{"as_of":"2026-08-09T09:11:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:abfc5f3501ce4871386b93c848d0454e309592bc3184bc03dd5abf754eda4cf0","coverage":[{"denominator":23,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":23,"source":"paper_references, paper_reference_links","source_observed_at":"2026-06-28T07:11:55.856137Z","state":"measured"},{"denominator":23,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":23,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-09T06:31:02.800959+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2606.04225/citation-record","integrity":"/paper/2606.04225/integrity","json":"/paper/2606.04225/citation-record.json","paper":"/paper/2606.04225"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T07:11:55.856137Z","title":null,"venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2606.04225","last_updated":"2026-06-02T21:23:05Z","snapshot_observed_at":"2026-08-02T02:28:28.172129Z","submitted_at":"2026-06-02T21:23:05Z","title":"On the fundamental solutions of two nonlocal parabolic equations related to logarithmic Laplacians","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-06-28T07:11:55.856137Z"},"links":{"citing_paper":"/paper/2606.04225"},"observation_digest":"sha256:5a002e8ce804caea802f51ab4a30fd7242bb4783d9c924170245e74c685ad8df","observation_id":"ee462518-fcef-4693-baa2-d75e15a00706","resolution":{"observed_at":"2026-06-28T07:11:55.856137Z","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":"2026-06-28T07:11:55.856137Z","title":"Chen and L","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2606.04225","last_updated":"2026-06-02T21:23:05Z","snapshot_observed_at":"2026-08-02T02:28:28.172129Z","submitted_at":"2026-06-02T21:23:05Z","title":"On the fundamental solutions of two nonlocal parabolic equations related to logarithmic Laplacians","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-06-28T07:11:55.856137Z"},"links":{"citing_paper":"/paper/2606.04225"},"observation_digest":"sha256:b5878df4c3947876b25c5f780a5c5d34af449f9255217aee3d4c608295a75a3b","observation_id":"a5c57051-e6b5-4068-a773-539813d106d3","resolution":{"observed_at":"2026-06-28T07:11:55.856137Z","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":"2026-06-28T07:11:55.856137Z","title":"Chen and T","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2606.04225","last_updated":"2026-06-02T21:23:05Z","snapshot_observed_at":"2026-08-02T02:28:28.172129Z","submitted_at":"2026-06-02T21:23:05Z","title":"On the fundamental solutions of two nonlocal parabolic equations related to logarithmic Laplacians","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-06-28T07:11:55.856137Z"},"links":{"citing_paper":"/paper/2606.04225"},"observation_digest":"sha256:597df778bf79e1c67236506581699f9dea26ccac366a1d0b2e02bbc152289298","observation_id":"de30cffc-988a-4229-aafd-e4ec6be1bd2d","resolution":{"observed_at":"2026-06-28T07:11:55.856137Z","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":"2026-06-28T07:11:55.856137Z","title":"Comtet,Advanced Combinatorics: The Art of Finite and Infinite Expansions, Reidel Publishing Company, Dor- drecht/Boston, 1974","venue":null,"work_id":null,"year":1974},"citing_paper":{"arxiv_id":"2606.04225","last_updated":"2026-06-02T21:23:05Z","snapshot_observed_at":"2026-08-02T02:28:28.172129Z","submitted_at":"2026-06-02T21:23:05Z","title":"On the fundamental solutions of two nonlocal parabolic equations related to logarithmic Laplacians","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-06-28T07:11:55.856137Z"},"links":{"citing_paper":"/paper/2606.04225"},"observation_digest":"sha256:cbb1a6ca3f3706594c93a434eac1c12b7ffd5f0e9992243fee39b69bb159c2ca","observation_id":"8ca074ab-9fd2-4439-b80c-29ab49d31e73","resolution":{"observed_at":"2026-06-28T07:11:55.856137Z","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":"2026-06-28T07:11:55.856137Z","title":null,"venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2606.04225","last_updated":"2026-06-02T21:23:05Z","snapshot_observed_at":"2026-08-02T02:28:28.172129Z","submitted_at":"2026-06-02T21:23:05Z","title":"On