{"as_of":"2026-08-23T12:57:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:fefc31baf4f7f78328c6a7885d4dd4dbf27862eb9b325cfbc2fa773babad00d5","coverage":[{"denominator":18,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":18,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-16T12:17:39.848399Z","state":"measured"},{"denominator":19,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":19,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-23T06:30:58.430688+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":"2026-08-16T01:01:44.982570Z","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":"2026-08-16T01:01:45.282191Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2504.13533","last_updated":"2025-07-17T12:40:49Z","snapshot_observed_at":"2026-08-21T02:38:38.682622Z","submitted_at":"2025-04-18T07:54:27Z","title":"Spectral Gap for the Stochastic Exchange Model","version":2},"cited_work":{"arxiv_id":"2504.13533","doi":null,"metadata_source":"pith","pith_arxiv_id":"2504.13533","snapshot_observed_at":"2026-08-16T01:01:45.282191Z","title":"Spectral Gap for the Stochastic Exchange Model","venue":"math.PR","work_id":"6da09fc4-8ae3-4d35-88e9-6bde166d3533","year":2025},"citing_paper":{"arxiv_id":"2505.02400","last_updated":"2025-05-05T06:46:05Z","snapshot_observed_at":"2026-08-20T22:02:12.343808Z","submitted_at":"2025-05-05T06:46:05Z","title":"Spectral gap of the KMP and other stochastic exchange models on arbitrary graphs","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-16T01:01:44.982570Z"},"links":{"cited_paper":"/paper/2504.13533","citing_paper":"/paper/2505.02400"},"observation_digest":"sha256:a45dad5ab144586e82a8e65bab3d1e1f1852195c5458fd6715fe6b77b72cd540","observation_id":"ade5b912-a35c-4e25-ba64-bc54bf6d83f3","resolution":{"observed_at":"2026-08-16T01:01:45.290111Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2504.13533/citation-record","integrity":"/paper/2504.13533/integrity","json":"/paper/2504.13533/citation-record.json","paper":"/paper/2504.13533"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T12:17:40.069104Z","title":"Caputo: Uniform Poincar´ e inequalities for unbounded conservative spin systems: the non-interacting case , Stoch","venue":null,"work_id":"4abdcf96-2275-45ea-8c57-356b2d3f77d7","year":2003},"citing_paper":{"arxiv_id":"2504.13533","last_updated":"2025-07-17T12:40:49Z","snapshot_observed_at":"2026-08-21T02:38:38.682622Z","submitted_at":"2025-04-18T07:54:27Z","title":"Spectral Gap for the Stochastic Exchange Model","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-16T12:17:39.786007Z"},"links":{"citing_paper":"/paper/2504.13533"},"observation_digest":"sha256:666c8fdd1eeda247a769afcf27d3152a9103aebf4e7bc877105c4823526371e5","observation_id":"b1d7d73c-d27f-4533-8a58-28e1facbdd91","resolution":{"observed_at":"2026-08-16T12:17:40.074496Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-16T12:17:40.057403Z","title":"Caputo: On the spectral gap of the Kac walk and other binary collision processes , ALEA Lat","venue":null,"work_id":"aabb9d01-6224-4de3-b44f-31dedeeb19e7","year":2008},"citing_paper":{"arxiv_id":"2504.13533","last_updated":"2025-07-17T12:40:49Z","snapshot_observed_at":"2026-08-21T02:38:38.682622Z","submitted_at":"2025-04-18T07:54:27Z","title":"Spectral Gap for the Stochastic Exchange Model","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-16T12:17:39.790425Z"},"links":{"citing_paper":"/paper/2504.13533"},"observation_digest":"sha256:a7805f7a7401171289106aff7fa53125bc671739c874f2cd80592e6f969d4e31","observation_id":"a6899891-d810-4c07-95d4-194ad87cf0e8","resolution":{"observed_at":"2026-08-16T12:17:40.061758Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-16T12:17:40.046030Z","title":"´Equations aux D´ eriv´ ees Partielles","venue":null,"work_id":"498ebd81-ec5c-4305-af39-0b534dd64e9e","year":2000},"citing_paper":{"arxiv_id":"2504.13533","last_updated":"2025-07-17T12:40:49Z","snapshot_observed_at":"2026-08-21T02:38:38.682622Z","submitted_at":"2025-04-18T07:54:27Z","title":"Spectral Gap for the Stochastic Exchange