{"as_of":"2026-08-20T04:23:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:bd1476c595f7b9d0ffe62521276c3aa0f0831ee3115790714905107dac5b698b","coverage":[{"denominator":21,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":21,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-09T22:53:18.070016Z","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":"2026-08-19T06:32:44.657259+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-15T22:38:28.857689Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"pith","source_observed_at":"2026-08-15T22:38:29.469755Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2501.18745","last_updated":"2025-01-30T20:49:59Z","snapshot_observed_at":"2026-08-20T02:01:50.081037Z","submitted_at":"2025-01-30T20:49:59Z","title":"A deterministic particle method for the porous media equation","version":1},"cited_work":{"arxiv_id":"2501.18745","doi":null,"metadata_source":"pith","pith_arxiv_id":"2501.18745","snapshot_observed_at":"2026-08-15T22:38:29.469755Z","title":"A deterministic particle method for the porous media equation","venue":"math.AP","work_id":"9b54fc7c-5106-401d-a4a0-caefec3aca2a","year":2025},"citing_paper":{"arxiv_id":"2505.07015","last_updated":"2025-05-11T15:21:40Z","snapshot_observed_at":"2026-08-19T20:52:43.571661Z","submitted_at":"2025-05-11T15:21:40Z","title":"Rate of Convergence for a Nonlocal-to-local Limit in One Dimension","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-15T22:38:28.857689Z"},"links":{"cited_paper":"/paper/2501.18745","citing_paper":"/paper/2505.07015"},"observation_digest":"sha256:7837c7540bcde714c1ff3f02a4e028cac7e744b560900de49467cf779d8b160d","observation_id":"fec9bb0b-de9a-4b4a-8455-eb05a6460130","resolution":{"observed_at":"2026-08-15T22:38:29.567586Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2501.18745/citation-record","integrity":"/paper/2501.18745/integrity","json":"/paper/2501.18745/citation-record.json","paper":"/paper/2501.18745"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-09T22:53:18.281968Z","title":"Ambrosio, N","venue":null,"work_id":"b4f1c791-6e6c-4ce1-9a4b-15cf27117400","year":2005},"citing_paper":{"arxiv_id":"2501.18745","last_updated":"2025-01-30T20:49:59Z","snapshot_observed_at":"2026-08-20T02:01:50.081037Z","submitted_at":"2025-01-30T20:49:59Z","title":"A deterministic particle method for the porous media equation","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-09T22:53:17.840947Z"},"links":{"citing_paper":"/paper/2501.18745"},"observation_digest":"sha256:9e61b6125ae6904a77fbae8bbada18a7a9e0948762b99c81ed1ac35727c26e10","observation_id":"e462bba7-1ae3-410d-adc9-3f62255d97d7","resolution":{"observed_at":"2026-08-09T22:53:18.284617Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-09T22:53:18.272266Z","title":"Aronson and J","venue":null,"work_id":"585ccc32-a7c0-49db-9418-a1e68b35d1c7","year":1987},"citing_paper":{"arxiv_id":"2501.18745","last_updated":"2025-01-30T20:49:59Z","snapshot_observed_at":"2026-08-20T02:01:50.081037Z","submitted_at":"2025-01-30T20:49:59Z","title":"A deterministic particle method for the porous media equation","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-09T22:53:17.902601Z"},"links":{"citing_paper":"/paper/2501.18745"},"observation_digest":"sha256:f5bc662690671fed60ddafe08cc5f33bd601eea814bef9bee6369b09182e2b5b","observation_id":"f6882b53-9467-4a6a-a4d6-1b60ab29f39e","resolution":{"observed_at":"2026-08-09T22:53:18.275616Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-09T22:53:18.262585Z","title":null,"venue":null,"work_id":"9e0992e9-ce84-4b36-b5e1-4e0cf94fcd8b","year":1969},"citing_paper":{"arxiv_id":"2501.18745","last_updated":"2025-01-30T20:49:59Z","snapshot_observed_at":"2026-08-20T02:01:50.081037Z","submitted_at":"2025-01-30T20:49:59Z","title":"A