the fundamental solutions of two nonlocal parabolic equations related to logarithmic Laplacians","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-06-28T07:11:55.856137Z"},"links":{"citing_paper":"/paper/2606.04225"},"observation_digest":"sha256:19c4040dce3ff451ffc98ac3d6066b2d0cb989d876af0ca6a0d8c3e77fd2b91e","observation_id":"7df9884f-7798-4f5e-81be-3d96079522de","resolution":{"observed_at":"2026-06-28T07:11:55.856137Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1312.1604","last_updated":"2013-12-05T16:23:54Z","snapshot_observed_at":"2026-07-06T03:30:05.359994Z","submitted_at":"2013-12-05T16:23:54Z","title":"Asymptotic expansions of exponentials of digamma function and identity for Bernoulli polynomials","version":1},"cited_work":{"arxiv_id":"1312.1604","doi":null,"metadata_source":"pith","pith_arxiv_id":"1312.1604","snapshot_observed_at":"2026-07-02T07:06:44.086604Z","title":"Asymptotic expansions of exponentials of digamma function and identity for Bernoulli polynomials","venue":"math.CA","work_id":"77581df9-37d5-46c3-8b97-bf04535aa864","year":2013},"citing_paper":{"arxiv_id":"2606.04225","last_updated":"2026-06-02T21:23:05Z","snapshot_observed_at":"2026-08-02T02:28:28.172129Z","submitted_at":"2026-06-02T21:23:05Z","title":"On the fundamental solutions of two nonlocal parabolic equations related to logarithmic Laplacians","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-06-28T07:11:55.856137Z"},"links":{"cited_paper":"/paper/1312.1604","citing_paper":"/paper/2606.04225"},"observation_digest":"sha256:9b8e40411575c6bb54bda01a83994aeafc0225af226f01308bfa40a80c4387b3","observation_id":"78122ea0-6b6c-45fa-ba37-889d0b106ed9","resolution":{"observed_at":"2026-07-02T07:06:44.087887Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_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},"cited_work":{"arxiv_id":"2507.21779","doi":"10.48550/arxiv.2507.21779","metadata_source":"arxiv_reference","pith_arxiv_id":"2507.21779","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"arXiv (Cornell University)","work_id":"222c7d03-2d68-4d29-a19b-fc5b7159ea66","year":2025},"citing_paper":{"arxiv_id":"2606.04225","last_updated":"2026-06-02T21:23:05Z","snapshot_observed_at":"2026-08-02T02:28:28.172129Z","submitted_at":"2026-06-02T21:23:05Z","title":"On the fundamental solutions of two nonlocal parabolic equations related to logarithmic Laplacians","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-06-28T07:11:55.856137Z"},"links":{"cited_paper":"/paper/2507.21779","citing_paper":"/paper/2606.04225"},"observation_digest":"sha256:0f9f1bd4237e51eb83468a013ce94b7c7c1683e815ca72bea7b4c8a7aabd5e9e","observation_id":"fa4cc0eb-1cab-45c3-98c0-63b640891dcc","resolution":{"observed_at":"2026-07-02T07:06:44.084968Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-06-28T07:11:55.856137Z","title":"Fucci, M","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2606.04225","last_updated":"2026-06-02T21:23:05Z","snapshot_observed_at":"2026-08-02T02:28:28.172129Z","submitted_at":"2026-06-02T21:23:05Z","title":"On the fundamental solutions of two nonlocal parabolic equations related to logarithmic Laplacians","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-06-28T07:11:55.856137Z"},"links":{"citing_paper":"/paper/2606.04225"},"observation_digest":"sha256:73b4d7b529c6b0e35b0eb90758604a53130875d9eb694e1b0e734d335f7ce6c8","observation_id":"ea66e02c-69b9-4bad-9139-f33c3b90056b","resolution":{"observed_at":"2026-06-28T07:11:55.856137Z","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":"10.1007/s00023-025-01587-7","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Fucci and J","venue":"Annales Henri Poincaré","work_id":"706b009b-623d-40b3-b3b7-9b07d5fd0d11","year":2025},"citing_paper":{"arxiv_id":"2606.04225","last_updated":"2026-06-02T21:23:05Z","snapshot_observed_at":"2026-08-02T02:28:28.172129Z","submitted_at":"2026-06-02T21:23:05Z","title":"On the fundamental solutions of two nonlocal parabolic equations