Model","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-16T12:17:39.794291Z"},"links":{"citing_paper":"/paper/2504.13533"},"observation_digest":"sha256:4cfab6b124e2ab9b027e140db33dddf5435fc7d015d228fe4f766168ce07c84c","observation_id":"23c5b2ef-8241-45f0-a254-22e5f04805bd","resolution":{"observed_at":"2026-08-16T12:17:40.049535Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-16T12:17:40.035158Z","title":"Carlen, M","venue":null,"work_id":"13b3b27d-8ca3-4861-8351-4751640c87aa","year":2003},"citing_paper":{"arxiv_id":"2504.13533","last_updated":"2025-07-17T12:40:49Z","snapshot_observed_at":"2026-08-21T02:38:38.682622Z","submitted_at":"2025-04-18T07:54:27Z","title":"Spectral Gap for the Stochastic Exchange Model","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-16T12:17:39.797995Z"},"links":{"citing_paper":"/paper/2504.13533"},"observation_digest":"sha256:2d28d344321f42012bd212eafacfb52a6179a49d5f38fbd8d4828e7abeb0d0c8","observation_id":"82dde5cc-825f-4238-b6c4-f7805dd6b8ec","resolution":{"observed_at":"2026-08-16T12:17:40.039049Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-16T12:17:40.021699Z","title":"Carlen, M","venue":null,"work_id":"aee481ae-509f-4081-9395-f49c2ffda546","year":2011},"citing_paper":{"arxiv_id":"2504.13533","last_updated":"2025-07-17T12:40:49Z","snapshot_observed_at":"2026-08-21T02:38:38.682622Z","submitted_at":"2025-04-18T07:54:27Z","title":"Spectral Gap for the Stochastic Exchange Model","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-16T12:17:39.801741Z"},"links":{"citing_paper":"/paper/2504.13533"},"observation_digest":"sha256:acb89f54e4e9308b26abd411213750ff9a586c9b6f08cc50d3ff47205fb4aa06","observation_id":"0a0ac38b-4e43-4936-b2bc-c0f18f7c9122","resolution":{"observed_at":"2026-08-16T12:17:40.025810Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-16T12:17:40.010048Z","title":null,"venue":null,"work_id":"1b95a7a3-c566-470d-9771-156400d7415a","year":2014},"citing_paper":{"arxiv_id":"2504.13533","last_updated":"2025-07-17T12:40:49Z","snapshot_observed_at":"2026-08-21T02:38:38.682622Z","submitted_at":"2025-04-18T07:54:27Z","title":"Spectral Gap for the Stochastic Exchange Model","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-16T12:17:39.806146Z"},"links":{"citing_paper":"/paper/2504.13533"},"observation_digest":"sha256:51e8a1c4d7dadf2356af4dd8362cd983f8c4c8d40d91f0315d3eac734b88f166","observation_id":"815889fb-187a-4b06-927c-825918e23818","resolution":{"observed_at":"2026-08-16T12:17:40.014489Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-16T12:17:39.996178Z","title":null,"venue":null,"work_id":"010de5b6-40ae-423a-a431-aa06005d750f","year":2020},"citing_paper":{"arxiv_id":"2504.13533","last_updated":"2025-07-17T12:40:49Z","snapshot_observed_at":"2026-08-21T02:38:38.682622Z","submitted_at":"2025-04-18T07:54:27Z","title":"Spectral Gap for the Stochastic Exchange Model","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-16T12:17:39.810299Z"},"links":{"citing_paper":"/paper/2504.13533"},"observation_digest":"sha256:856833d41ba8eed09f20a563590690f891b89f68df6307ce57f5c609daeed4c9","observation_id":"f155427d-b0b8-4b6b-83b8-489428527307","resolution":{"observed_at":"2026-08-16T12:17:40.001196Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-16T12:17:39.983041Z","title":"Carlen, J","venue":null,"work_id":"345f11dd-1cf2-444e-8433-4cefc54aa8c3","year":2008},"citing_paper":{"arxiv_id":"2504.13533","last_updated":"2025-07-17T12:40:49Z","snapshot_observed_at":"2026-08-21T02:38:38.682622Z","submitted_at":"2025-04-18T07:54:27Z","title":"Spectral Gap for the Stochastic Exchange Model","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-16T12:17:39.813616Z"},"links":{"citing_paper":"/paper/2504.13533"},"observation_digest":"sha256:27b158fe5e1fb1344d6cec145af083f8e3f5b484adf2f61a95f68267af1573bb","observation_id":"9ea92a30-2fb4-4cbf-b889-f9cd663676e5","resolution":{"observed_at":"2026-08-16T12:17:39.987400Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-16T12:17:39.971580Z","title":"Gaspard, and