{"as_of":"2026-08-07T19:52:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:cec04cc9ec6e1029beab25b0f6d744c38bf48eac6cfdad84b737774d6dcf79e8","coverage":[{"denominator":12,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":12,"source":"paper_references, paper_reference_links","source_observed_at":"2026-05-22T18:29:19.209379Z","state":"measured"},{"denominator":12,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":12,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-07T06:34:17.273281+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/2504.16168/citation-record","integrity":"/paper/2504.16168/integrity","json":"/paper/2504.16168/citation-record.json","paper":"/paper/2504.16168"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"4f296e7b-03ff-4b0d-93e8-9c4866eacb79","year":2001},"citing_paper":{"arxiv_id":"2504.16168","last_updated":"2025-09-20T18:25:35Z","snapshot_observed_at":"2026-08-06T13:56:49.676721Z","submitted_at":"2025-04-22T18:00:45Z","title":"The existence and local uniqueness of the eigenfunctions of the non-linear operator $ \\Delta_H u^{n}$ in the hyperbolic Poincar\\'e half-plane","version":3},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-05-22T18:29:19.209379Z"},"links":{"citing_paper":"/paper/2504.16168"},"observation_digest":"sha256:f6125c8c27d32e29f3b62cd525b7b6a00bda6a54eb394aaf2ca3ceae30fcfc7e","observation_id":"cdd00773-38e6-4957-a160-0687128647ed","resolution":{"observed_at":"2026-05-22T18:31:56.026140Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2309.13400","last_updated":"2023-09-23T15:22:17Z","snapshot_observed_at":"2026-07-06T16:22:46.711142Z","submitted_at":"2023-09-23T15:22:17Z","title":"A note on nonlinear diffusive equations on Poincar\\'e half plane","version":1},"cited_work":{"arxiv_id":"2309.13400","doi":"10.48550/arxiv.2309.13400","metadata_source":"arxiv_reference","pith_arxiv_id":"2309.13400","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"arXiv preprint","venue":"arXiv (Cornell University)","work_id":"23485110-29e4-4556-8031-8a167417e065","year":2023},"citing_paper":{"arxiv_id":"2504.16168","last_updated":"2025-09-20T18:25:35Z","snapshot_observed_at":"2026-08-06T13:56:49.676721Z","submitted_at":"2025-04-22T18:00:45Z","title":"The existence and local uniqueness of the eigenfunctions of the non-linear operator $ \\Delta_H u^{n}$ in the hyperbolic Poincar\\'e half-plane","version":3},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-05-22T18:29:19.209379Z"},"links":{"cited_paper":"/paper/2309.13400","citing_paper":"/paper/2504.16168"},"observation_digest":"sha256:25690b321f801ba8d2a935ff188a0509ea370cc7ecc6b0073aa1d41c91d16aa5","observation_id":"b5dd8768-34fd-4942-aee1-ae48ba629110","resolution":{"observed_at":"2026-05-22T18:31:55.778156Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-06-05T21:23:00.469572Z","title":"Construction of exact solutions for fractional order differential equations by the invariant subspace methodComputers and Mathematics with Applications 66(2013) 576–584","venue":null,"work_id":"b0ec7f04-ade9-49b6-adf1-0fff5f4b47b9","year":2013},"citing_paper":{"arxiv_id":"2504.16168","last_updated":"2025-09-20T18:25:35Z","snapshot_observed_at":"2026-08-06T13:56:49.676721Z","submitted_at":"2025-04-22T18:00:45Z","title":"The existence and local uniqueness of the eigenfunctions of the non-linear operator $ \\Delta_H u^{n}$ in the hyperbolic Poincar\\'e half-plane","version":3},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-05-22T18:29:19.209379Z"},"links":{"citing_paper":"/paper/2504.16168"},"observation_digest":"sha256:dc6007228caf6813628a5c1ec3ced614d63df4dd15fcc9530cb34c940390a6d8","observation_id":"e3d9a321-18d4-4f1b-93e1-e9d091a5a420","resolution":{"observed_at":"2026-05-22T18:31:56.030320Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1080/17442500701433509","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Stochastics: An International Journal of Probability and Stochastics Processes, 79:6, 505-522, DOI:10.1080/17442500701433509","venue":"Stochastics","work_id":"0e179276-5ff7-4278-ad00-fef2185050e7","year":2007},"citing_paper":{"arxiv_id":"2504.16168","last_updated":"2025-09-20T18:25:35Z","snapshot_observed_at":"2026-08-06T13:56:49.676721Z","submitted_at":"2025-04-22T18:00:45Z","title":"The existence and local uniqueness of the eigenfunctions of the non-linear