related to logarithmic Laplacians","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-06-28T07:11:55.856137Z"},"links":{"citing_paper":"/paper/2606.04225"},"observation_digest":"sha256:62fbcb6389883647e7f9bbdd260dab98fb16d7d882568c415fe537cb9bde7d63","observation_id":"eaa00896-0722-40cf-b953-1e0417fa28cc","resolution":{"observed_at":"2026-06-28T07:21:45.160646Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-06-28T07:11:55.856137Z","title":"Garbaczewski and V","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2606.04225","last_updated":"2026-06-02T21:23:05Z","snapshot_observed_at":"2026-08-02T02:28:28.172129Z","submitted_at":"2026-06-02T21:23:05Z","title":"On the fundamental solutions of two nonlocal parabolic equations related to logarithmic Laplacians","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-06-28T07:11:55.856137Z"},"links":{"citing_paper":"/paper/2606.04225"},"observation_digest":"sha256:f6e4229437aee253829e0f285d9ee84cf23e267b20b3caa6322498253f5a2ea4","observation_id":"f7375005-9a5c-45fa-a1d3-b10b6ebdac68","resolution":{"observed_at":"2026-06-28T07:11:55.856137Z","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":"2026-06-28T07:11:55.856137Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2606.04225","last_updated":"2026-06-02T21:23:05Z","snapshot_observed_at":"2026-08-02T02:28:28.172129Z","submitted_at":"2026-06-02T21:23:05Z","title":"On the fundamental solutions of two nonlocal parabolic equations related to logarithmic Laplacians","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-06-28T07:11:55.856137Z"},"links":{"citing_paper":"/paper/2606.04225"},"observation_digest":"sha256:22a12a240981feff489378edccad0b40fe40e6662ff02366d95b691dcb9ad82d","observation_id":"452be209-cb43-486e-a3b6-90ad8b3090fa","resolution":{"observed_at":"2026-06-28T07:11:55.856137Z","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":"2026-06-28T07:11:55.856137Z","title":"Gessel,On Miki’s identity for Bernoulli numbers, J","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2606.04225","last_updated":"2026-06-02T21:23:05Z","snapshot_observed_at":"2026-08-02T02:28:28.172129Z","submitted_at":"2026-06-02T21:23:05Z","title":"On the fundamental solutions of two nonlocal parabolic equations related to logarithmic Laplacians","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-06-28T07:11:55.856137Z"},"links":{"citing_paper":"/paper/2606.04225"},"observation_digest":"sha256:2009c1b4b6cf51e02bac3dd837801a26c6acb6b0db11efcecb66ce395246daa2","observation_id":"cc0bc03c-22c5-48b5-897f-966b585ad91a","resolution":{"observed_at":"2026-06-28T07:11:55.856137Z","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":"2026-06-28T07:11:55.856137Z","title":"Laptev and T","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2606.04225","last_updated":"2026-06-02T21:23:05Z","snapshot_observed_at":"2026-08-02T02:28:28.172129Z","submitted_at":"2026-06-02T21:23:05Z","title":"On the fundamental solutions of two nonlocal parabolic equations related to logarithmic Laplacians","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-06-28T07:11:55.856137Z"},"links":{"citing_paper":"/paper/2606.04225"},"observation_digest":"sha256:11378349fdf8c900c231936538608cc511212364a1cc0d329c6dfb92c4b1ae30","observation_id":"16833575-349b-4de8-847f-6778ded92d7b","resolution":{"observed_at":"2026-06-28T07:11:55.856137Z","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":"2026-06-28T07:11:55.856137Z","title":"Luke,The Special Functions and Their Approximations, vol","venue":null,"work_id":null,"year":1969},"citing_paper":{"arxiv_id":"2606.04225","last_updated":"2026-06-02T21:23:05Z","snapshot_observed_at":"2026-08-02T02:28:28.172129Z","submitted_at":"2026-06-02T21:23:05Z","title":"On the fundamental solutions of two nonlocal parabolic equations related to logarithmic