L aplacian: an approach via the division problem","venue":null,"work_id":"4b388653-a69f-479d-b2f0-00865c10626a","year":2025},"citing_paper":{"arxiv_id":"2606.21056","last_updated":"2026-06-19T02:48:01Z","snapshot_observed_at":"2026-08-11T12:42:14.102310Z","submitted_at":"2026-06-19T02:48:01Z","title":"On $m$-order logarithmic Schr\\\"odinger operator","version":1},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-06-26T14:08:09.929477Z"},"links":{"cited_paper":"/paper/2506.20121","citing_paper":"/paper/2606.21056"},"observation_digest":"sha256:e477ca4822d260bd776981d60fa2abdfc0c4120ff2c59fe024cadfc3aa9772a1","observation_id":"f9161a98-6b75-436c-bf6a-a6710a9a2a13","resolution":{"observed_at":"2026-07-04T06:49:38.093417Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2506.20121/citation-record","integrity":"/paper/2506.20121/integrity","json":"/paper/2506.20121/citation-record.json","paper":"/paper/2506.20121"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:31:10.994286Z","title":"A guide to distribution theory and Fourier transforms","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2506.20121","last_updated":"2025-06-25T04:21:31Z","snapshot_observed_at":"2026-08-21T17:33:28.885820Z","submitted_at":"2025-06-25T04:21:31Z","title":"Fundamental Solutions of the Logarithmic Laplacian: An Approach via the Division Problem","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-15T18:31:10.994286Z"},"links":{"citing_paper":"/paper/2506.20121"},"observation_digest":"sha256:0bdcc05f1ba49ef69a127597637281ba01022ba522fe64158e17d6e65d0e7350","observation_id":"a4693f7d-7847-4ba8-a5b4-f045140431f0","resolution":{"observed_at":"2026-08-15T18:31:10.994286Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:31:11.429715Z","title":"Representation theorems for solutions of the H elmholtz equation on R ^n","venue":null,"work_id":"1dcb11d8-7065-43b4-afaa-2a77e1e99c2d","year":1999},"citing_paper":{"arxiv_id":"2506.20121","last_updated":"2025-06-25T04:21:31Z","snapshot_observed_at":"2026-08-21T17:33:28.885820Z","submitted_at":"2025-06-25T04:21:31Z","title":"Fundamental Solutions of the Logarithmic Laplacian: An Approach via the Division Problem","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-15T18:31:11.000456Z"},"links":{"citing_paper":"/paper/2506.20121"},"observation_digest":"sha256:622c330c4187731ea000a11bb83d7b835dd25f423b2f1482038c1824706d3563","observation_id":"89575bae-0c1e-44bc-8dc9-5667c55c92c8","resolution":{"observed_at":"2026-08-15T18:31:11.440674Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:31:11.005125Z","title":"Helmholtz equations for the L aplace operator and its powers","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2506.20121","last_updated":"2025-06-25T04:21:31Z","snapshot_observed_at":"2026-08-21T17:33:28.885820Z","submitted_at":"2025-06-25T04:21:31Z","title":"Fundamental Solutions of the Logarithmic Laplacian: An Approach via the Division Problem","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-15T18:31:11.005125Z"},"links":{"citing_paper":"/paper/2506.20121"},"observation_digest":"sha256:5594ad959090e1e81323dbebee846f1cca7e887fa3725ae9032f3b205880db7a","observation_id":"540c9545-5f39-4cfd-9e2f-a6c232f57ac8","resolution":{"observed_at":"2026-08-15T18:31:11.005125Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:31:11.009851Z","title":"Localization for general H elmholtz","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2506.20121","last_updated":"2025-06-25T04:21:31Z","snapshot_observed_at":"2026-08-21T17:33:28.885820Z","submitted_at":"2025-06-25T04:21:31Z","title":"Fundamental Solutions of the Logarithmic Laplacian: An Approach via the Division Problem","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-15T18:31:11.009851Z"},"links":{"citing_paper":"/paper/2506.20121"},"observation_digest":"sha256:2ce1792171976ca5ea90532196b466c361a318daf52271587a9208e985c3ccc5","observation_id":"344deee1-1bf0-4ec6-be96-3831cebc6540","resolution":{"observed_at":"2026-08-15T18:31:11.009851Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:31:11.380547Z","title":"The C auchy problem associated to the logarithmic L aplacian with an application to the fundamental solution","venue":null,"work_id":"417575ee-141b-49f8-9c9a-b4251e3b6495","year":2024},"citing_paper":{"arxiv_id":"2506.20121","last_updated":"2025-06-25T04:21:31Z","snapshot_observed_at":"2026-08-21T17:33:28.885820Z","submitted_at":"2025-06-25T04:21:31Z","title":"Fundamental