T","venue":null,"work_id":"f6a3f681-5f09-424a-86b1-833fca2dc579","year":2008},"citing_paper":{"arxiv_id":"2504.13533","last_updated":"2025-07-17T12:40:49Z","snapshot_observed_at":"2026-08-21T02:38:38.682622Z","submitted_at":"2025-04-18T07:54:27Z","title":"Spectral Gap for the Stochastic Exchange Model","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-16T12:17:39.817177Z"},"links":{"citing_paper":"/paper/2504.13533"},"observation_digest":"sha256:1e96280dfa680d57019bcd2de642705ab04e8194fc833c218e4630b1387e9304","observation_id":"a06294e4-5a4b-46ad-8d51-d681c052a336","resolution":{"observed_at":"2026-08-16T12:17:39.975656Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-16T12:17:39.961308Z","title":"Gaspard, and T","venue":null,"work_id":"bd9e6263-5a36-487d-9a8f-89c88dedbda8","year":2009},"citing_paper":{"arxiv_id":"2504.13533","last_updated":"2025-07-17T12:40:49Z","snapshot_observed_at":"2026-08-21T02:38:38.682622Z","submitted_at":"2025-04-18T07:54:27Z","title":"Spectral Gap for the Stochastic Exchange Model","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-16T12:17:39.820576Z"},"links":{"citing_paper":"/paper/2504.13533"},"observation_digest":"sha256:9b4aeabb95d0dce9db04506641b67e92e9992c1165baf157e80bc41ba5b2c7e2","observation_id":"47629079-4eff-4251-bd99-2b02a3e5b3f1","resolution":{"observed_at":"2026-08-16T12:17:39.964984Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-16T12:17:39.951813Z","title":"Giroux and R","venue":null,"work_id":"295d1316-45ab-46bc-af97-5d7668d998c5","year":2008},"citing_paper":{"arxiv_id":"2504.13533","last_updated":"2025-07-17T12:40:49Z","snapshot_observed_at":"2026-08-21T02:38:38.682622Z","submitted_at":"2025-04-18T07:54:27Z","title":"Spectral Gap for the Stochastic Exchange Model","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-16T12:17:39.824171Z"},"links":{"citing_paper":"/paper/2504.13533"},"observation_digest":"sha256:4261a08180bc07404c064d879be287fae9412bf46ac4ad444e14f83ce11c2d80","observation_id":"493a62fb-b9be-4eb2-8fb4-a6585313685a","resolution":{"observed_at":"2026-08-16T12:17:39.955219Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-16T12:17:39.942386Z","title":"Grigo, K","venue":null,"work_id":"28e1ffc6-85a4-47fd-9b11-4acbe4298438","year":2012},"citing_paper":{"arxiv_id":"2504.13533","last_updated":"2025-07-17T12:40:49Z","snapshot_observed_at":"2026-08-21T02:38:38.682622Z","submitted_at":"2025-04-18T07:54:27Z","title":"Spectral Gap for the Stochastic Exchange Model","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-16T12:17:39.827312Z"},"links":{"citing_paper":"/paper/2504.13533"},"observation_digest":"sha256:f458b0c459997e3a5e4422bb01bb2136a7d21b52663029fa8a5b69dbe70b309b","observation_id":"258bc4cf-907e-4053-adda-02cfb3a7c988","resolution":{"observed_at":"2026-08-16T12:17:39.945629Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-16T12:17:39.930948Z","title":"Janvresse: Spectral gap for Kac’s model of Boltzmann equation , Ann","venue":null,"work_id":"0bfa878c-908d-48e7-a9f0-eed6fa841b86","year":2001},"citing_paper":{"arxiv_id":"2504.13533","last_updated":"2025-07-17T12:40:49Z","snapshot_observed_at":"2026-08-21T02:38:38.682622Z","submitted_at":"2025-04-18T07:54:27Z","title":"Spectral Gap for the Stochastic Exchange Model","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-16T12:17:39.830894Z"},"links":{"citing_paper":"/paper/2504.13533"},"observation_digest":"sha256:62fe556ae426ed8b619ff71efb982293a160ce8078421fb72dceea09c89f94a6","observation_id":"a1f3258c-6825-402e-a36d-c9a833d630cf","resolution":{"observed_at":"2026-08-16T12:17:39.934967Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-16T12:17:39.919707Z","title":"Kac: Foundations of kinetic theory , Proc","venue":null,"work_id":"293a773d-4a98-43dd-b300-0d42c7c5dfd7","year":1956},"citing_paper":{"arxiv_id":"2504.13533","last_updated":"2025-07-17T12:40:49Z","snapshot_observed_at":"2026-08-21T02:38:38.682622Z","submitted_at":"2025-04-18T07:54:27Z","title":"Spectral Gap for the Stochastic Exchange