deterministic particle method for the porous media equation","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-09T22:53:17.958645Z"},"links":{"citing_paper":"/paper/2501.18745"},"observation_digest":"sha256:6a35a9c43c7c6f80638351dab924d4d1bd2e53f1260c42e3eba56b4917460745","observation_id":"56862425-1532-48ad-9ba6-67303c13a369","resolution":{"observed_at":"2026-08-09T22:53:18.266671Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-09T22:53:18.252635Z","title":"Benamou and Y","venue":null,"work_id":"a77b6ac4-938e-4977-992d-c348cc905204","year":2000},"citing_paper":{"arxiv_id":"2501.18745","last_updated":"2025-01-30T20:49:59Z","snapshot_observed_at":"2026-08-20T02:01:50.081037Z","submitted_at":"2025-01-30T20:49:59Z","title":"A deterministic particle method for the porous media equation","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-09T22:53:18.001789Z"},"links":{"citing_paper":"/paper/2501.18745"},"observation_digest":"sha256:e6e5dad812f1526a9609e8af6dea535840a55c636a520f2693159a3b2955fe0b","observation_id":"af6d6d25-ca35-41f5-bd11-56043699e902","resolution":{"observed_at":"2026-08-09T22:53:18.256081Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-09T22:53:18.243394Z","title":"B ´enilan, M","venue":null,"work_id":"db94bb0d-b6b1-4dde-8a34-9d38692846ef","year":1984},"citing_paper":{"arxiv_id":"2501.18745","last_updated":"2025-01-30T20:49:59Z","snapshot_observed_at":"2026-08-20T02:01:50.081037Z","submitted_at":"2025-01-30T20:49:59Z","title":"A deterministic particle method for the porous media equation","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-09T22:53:18.011194Z"},"links":{"citing_paper":"/paper/2501.18745"},"observation_digest":"sha256:93bf90cbf108ad26685e5f12294dcfe43706b94e78fbfec8cf458c307b065f69","observation_id":"20367a7f-1474-45b2-bf93-64e0012c0f93","resolution":{"observed_at":"2026-08-09T22:53:18.246818Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-09T22:53:18.233981Z","title":"Burger and A","venue":null,"work_id":"006d111e-066a-46eb-8c31-edabdb709982","year":2023},"citing_paper":{"arxiv_id":"2501.18745","last_updated":"2025-01-30T20:49:59Z","snapshot_observed_at":"2026-08-20T02:01:50.081037Z","submitted_at":"2025-01-30T20:49:59Z","title":"A deterministic particle method for the porous media equation","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-09T22:53:18.015358Z"},"links":{"citing_paper":"/paper/2501.18745"},"observation_digest":"sha256:833a02857555e36f866242331233d5b83aedaed6cc5f9e3bc892a1b4a6649715","observation_id":"9f934dc3-7ffe-4263-ade7-43031abc5cdd","resolution":{"observed_at":"2026-08-09T22:53:18.237315Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-09T22:53:18.226322Z","title":null,"venue":null,"work_id":"d7db96e1-0a0b-4a45-bdc8-f0ef2f192122","year":1987},"citing_paper":{"arxiv_id":"2501.18745","last_updated":"2025-01-30T20:49:59Z","snapshot_observed_at":"2026-08-20T02:01:50.081037Z","submitted_at":"2025-01-30T20:49:59Z","title":"A deterministic particle method for the porous media equation","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-09T22:53:18.018986Z"},"links":{"citing_paper":"/paper/2501.18745"},"observation_digest":"sha256:c4d6a7e1b3d45d3320f6c07e8772c99ff8a3d5b2498a911d64b3ba250ff6155c","observation_id":"7ffa5d7b-0d38-4156-8e21-3aad2dd6309d","resolution":{"observed_at":"2026-08-09T22:53:18.229145Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-09T22:53:18.216648Z","title":null,"venue":null,"work_id":"1ddf8df6-d088-401e-b419-482cb75a9f5d","year":2019},"citing_paper":{"arxiv_id":"2501.18745","last_updated":"2025-01-30T20:49:59Z","snapshot_observed_at":"2026-08-20T02:01:50.081037Z","submitted_at":"2025-01-30T20:49:59Z","title":"A deterministic particle method for the porous media