Solutions of the Logarithmic Laplacian: An Approach via the Division Problem","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-15T18:31:11.014798Z"},"links":{"citing_paper":"/paper/2506.20121"},"observation_digest":"sha256:ae2cd8fa01b1c0efd56464631df5cee08a45e8bf7714c6549c64047de8bd5d34","observation_id":"e007a2c9-8367-4ff9-b776-3cb5e2262542","resolution":{"observed_at":"2026-08-15T18:31:11.389293Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:31:11.019411Z","title":"The D irichlet problem for the logarithmic L aplacian","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2506.20121","last_updated":"2025-06-25T04:21:31Z","snapshot_observed_at":"2026-08-21T17:33:28.885820Z","submitted_at":"2025-06-25T04:21:31Z","title":"Fundamental Solutions of the Logarithmic Laplacian: An Approach via the Division Problem","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-15T18:31:11.019411Z"},"links":{"citing_paper":"/paper/2506.20121"},"observation_digest":"sha256:a151c1f9b09d47f1d4f84aae96c272514edf63719870ee1344315516c5dd2494","observation_id":"86295504-9378-4e3d-ae6b-ca694c798819","resolution":{"observed_at":"2026-08-15T18:31:11.019411Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:31:11.349566Z","title":"Solution of some problems of division","venue":null,"work_id":"8ba65a22-9057-48c7-86cd-7d170df0d6f0","year":1954},"citing_paper":{"arxiv_id":"2506.20121","last_updated":"2025-06-25T04:21:31Z","snapshot_observed_at":"2026-08-21T17:33:28.885820Z","submitted_at":"2025-06-25T04:21:31Z","title":"Fundamental Solutions of the Logarithmic Laplacian: An Approach via the Division Problem","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-15T18:31:11.024526Z"},"links":{"citing_paper":"/paper/2506.20121"},"observation_digest":"sha256:885adfee72867029d7c895185e9bbc6cfa1d443426afad14fd2f7602bcf3201b","observation_id":"513a23c0-254e-4477-838a-2223760b7cfb","resolution":{"observed_at":"2026-08-15T18:31:11.356664Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:31:11.328987Z","title":"Solution of some problems of division","venue":null,"work_id":"e73d8246-4ece-4373-947e-acb72369ec5b","year":1955},"citing_paper":{"arxiv_id":"2506.20121","last_updated":"2025-06-25T04:21:31Z","snapshot_observed_at":"2026-08-21T17:33:28.885820Z","submitted_at":"2025-06-25T04:21:31Z","title":"Fundamental Solutions of the Logarithmic Laplacian: An Approach via the Division Problem","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-15T18:31:11.029015Z"},"links":{"citing_paper":"/paper/2506.20121"},"observation_digest":"sha256:aa406b19e7003d23e422af36a3247294f6a569122f953886545dbf08a43ba808","observation_id":"c9971586-8724-4bdf-887e-3f8d74346dde","resolution":{"observed_at":"2026-08-15T18:31:11.335372Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:31:11.033995Z","title":"Entire s -harmonic functions are affine","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2506.20121","last_updated":"2025-06-25T04:21:31Z","snapshot_observed_at":"2026-08-21T17:33:28.885820Z","submitted_at":"2025-06-25T04:21:31Z","title":"Fundamental Solutions of the Logarithmic Laplacian: An Approach via the Division Problem","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-15T18:31:11.033995Z"},"links":{"citing_paper":"/paper/2506.20121"},"observation_digest":"sha256:882b1844c1de7b166dbd46b856f72e4c028a09b7b8b968fc35164b47723f6c78","observation_id":"01c0fe76-24e3-4385-bec8-0f96f61aa9cb","resolution":{"observed_at":"2026-08-15T18:31:11.033995Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:31:11.038588Z","title":"Liouville theorems for a general class of nonlocal operators","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2506.20121","last_updated":"2025-06-25T04:21:31Z","snapshot_observed_at":"2026-08-21T17:33:28.885820Z","submitted_at":"2025-06-25T04:21:31Z","title":"Fundamental Solutions of the Logarithmic Laplacian: An Approach via the Division Problem","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-15T18:31:11.038588Z"},"links":{"citing_paper":"/paper/2506.20121"},"observation_digest":"sha256:a8b33b6ca6f8f9c357be1f6ca464a59729f9156b6b06151ec1476268e4224ced","observation_id":"81ff8d16-0135-441e-8753-42026cca6d7c","resolution":{"observed_at":"2026-08-15T18:31:11.038588Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:31:11.043245Z","title":"Helmholtz solutions for the fractional L aplacian and other related