Model","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-16T12:17:39.834933Z"},"links":{"citing_paper":"/paper/2504.13533"},"observation_digest":"sha256:e655cf45999988abc5c635ec372338de1d8bd83887958b7b1e2f256f58c6699f","observation_id":"3cc888ba-a5b7-4cb8-a943-f11b63a76ad8","resolution":{"observed_at":"2026-08-16T12:17:39.923346Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-16T12:17:39.908833Z","title":"Kac: Probability and Related Topics in Physical Sciences, Interscience Publ","venue":null,"work_id":"cdb608af-f1d4-4b1d-8649-07b0daef3dc7","year":1959},"citing_paper":{"arxiv_id":"2504.13533","last_updated":"2025-07-17T12:40:49Z","snapshot_observed_at":"2026-08-21T02:38:38.682622Z","submitted_at":"2025-04-18T07:54:27Z","title":"Spectral Gap for the Stochastic Exchange Model","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-16T12:17:39.838309Z"},"links":{"citing_paper":"/paper/2504.13533"},"observation_digest":"sha256:16aad86d125940e347b766b82ba0d89099beb329395385ef1910108a99ac379a","observation_id":"abd30be4-c9c2-42ba-b069-56e206b17355","resolution":{"observed_at":"2026-08-16T12:17:39.912839Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-16T12:17:39.897996Z","title":"Sasada: On the Spectral Gap of the Kac Walk and Other Binary Collision Processes on d-Dimensional Lattice, in K","venue":null,"work_id":"ccca1b7f-c72f-439a-b0fb-8ead19210b71","year":2013},"citing_paper":{"arxiv_id":"2504.13533","last_updated":"2025-07-17T12:40:49Z","snapshot_observed_at":"2026-08-21T02:38:38.682622Z","submitted_at":"2025-04-18T07:54:27Z","title":"Spectral Gap for the Stochastic Exchange Model","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-16T12:17:39.841743Z"},"links":{"citing_paper":"/paper/2504.13533"},"observation_digest":"sha256:6d9594b9c06c1ca1806ae9f9fad862e202fc1b6073d2d8b1958cd7253e1cd6e5","observation_id":"18571bcf-c8bf-43c8-909f-535fdab86aab","resolution":{"observed_at":"2026-08-16T12:17:39.901658Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-16T12:17:39.887051Z","title":"Sasada: Spectral gap for stochastic energy exchange model with nonuniformly positive rate function , Ann","venue":null,"work_id":"09573343-d8fb-401d-9e8c-add0350082d5","year":2015},"citing_paper":{"arxiv_id":"2504.13533","last_updated":"2025-07-17T12:40:49Z","snapshot_observed_at":"2026-08-21T02:38:38.682622Z","submitted_at":"2025-04-18T07:54:27Z","title":"Spectral Gap for the Stochastic Exchange Model","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-16T12:17:39.845067Z"},"links":{"citing_paper":"/paper/2504.13533"},"observation_digest":"sha256:3482c6853b862d4ec6d9b8a2860a7b289c79cc925b8f66c8fc76460b8ef0154c","observation_id":"2e59f8c4-100f-4201-8c40-38c1c5b97174","resolution":{"observed_at":"2026-08-16T12:17:39.890923Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-16T12:17:39.873914Z","title":"Villani: Cercignani’s conjecture is sometimes true and always almost true","venue":null,"work_id":"28d97126-8cab-411a-a220-045cc73ea709","year":2003},"citing_paper":{"arxiv_id":"2504.13533","last_updated":"2025-07-17T12:40:49Z","snapshot_observed_at":"2026-08-21T02:38:38.682622Z","submitted_at":"2025-04-18T07:54:27Z","title":"Spectral Gap for the Stochastic Exchange Model","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-16T12:17:39.848399Z"},"links":{"citing_paper":"/paper/2504.13533"},"observation_digest":"sha256:bbf97e8fe0ee0da5b5e787eb7471d35e13e98b715101a4603871338f4f7ad486","observation_id":"6bcacec4-0d5d-44b8-9d74-e5857550f555","resolution":{"observed_at":"2026-08-16T12:17:39.880019Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2504.13533","last_updated":"2025-07-17T12:40:49Z","latest_version":2,"primary_category":"math.PR","snapshot_observed_at":"2026-08-21T02:38:38.682622Z","submitted_at":"2025-04-18T07:54:27Z","title":"Spectral Gap for the Stochastic Exchange Model"},"reference_resolution":{"displayed":18,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":2,"verified_exact":0,"verified_fuzzy":16},"total_outbound_references":18},"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":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"thesis":"As of 23 August 2026, this Paper Citation Record lists 18 of 18 outbound references and 1 inbound Pith citation observation for arXiv:2504.13533."}