equation","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-09T22:53:18.022115Z"},"links":{"citing_paper":"/paper/2501.18745"},"observation_digest":"sha256:ab915f3688d8b4d0274e9be413efdf1ddeedbbb45c31daaea222d9b087b61673","observation_id":"75769c6b-5b45-430d-a85d-c815901de7c0","resolution":{"observed_at":"2026-08-09T22:53:18.219709Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2408.02345","last_updated":"2024-08-05T09:44:59Z","snapshot_observed_at":"2026-08-16T13:28:32.304237Z","submitted_at":"2024-08-05T09:44:59Z","title":"Nonlocal particle approximation for linear and fast diffusion equations","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2408.02345","snapshot_observed_at":"2026-08-09T22:53:18.025595Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2501.18745","last_updated":"2025-01-30T20:49:59Z","snapshot_observed_at":"2026-08-20T02:01:50.081037Z","submitted_at":"2025-01-30T20:49:59Z","title":"A deterministic particle method for the porous media equation","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-09T22:53:18.025595Z"},"links":{"cited_paper":"/paper/2408.02345","citing_paper":"/paper/2501.18745"},"observation_digest":"sha256:b49affd19d1739419daeaf855c8f50baa76252d47b65ae91d2401b3a4be0b283","observation_id":"9e06d86f-0e58-4904-96b8-bb439640c9c6","resolution":{"observed_at":"2026-08-09T22:53:18.025595Z","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":"2026-08-09T22:53:18.207673Z","title":null,"venue":null,"work_id":"08dc8a99-60d8-4e38-ae8a-39a289b06fdb","year":2024},"citing_paper":{"arxiv_id":"2501.18745","last_updated":"2025-01-30T20:49:59Z","snapshot_observed_at":"2026-08-20T02:01:50.081037Z","submitted_at":"2025-01-30T20:49:59Z","title":"A deterministic particle method for the porous media equation","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-09T22:53:18.029820Z"},"links":{"citing_paper":"/paper/2501.18745"},"observation_digest":"sha256:346f8c10fee8be97dd09a6239af69c04204c68e940282826043283d58c1511be","observation_id":"d0fd412b-2692-4a50-baf8-e9da516a3548","resolution":{"observed_at":"2026-08-09T22:53:18.211395Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-09T22:53:18.197428Z","title":null,"venue":null,"work_id":"e5cebdc8-1587-407c-8cfd-46dca7a976ca","year":2021},"citing_paper":{"arxiv_id":"2501.18745","last_updated":"2025-01-30T20:49:59Z","snapshot_observed_at":"2026-08-20T02:01:50.081037Z","submitted_at":"2025-01-30T20:49:59Z","title":"A deterministic particle method for the porous media equation","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-09T22:53:18.033444Z"},"links":{"citing_paper":"/paper/2501.18745"},"observation_digest":"sha256:34d0d0a150d1280ddf0f6d1032dc31d50faf94f89b3bda693cd3c8d636dcdd79","observation_id":"1e5d9932-a019-435b-bfd0-614b67764768","resolution":{"observed_at":"2026-08-09T22:53:18.200403Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-09T22:53:18.187659Z","title":null,"venue":null,"work_id":"573a5966-a2de-4f6c-90df-d473424a8a9b","year":2003},"citing_paper":{"arxiv_id":"2501.18745","last_updated":"2025-01-30T20:49:59Z","snapshot_observed_at":"2026-08-20T02:01:50.081037Z","submitted_at":"2025-01-30T20:49:59Z","title":"A deterministic particle method for the porous media equation","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-09T22:53:18.037488Z"},"links":{"citing_paper":"/paper/2501.18745"},"observation_digest":"sha256:f49ea654510065082619aab745ff932befe763470f29442b142acb902fb740d7","observation_id":"71dbeb60-bf85-4c81-abb3-92ff1332ea0f","resolution":{"observed_at":"2026-08-09T22:53:18.190602Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-09T22:53:18.178194Z","title":"Chertock, A practical guide to deterministic particle methods , in Handbook of numerical