operator $ \\Delta_H u^{n}$ in the hyperbolic Poincar\\'e half-plane","version":3},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-05-22T18:29:19.209379Z"},"links":{"citing_paper":"/paper/2504.16168"},"observation_digest":"sha256:70294de0d8ad2e7b9e1efca625f217a121a8432d66474c0bd6e50eb5c8ed079f","observation_id":"c6f1081b-7bb7-4f4c-9447-e67fe8a270f5","resolution":{"observed_at":"2026-05-22T18:31:55.780234Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-06-05T21:23:00.469572Z","title":"Teorema di Cauchy-Kovalevskaja per le equazioni differenzialiRivoluzioni Matematiche I grandi teoremi da Pitagora a Nash, Le Scienze19(2024) 84-85","venue":null,"work_id":"5c5e336b-2b80-4f6c-acd5-e1cbbca6fa75","year":2024},"citing_paper":{"arxiv_id":"2504.16168","last_updated":"2025-09-20T18:25:35Z","snapshot_observed_at":"2026-08-06T13:56:49.676721Z","submitted_at":"2025-04-22T18:00:45Z","title":"The existence and local uniqueness of the eigenfunctions of the non-linear operator $ \\Delta_H u^{n}$ in the hyperbolic Poincar\\'e half-plane","version":3},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-05-22T18:29:19.209379Z"},"links":{"citing_paper":"/paper/2504.16168"},"observation_digest":"sha256:b113edd85342975742f54f833e7330b5ee0bdb8c5adbfeb277b685d988404f6a","observation_id":"dd8cc3ae-9891-40a5-9f8e-0798cecb53ba","resolution":{"observed_at":"2026-05-22T18:31:56.028119Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2411.04971","last_updated":"2024-11-07T18:47:34Z","snapshot_observed_at":"2026-08-05T06:40:04.336306Z","submitted_at":"2024-11-07T18:47:34Z","title":"A non-homogeneous generalization of Burgers equations","version":1},"cited_work":{"arxiv_id":"2411.04971","doi":"10.48550/arxiv.2411.04971","metadata_source":"arxiv_reference","pith_arxiv_id":"2411.04971","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"arXiv preprint","venue":"arXiv (Cornell University)","work_id":"74947ed9-9180-4ed3-ad8f-c83e87e2ec5a","year":2024},"citing_paper":{"arxiv_id":"2504.16168","last_updated":"2025-09-20T18:25:35Z","snapshot_observed_at":"2026-08-06T13:56:49.676721Z","submitted_at":"2025-04-22T18:00:45Z","title":"The existence and local uniqueness of the eigenfunctions of the non-linear operator $ \\Delta_H u^{n}$ in the hyperbolic Poincar\\'e half-plane","version":3},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-05-22T18:29:19.209379Z"},"links":{"cited_paper":"/paper/2411.04971","citing_paper":"/paper/2504.16168"},"observation_digest":"sha256:0edf6f85ff51cf0f44710b469054133486bdb823b72dea029c5250678ee65a14","observation_id":"6829b32f-4b15-4bda-bcaf-b00e3db1afa2","resolution":{"observed_at":"2026-05-22T18:31:55.775190Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"39a6cdb4-bfc0-468b-8a4c-a68f9bfba844","year":2005},"citing_paper":{"arxiv_id":"2504.16168","last_updated":"2025-09-20T18:25:35Z","snapshot_observed_at":"2026-08-06T13:56:49.676721Z","submitted_at":"2025-04-22T18:00:45Z","title":"The existence and local uniqueness of the eigenfunctions of the non-linear operator $ \\Delta_H u^{n}$ in the hyperbolic Poincar\\'e half-plane","version":3},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-05-22T18:29:19.209379Z"},"links":{"citing_paper":"/paper/2504.16168"},"observation_digest":"sha256:16066610bd5aee54dba1f071625a7d1e17cfcee151d733651a989ab6a5e87102","observation_id":"95bc1b0c-9ea3-4df4-8810-de52976ce9eb","resolution":{"observed_at":"2026-05-22T18:31:56.039480Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-06-05T21:23:00.469572Z","title":"Note per il corso Equazioni Differenziali I parte,Universit` a degli studi di Roma ”La Sapienza”(versione 1.1 March 9, 2006), http://www.mat.uniroma1.it/people/mascia/edo0506.html","venue":null,"work_id":"786e4e07-a129-4d09-ba03-577b113d91da","year":2006},"citing_paper":{"arxiv_id":"2504.16168","last_updated":"2025-09-20T18:25:35Z","snapshot_observed_at":"2026-08-06T13:56:49.676721Z","submitted_at":"2025-04-22T18:00:45Z","title":"The existence and local uniqueness of the eigenfunctions of the non-linear operator $ \\Delta_H u^{n}$ in the hyperbolic Poincar\\'e half-plane","version":3},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-05-22T18:29:19.209379Z"},"links":{"citing_paper":"/paper/2504.16168"},"observation_digest":"sha256:e59f20a096b14cc488f5e76f4e36da10521f1b4042613d15d9999a56c76efb65","observation_id":"67692e1e-a2e2-4624-b71e-a01b6939aa87","resolution":{"observed_at":"2026-05-22T18:31:56.037613Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-06-05T21:23:00.469572Z","title":"Teorema