operators","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2506.20121","last_updated":"2025-06-25T04:21:31Z","snapshot_observed_at":"2026-08-21T17:33:28.885820Z","submitted_at":"2025-06-25T04:21:31Z","title":"Fundamental Solutions of the Logarithmic Laplacian: An Approach via the Division Problem","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-15T18:31:11.043245Z"},"links":{"citing_paper":"/paper/2506.20121"},"observation_digest":"sha256:d2f2c88b26483e0cb5045778fd95d5456a93974e9e8f9dd565c6c21ab64c8a89","observation_id":"939b5a49-c519-4e5b-a88d-24022efd3dbf","resolution":{"observed_at":"2026-08-15T18:31:11.043245Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:31:11.048145Z","title":"Classical F ourier analysis , volume 249 of Graduate Texts in Mathematics","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2506.20121","last_updated":"2025-06-25T04:21:31Z","snapshot_observed_at":"2026-08-21T17:33:28.885820Z","submitted_at":"2025-06-25T04:21:31Z","title":"Fundamental Solutions of the Logarithmic Laplacian: An Approach via the Division Problem","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-15T18:31:11.048145Z"},"links":{"citing_paper":"/paper/2506.20121"},"observation_digest":"sha256:b68b7086be6d3a2602ed21437219aeef95cbb579777cdb3e060043048836025e","observation_id":"e9b1de90-5fe6-4c77-8223-2a86e70d82ab","resolution":{"observed_at":"2026-08-15T18:31:11.048145Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2306.17562","last_updated":"2023-06-30T11:31:48Z","snapshot_observed_at":"2026-08-16T15:19:46.612216Z","submitted_at":"2023-06-30T11:31:48Z","title":"Characterization of solutions of a generalized Helmholtz problem","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2306.17562","snapshot_observed_at":"2026-08-15T18:31:11.053081Z","title":"Characterization of solutions of a generalized helmholtz problem","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2506.20121","last_updated":"2025-06-25T04:21:31Z","snapshot_observed_at":"2026-08-21T17:33:28.885820Z","submitted_at":"2025-06-25T04:21:31Z","title":"Fundamental Solutions of the Logarithmic Laplacian: An Approach via the Division Problem","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-15T18:31:11.053081Z"},"links":{"cited_paper":"/paper/2306.17562","citing_paper":"/paper/2506.20121"},"observation_digest":"sha256:81ba37e1187d4609353d9a07b94944616be58926f5429c8a80ae632f770e306a","observation_id":"e6f8a24e-d19f-4c0d-92d9-189f9960c358","resolution":{"observed_at":"2026-08-15T18:31:11.053081Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:31:11.259120Z","title":"Existence et approximation des solutions des \\' e quations aux d\\' e riv\\' e es partielles et des \\' e quations de convolution","venue":null,"work_id":"2526350b-132d-48f1-b3ac-1994a29511dc","year":1955},"citing_paper":{"arxiv_id":"2506.20121","last_updated":"2025-06-25T04:21:31Z","snapshot_observed_at":"2026-08-21T17:33:28.885820Z","submitted_at":"2025-06-25T04:21:31Z","title":"Fundamental Solutions of the Logarithmic Laplacian: An Approach via the Division Problem","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-15T18:31:11.057780Z"},"links":{"citing_paper":"/paper/2506.20121"},"observation_digest":"sha256:b7026c4887842c4f056f6e9668eda5e9cc83b710a11b7881eaa98d8e25f66429","observation_id":"baecb9be-b23d-4aa9-9410-341aa3c9e2ae","resolution":{"observed_at":"2026-08-15T18:31:11.264853Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:31:11.240901Z","title":"Distributions, partial differential equations, and harmonic analysis","venue":null,"work_id":"f3785a9c-a1fb-4600-b74e-41ca2fe65bcb","year":2018},"citing_paper":{"arxiv_id":"2506.20121","last_updated":"2025-06-25T04:21:31Z","snapshot_observed_at":"2026-08-21T17:33:28.885820Z","submitted_at":"2025-06-25T04:21:31Z","title":"Fundamental Solutions of the Logarithmic Laplacian: An Approach via the Division Problem","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-15T18:31:11.062038Z"},"links":{"citing_paper":"/paper/2506.20121"},"observation_digest":"sha256:e041c09300d159ced07d4f5bfd87117e9b786c7526b3a71f5b36499f911675f4","observation_id":"baf2ba7e-2907-45f7-88dd-b03284133ce1","resolution":{"observed_at":"2026-08-15T18:31:11.246935Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:31:11.221736Z","title":"Fundamental solutions of linear partial differential operators","venue":null,"work_id":"2be1595f-50ca-4f25-8365-a8fe508feb48","year":2015},"citing_paper":{"arxiv_id":"2506.20121","last_updated":"2025-06-25T04:21:31Z","snapshot_observed_at":"2026-08-21T17:33:28.885820Z","submitted_at":"2025-06-25T04:21:31Z","title":"Fundamental