analysis, vol","venue":null,"work_id":"4b3da8a1-bbfe-4259-a717-9c2f6a6270e7","year":2017},"citing_paper":{"arxiv_id":"2501.18745","last_updated":"2025-01-30T20:49:59Z","snapshot_observed_at":"2026-08-20T02:01:50.081037Z","submitted_at":"2025-01-30T20:49:59Z","title":"A deterministic particle method for the porous media equation","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-09T22:53:18.041352Z"},"links":{"citing_paper":"/paper/2501.18745"},"observation_digest":"sha256:d5679bb3cff3f5ab61eaa04a92108d1f5f9e086177cd549ad972f28cc81c9cf2","observation_id":"3604ebf8-1356-419e-875e-c9e38b6de7d9","resolution":{"observed_at":"2026-08-09T22:53:18.181339Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-09T22:53:18.169189Z","title":"Degond and F.-J","venue":null,"work_id":"39acc48b-3dc1-4c98-b3b1-50a070f880ca","year":null},"citing_paper":{"arxiv_id":"2501.18745","last_updated":"2025-01-30T20:49:59Z","snapshot_observed_at":"2026-08-20T02:01:50.081037Z","submitted_at":"2025-01-30T20:49:59Z","title":"A deterministic particle method for the porous media equation","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-09T22:53:18.044739Z"},"links":{"citing_paper":"/paper/2501.18745"},"observation_digest":"sha256:3e06b03d43a96c60e1f1637ee0008d59fa98cf210df1182e8b1b23456a7f3e5a","observation_id":"e460d0fe-29ac-4bfe-b861-0ab94ec9dbd7","resolution":{"observed_at":"2026-08-09T22:53:18.172527Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-09T22:53:18.160346Z","title":"Di Francesco, A","venue":null,"work_id":"7052ba9e-df0b-47e9-a116-ef9516481cfa","year":2021},"citing_paper":{"arxiv_id":"2501.18745","last_updated":"2025-01-30T20:49:59Z","snapshot_observed_at":"2026-08-20T02:01:50.081037Z","submitted_at":"2025-01-30T20:49:59Z","title":"A deterministic particle method for the porous media equation","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-09T22:53:18.049032Z"},"links":{"citing_paper":"/paper/2501.18745"},"observation_digest":"sha256:0fbdf6172b0540cd9d81f3d57d655ce52e3df185d6b94a2e58209b633820522c","observation_id":"e7d06f16-bcb4-430c-9d88-3b0cdd46a1b4","resolution":{"observed_at":"2026-08-09T22:53:18.163197Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-09T22:53:18.150011Z","title":"Lacombe, Analyse d’une ´ equation de vitesse de diﬀusion, Comptes Rendus de l’Acad´ emie des Sciences-Series I-Mathematics, 329 (1999), pp","venue":null,"work_id":"ac004947-01ba-4c02-a050-0a35ef3bb63b","year":1999},"citing_paper":{"arxiv_id":"2501.18745","last_updated":"2025-01-30T20:49:59Z","snapshot_observed_at":"2026-08-20T02:01:50.081037Z","submitted_at":"2025-01-30T20:49:59Z","title":"A deterministic particle method for the porous media equation","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-09T22:53:18.053027Z"},"links":{"citing_paper":"/paper/2501.18745"},"observation_digest":"sha256:d0cf0c0ab265ef88c6c770a9dad2bd16d957f53025b41b2ced66453addabadea","observation_id":"725e8b1b-0e77-4aa7-832e-6e055c44e714","resolution":{"observed_at":"2026-08-09T22:53:18.153149Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-09T22:53:18.141499Z","title":"Lacombe and S","venue":null,"work_id":"dad82f4e-88d6-4ea1-a0d9-ff9874b4935d","year":1999},"citing_paper":{"arxiv_id":"2501.18745","last_updated":"2025-01-30T20:49:59Z","snapshot_observed_at":"2026-08-20T02:01:50.081037Z","submitted_at":"2025-01-30T20:49:59Z","title":"A deterministic particle method for the porous media equation","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-09T22:53:18.056106Z"},"links":{"citing_paper":"/paper/2501.18745"},"observation_digest":"sha256:ec377a3115321ca45c8995e7685a903be43537059d2f6f1c28c74054d52fabb0","observation_id":"d3cda7f5-056e-4054-ba14-90b26af6f74d","resolution":{"observed_at":"2026-08-09T22:53:18.143977Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-09T22:53:18.131881Z","title":"Lions