Laplacians","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-06-28T07:11:55.856137Z"},"links":{"citing_paper":"/paper/2606.04225"},"observation_digest":"sha256:71dc6c8e7d065e3843221a07e0b88d32858a600bd52cfbec6a24d8b390607ca1","observation_id":"14bcf039-2b25-456e-bf36-3e5268fda596","resolution":{"observed_at":"2026-06-28T07:11:55.856137Z","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":"2026-06-28T07:11:55.856137Z","title":"Maximon,A generating function for the product of two Legendre polynomials, Norske Vid","venue":null,"work_id":null,"year":1956},"citing_paper":{"arxiv_id":"2606.04225","last_updated":"2026-06-02T21:23:05Z","snapshot_observed_at":"2026-08-02T02:28:28.172129Z","submitted_at":"2026-06-02T21:23:05Z","title":"On the fundamental solutions of two nonlocal parabolic equations related to logarithmic Laplacians","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-06-28T07:11:55.856137Z"},"links":{"citing_paper":"/paper/2606.04225"},"observation_digest":"sha256:6f673976ae3ccc4c74dcea16fee958a1a5759629dcf97cd809abb1adf2d56201","observation_id":"ef4b6bc5-51fe-4493-bdd0-de6a20aa6aab","resolution":{"observed_at":"2026-06-28T07:11:55.856137Z","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":"2026-06-28T07:11:55.856137Z","title":"Maz’ya,Seventy Five (Thousand) Unsolved Problems in Analysis and Partial Differential Equations, Integr","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2606.04225","last_updated":"2026-06-02T21:23:05Z","snapshot_observed_at":"2026-08-02T02:28:28.172129Z","submitted_at":"2026-06-02T21:23:05Z","title":"On the fundamental solutions of two nonlocal parabolic equations related to logarithmic Laplacians","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-06-28T07:11:55.856137Z"},"links":{"citing_paper":"/paper/2606.04225"},"observation_digest":"sha256:336f0458c9a4f524131a949a4d96fda77635b2768f65c2578da1d437de677fd2","observation_id":"e1297847-1ea2-42a7-b71c-eb43cf566602","resolution":{"observed_at":"2026-06-28T07:11:55.856137Z","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":"2026-06-28T07:11:55.856137Z","title":"Maz’ya, S","venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2606.04225","last_updated":"2026-06-02T21:23:05Z","snapshot_observed_at":"2026-08-02T02:28:28.172129Z","submitted_at":"2026-06-02T21:23:05Z","title":"On the fundamental solutions of two nonlocal parabolic equations related to logarithmic Laplacians","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-06-28T07:11:55.856137Z"},"links":{"citing_paper":"/paper/2606.04225"},"observation_digest":"sha256:0dee0f4034702b26e40777d41f1da0520085e96e92a39a2a7e9bba23ad957e07","observation_id":"e90c1b65-8891-455f-9c57-294a3ac63067","resolution":{"observed_at":"2026-06-28T07:11:55.856137Z","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":"2026-06-28T07:11:55.856137Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2606.04225","last_updated":"2026-06-02T21:23:05Z","snapshot_observed_at":"2026-08-02T02:28:28.172129Z","submitted_at":"2026-06-02T21:23:05Z","title":"On the fundamental solutions of two nonlocal parabolic equations related to logarithmic Laplacians","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-06-28T07:11:55.856137Z"},"links":{"citing_paper":"/paper/2606.04225"},"observation_digest":"sha256:0b2ba83bf5ed29c28361dc3c3e99c16289e9169b8eca5512bc7f33b50abe264a","observation_id":"9057d316-9791-457e-b798-990889826446","resolution":{"observed_at":"2026-06-28T07:11:55.856137Z","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":"2026-06-28T07:11:55.856137Z","title":"O’Sullivan,De Moivre and Bell polynomials, Expo","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2606.04225","last_updated":"2026-06-02T21:23:05Z","snapshot_observed_at":"2026-08-02T02:28:28.172129Z","submitted_at":"2026-06-02T21:23:05Z","title":"On the fundamental solutions of two nonlocal parabolic equations related to logarithmic Laplacians","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-06-28T07:11:55.856137Z"},"links":{"citing_paper":"/paper/2606.04225"},"observation_digest":"sha256:e7bb192615276515c3eeea4f93ca78363a2a2470121f0f072e7486533316f8ff","observation_id":"532613d8-9485-40a1-88f6-629a6aca5e04","resolution":{"observed_at":"2026-06-28T07:11:55.856137Z","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":"2026-06-28T07:11:55.856137Z","title":"Szeg¨ o,Orthogonal Polynomials, American Mathematical Society, Providence, RI, 1939","venue":null,"work_id":null,"year":1939},"citing_paper":{"arxiv_id":"2606.04225","last_updated":"2026-06-02T21:23:05Z","snapshot_observed_at":"2026-08-02T02:28:28.172129Z","submitted_at":"2026-06-02T21:23:05Z","title":"On the fundamental solutions of two nonlocal parabolic equations related to logarithmic Laplacians","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-06-28T07:11:55.856137Z"},"links":{"citing_paper":"/paper/2606.04225"},"observation_digest":"sha256:6f1556c159f961b86aee23720dd9a0b67a733c112db4ba28759e56b9a40c8337","observation_id":"35b11c1f-fcde-4f76-810c-f09daf03d4cc","resolution":{"observed_at":"2026-06-28T07:11:55.856137Z","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":"2026-06-28T07:11:55.856137Z","title":"Tuck,Some methods for flows past blunt slender bodies, J","venue":null,"work_id":null,"year":1964},"citing_paper":{"arxiv_id":"2606.04225","last_updated":"2026-06-02T21:23:05Z","snapshot_observed_at":"2026-08-02T02:28:28.172129Z","submitted_at":"2026-06-02T21:23:05Z","title":"On the fundamental solutions of two nonlocal parabolic equations related to logarithmic Laplacians","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-06-28T07:11:55.856137Z"},"links":{"citing_paper":"/paper/2606.04225"},"observation_digest":"sha256:76a82327c2478e9d08c508ec4574101a3244a6cfec3cf7c6221b956f00d6466b","observation_id":"b9c3bf3e-78aa-481a-ac28-d35ba9de2c68","resolution":{"observed_at":"2026-06-28T07:11:55.856137Z","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":"2026-06-28T07:11:55.856137Z","title":"Yang,On an open problem of Chen and Mortici concerning the Euler–Mascheroni constant, J","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2606.04225","last_updated":"2026-06-02T21:23:05Z","snapshot_observed_at":"2026-08-02T02:28:28.172129Z","submitted_at":"2026-06-02T21:23:05Z","title":"On the fundamental solutions of two nonlocal parabolic equations related to logarithmic Laplacians","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-06-28T07:11:55.856137Z"},"links":{"citing_paper":"/paper/2606.04225"},"observation_digest":"sha256:c8cb2417167de8ff8a0bac5e1d97e231f8e0de8548fe2e0aa9aa9177eceb3e5f","observation_id":"b5e4e7d2-97aa-484e-ab96-7899f6cf967c","resolution":{"observed_at":"2026-06-28T07:11:55.856137Z","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":"2026-06-28T07:11:55.856137Z","title":"Zagier,Curious and exotic identities for Bernoulli numbersin T","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2606.04225","last_updated":"2026-06-02T21:23:05Z","snapshot_observed_at":"2026-08-02T02:28:28.172129Z","submitted_at":"2026-06-02T21:23:05Z","title":"On the fundamental solutions of two nonlocal parabolic equations related to logarithmic Laplacians","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-06-28T07:11:55.856137Z"},"links":{"citing_paper":"/paper/2606.04225"},"observation_digest":"sha256:703203f05418bf114643a5ab55b9faf34c06369a8d51c945f4c69cc64f83bc68","observation_id":"ce3ddfcd-c9de-4d5c-bb8b-bbbcc453f4dc","resolution":{"observed_at":"2026-06-28T07:11:55.856137Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2606.04225","last_updated":"2026-06-02T21:23:05Z","latest_version":1,"primary_category":"math.CV","snapshot_observed_at":"2026-08-02T02:28:28.172129Z","submitted_at":"2026-06-02T21:23:05Z","title":"On the fundamental solutions of two nonlocal parabolic equations related to logarithmic Laplacians"},"reference_resolution":{"displayed":23,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":20,"verified_exact":3,"verified_fuzzy":0},"total_outbound_references":23},"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":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"thesis":"As of 9 August 2026, this Paper Citation Record lists 23 of 23 outbound references and 0 inbound Pith citation observations for arXiv:2606.04225."}