Solutions of the Logarithmic Laplacian: An Approach via the Division Problem","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-15T18:31:11.066388Z"},"links":{"citing_paper":"/paper/2506.20121"},"observation_digest":"sha256:dfe1fd4c00ee660ddf45f777be926cea1ab5fd8f80065ba0bba0acaf4cf63319","observation_id":"4630680c-1d60-4333-9026-14ab2818526f","resolution":{"observed_at":"2026-08-15T18:31:11.226953Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:31:11.201752Z","title":"Regularised integrals, sums and traces , volume 59 of University Lecture Series","venue":null,"work_id":"62069095-d55e-40db-96a4-09cf77403398","year":2012},"citing_paper":{"arxiv_id":"2506.20121","last_updated":"2025-06-25T04:21:31Z","snapshot_observed_at":"2026-08-21T17:33:28.885820Z","submitted_at":"2025-06-25T04:21:31Z","title":"Fundamental Solutions of the Logarithmic Laplacian: An Approach via the Division Problem","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-15T18:31:11.071040Z"},"links":{"citing_paper":"/paper/2506.20121"},"observation_digest":"sha256:8aebc519887940bb7a91bfcc9c2b90bea6e24ccd5a1bf6a2bd4a291a37e166ec","observation_id":"2b0eed99-f5b1-4b7a-95c3-70a4a0bb83ad","resolution":{"observed_at":"2026-08-15T18:31:11.208824Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:31:11.075185Z","title":null,"venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2506.20121","last_updated":"2025-06-25T04:21:31Z","snapshot_observed_at":"2026-08-21T17:33:28.885820Z","submitted_at":"2025-06-25T04:21:31Z","title":"Fundamental Solutions of the Logarithmic Laplacian: An Approach via the Division Problem","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-15T18:31:11.075185Z"},"links":{"citing_paper":"/paper/2506.20121"},"observation_digest":"sha256:3326f73bce7565afef7490d70c0b385f6e24f1b25d08a2aa3512a6f230fa91e7","observation_id":"7ed4b8b9-7966-47ca-b80b-71c92cc63082","resolution":{"observed_at":"2026-08-15T18:31:11.075185Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:31:11.080560Z","title":"Th\\' e orie des distributions","venue":null,"work_id":null,"year":1966},"citing_paper":{"arxiv_id":"2506.20121","last_updated":"2025-06-25T04:21:31Z","snapshot_observed_at":"2026-08-21T17:33:28.885820Z","submitted_at":"2025-06-25T04:21:31Z","title":"Fundamental Solutions of the Logarithmic Laplacian: An Approach via the Division Problem","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-15T18:31:11.080560Z"},"links":{"citing_paper":"/paper/2506.20121"},"observation_digest":"sha256:a44bdf55e61e0a4f53ceef6d4ace31d5f1cdd53f4a324e97218471cbc72741e6","observation_id":"6506d546-ffe0-4111-a834-c9437cec9f2e","resolution":{"observed_at":"2026-08-15T18:31:11.080560Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:31:11.151613Z","title":"Convergence rates of the fractional to the local dirichlet problem, 2024","venue":null,"work_id":"39c463af-e2f7-4704-b357-d50fd68151e8","year":2024},"citing_paper":{"arxiv_id":"2506.20121","last_updated":"2025-06-25T04:21:31Z","snapshot_observed_at":"2026-08-21T17:33:28.885820Z","submitted_at":"2025-06-25T04:21:31Z","title":"Fundamental Solutions of the Logarithmic Laplacian: An Approach via the Division Problem","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-15T18:31:11.084857Z"},"links":{"citing_paper":"/paper/2506.20121"},"observation_digest":"sha256:e7a37a18a0234eba966f1e8d1b16d1ca205c933a6d3fe8d766e70b958732a4a3","observation_id":"33b7c0cc-ac97-4f18-9c0e-5bd6da5f04d7","resolution":{"observed_at":"2026-08-15T18:31:11.158826Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2506.20121","last_updated":"2025-06-25T04:21:31Z","latest_version":1,"primary_category":"math.AP","snapshot_observed_at":"2026-08-21T17:33:28.885820Z","submitted_at":"2025-06-25T04:21:31Z","title":"Fundamental Solutions of the Logarithmic Laplacian: An Approach via the Division Problem"},"reference_resolution":{"displayed":20,"state_counts":{"malformed_identifier":1,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":10,"verified_exact":0,"verified_fuzzy":9},"total_outbound_references":20},"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":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"thesis":"As of 22 August 2026, this Paper Citation Record lists 20 of 20 outbound references and 2 inbound Pith citation observations for arXiv:2506.20121."}