and S","venue":null,"work_id":"5f8b4339-6dca-4833-b295-2d98fbe7b354","year":2001},"citing_paper":{"arxiv_id":"2501.18745","last_updated":"2025-01-30T20:49:59Z","snapshot_observed_at":"2026-08-20T02:01:50.081037Z","submitted_at":"2025-01-30T20:49:59Z","title":"A deterministic particle method for the porous media equation","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-09T22:53:18.059884Z"},"links":{"citing_paper":"/paper/2501.18745"},"observation_digest":"sha256:e2cd964cc58b1bda7c4b8305dce583f2a48a21f688e8f4fd6a847a4df1a8ac04","observation_id":"c4718841-613c-4fe3-aabc-24018efac8ff","resolution":{"observed_at":"2026-08-09T22:53:18.135482Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-09T22:53:18.120611Z","title":"Otto , The geometry of dissipative evolution equations: the porou s medium equation , Comm","venue":null,"work_id":"81b1dafb-0469-42c2-82bd-aa54d9a9c9a1","year":2001},"citing_paper":{"arxiv_id":"2501.18745","last_updated":"2025-01-30T20:49:59Z","snapshot_observed_at":"2026-08-20T02:01:50.081037Z","submitted_at":"2025-01-30T20:49:59Z","title":"A deterministic particle method for the porous media equation","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-09T22:53:18.063627Z"},"links":{"citing_paper":"/paper/2501.18745"},"observation_digest":"sha256:df54d995dc937a6b60615e39998d13a8aa18878fc94febab65716a03adf9e077","observation_id":"064aab27-8bfd-4d62-a662-0e41a3ef49f6","resolution":{"observed_at":"2026-08-09T22:53:18.125312Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-09T22:53:18.110712Z","title":null,"venue":null,"work_id":"9cdcc64e-f975-4e86-9f89-2d683be6ca9f","year":2007},"citing_paper":{"arxiv_id":"2501.18745","last_updated":"2025-01-30T20:49:59Z","snapshot_observed_at":"2026-08-20T02:01:50.081037Z","submitted_at":"2025-01-30T20:49:59Z","title":"A deterministic particle method for the porous media equation","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-09T22:53:18.066813Z"},"links":{"citing_paper":"/paper/2501.18745"},"observation_digest":"sha256:2f6824261f885bfccbc74ee503caf5d05ec3ec3b9eb7514c542e0c0130b3b057","observation_id":"bf9e059f-dac0-4b59-b4ce-b7a3c7a5d851","resolution":{"observed_at":"2026-08-09T22:53:18.113998Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-09T22:53:18.100256Z","title":"Villani , Optimal Transport: Old and New , vol","venue":null,"work_id":"d558480e-598b-48f6-b88f-5e654f1b89d0","year":2009},"citing_paper":{"arxiv_id":"2501.18745","last_updated":"2025-01-30T20:49:59Z","snapshot_observed_at":"2026-08-20T02:01:50.081037Z","submitted_at":"2025-01-30T20:49:59Z","title":"A deterministic particle method for the porous media equation","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-09T22:53:18.070016Z"},"links":{"citing_paper":"/paper/2501.18745"},"observation_digest":"sha256:738af57975109bf58a9efbeba3cf4901fb570f588a85857822954bc34741c926","observation_id":"893a3004-a018-432e-b87a-5a4220670049","resolution":{"observed_at":"2026-08-09T22:53:18.104445Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2501.18745","last_updated":"2025-01-30T20:49:59Z","latest_version":1,"primary_category":"math.AP","snapshot_observed_at":"2026-08-20T02:01:50.081037Z","submitted_at":"2025-01-30T20:49:59Z","title":"A deterministic particle method for the porous media equation"},"reference_resolution":{"displayed":21,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":8,"verified_exact":0,"verified_fuzzy":13},"total_outbound_references":21},"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":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"thesis":"As of 20 August 2026, this Paper Citation Record lists 21 of 21 outbound references and 1 inbound Pith citation observation for arXiv:2501.18745."}