di Dini sulle funzioni impliciteRivoluzioni Matematiche I grandi teoremi da Pitagora a Nash, Le Scienze 28(2025) 84-85","venue":null,"work_id":"6a60efb1-5adf-4cf4-aaf0-31b05d9b8d78","year":2025},"citing_paper":{"arxiv_id":"2504.16168","last_updated":"2025-09-20T18:25:35Z","snapshot_observed_at":"2026-08-06T13:56:49.676721Z","submitted_at":"2025-04-22T18:00:45Z","title":"The existence and local uniqueness of the eigenfunctions of the non-linear operator $ \\Delta_H u^{n}$ in the hyperbolic Poincar\\'e half-plane","version":3},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-05-22T18:29:19.209379Z"},"links":{"citing_paper":"/paper/2504.16168"},"observation_digest":"sha256:434ec60f7083a643142f6ccc0675b273e7535f0e1e1926a61954487aa14ec79a","observation_id":"5a8ff36c-4ad3-4cbd-bfda-432746185055","resolution":{"observed_at":"2026-05-22T18:31:56.035559Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"c2a433c1-4f08-4bad-82db-0fde41f407ad","year":2020},"citing_paper":{"arxiv_id":"2504.16168","last_updated":"2025-09-20T18:25:35Z","snapshot_observed_at":"2026-08-06T13:56:49.676721Z","submitted_at":"2025-04-22T18:00:45Z","title":"The existence and local uniqueness of the eigenfunctions of the non-linear operator $ \\Delta_H u^{n}$ in the hyperbolic Poincar\\'e half-plane","version":3},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-05-22T18:29:19.209379Z"},"links":{"citing_paper":"/paper/2504.16168"},"observation_digest":"sha256:a2ca545a8b91c3a484a1ba1b3dcc0aee0165c5f82b23dbeb6cd1e42a09e8b29d","observation_id":"4c2df40c-3a5e-4d1b-8d46-84471e482ccd","resolution":{"observed_at":"2026-05-22T18:31:56.033698Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"b18b70e7-2cac-4200-b5d0-9080a173bfd6","year":2015},"citing_paper":{"arxiv_id":"2504.16168","last_updated":"2025-09-20T18:25:35Z","snapshot_observed_at":"2026-08-06T13:56:49.676721Z","submitted_at":"2025-04-22T18:00:45Z","title":"The existence and local uniqueness of the eigenfunctions of the non-linear operator $ \\Delta_H u^{n}$ in the hyperbolic Poincar\\'e half-plane","version":3},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-05-22T18:29:19.209379Z"},"links":{"citing_paper":"/paper/2504.16168"},"observation_digest":"sha256:ab63bab6409b7330cab5123aea1255404881cee08eb6665feadaab70265148d7","observation_id":"1e351a71-137e-4c9b-9aab-e792e797b96d","resolution":{"observed_at":"2026-05-22T18:31:56.032018Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1080/10236199508808006","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"”The J.C.P","venue":"The Journal of Difference Equations and Applications","work_id":"04de93ce-096b-44e7-a41c-50a3645e73de","year":1995},"citing_paper":{"arxiv_id":"2504.16168","last_updated":"2025-09-20T18:25:35Z","snapshot_observed_at":"2026-08-06T13:56:49.676721Z","submitted_at":"2025-04-22T18:00:45Z","title":"The existence and local uniqueness of the eigenfunctions of the non-linear operator $ \\Delta_H u^{n}$ in the hyperbolic Poincar\\'e half-plane","version":3},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-05-22T18:29:19.209379Z"},"links":{"citing_paper":"/paper/2504.16168"},"observation_digest":"sha256:0c4644c7205a2e30949f2f8241b7e00a7f7d535c20117998380ad9bd3e6599e6","observation_id":"31cec1f4-2bc4-41d3-a88b-f2ee7889f436","resolution":{"observed_at":"2026-05-22T18:31:55.782039Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2504.16168","last_updated":"2025-09-20T18:25:35Z","latest_version":3,"primary_category":"math.AP","snapshot_observed_at":"2026-08-06T13:56:49.676721Z","submitted_at":"2025-04-22T18:00:45Z","title":"The existence and local uniqueness of the eigenfunctions of the non-linear operator $ \\Delta_H u^{n}$ in the hyperbolic Poincar\\'e half-plane"},"reference_resolution":{"displayed":12,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":4,"verified_exact":4,"verified_fuzzy":4},"total_outbound_references":12},"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":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"thesis":"As of 7 August 2026, this Paper Citation Record lists 12 of 12 outbound references and 0 inbound Pith citation observations for arXiv:2504.16168."}