{"as_of":"2026-08-17T02:12:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:24eb48ebe27c8036c99fe1f180511e5811c167ba8601e1adc14f639bb0367476","coverage":[{"denominator":29,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":29,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-14T12:36:00.247478Z","state":"measured"},{"denominator":29,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":29,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-16T06:30:59.297886+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/1908.07075/citation-record","integrity":"/paper/1908.07075/integrity","json":"/paper/1908.07075/citation-record.json","paper":"/paper/1908.07075"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T12:36:00.800730Z","title":null,"venue":null,"work_id":"92111e53-1b5a-4ffc-9e6d-f8eba521d842","year":1994},"citing_paper":{"arxiv_id":"1908.07075","last_updated":"2020-08-21T10:58:56Z","snapshot_observed_at":"2026-08-14T12:24:58.755981Z","submitted_at":"2019-08-19T21:26:50Z","title":"Drift, stabilizing and destabilizing for a Patlak-Keller-Segel system with the short-wavelength external signal","version":3},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-14T12:36:00.140391Z"},"links":{"citing_paper":"/paper/1908.07075"},"observation_digest":"sha256:9099663b67dd386273b41c46dd5aa33788d6aa950c275415daf2084230db8b00","observation_id":"ee104450-95d7-4c56-8c15-61ae98adde58","resolution":{"observed_at":"2026-08-14T12:36:00.805005Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T12:36:00.786402Z","title":"Quasisoliton interaction of pur- suitevasion waves in a predator-prey system.Phys","venue":null,"work_id":"3aa231d2-83d4-4894-ad77-30e5b68e8ee1","year":2003},"citing_paper":{"arxiv_id":"1908.07075","last_updated":"2020-08-21T10:58:56Z","snapshot_observed_at":"2026-08-14T12:24:58.755981Z","submitted_at":"2019-08-19T21:26:50Z","title":"Drift, stabilizing and destabilizing for a Patlak-Keller-Segel system with the short-wavelength external signal","version":3},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-14T12:36:00.144988Z"},"links":{"citing_paper":"/paper/1908.07075"},"observation_digest":"sha256:ef08c90d37323acae1ef07fec2d96a620e24f30c51663b0e3fd9f3a3d1a53834","observation_id":"fcb688f3-9c44-4b72-bffd-f462c7ba97d7","resolution":{"observed_at":"2026-08-14T12:36:00.790848Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T12:36:00.771460Z","title":"Soliton-like phenomena in one- dimensional cross-diffusion systems: a predator–prey pursuit and evasion example","venue":null,"work_id":"d1cea17e-38c1-4c0e-9cfc-4df6a6502242","year":2004},"citing_paper":{"arxiv_id":"1908.07075","last_updated":"2020-08-21T10:58:56Z","snapshot_observed_at":"2026-08-14T12:24:58.755981Z","submitted_at":"2019-08-19T21:26:50Z","title":"Drift, stabilizing and destabilizing for a Patlak-Keller-Segel system with the short-wavelength external signal","version":3},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-14T12:36:00.149145Z"},"links":{"citing_paper":"/paper/1908.07075"},"observation_digest":"sha256:5146031ec607b4686d18fe8d71b0a4ed1e396f5c211a795c0dd1335e36a40478","observation_id":"193c4e18-130c-40b8-8bf0-300d8aa05d3d","resolution":{"observed_at":"2026-08-14T12:36:00.776225Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T12:36:00.753528Z","title":"Half-soliton interaction of population taxis waves in predator-prey systems with pursuit and evasion","venue":null,"work_id":"39298915-dbca-44fc-a491-b543ea71de78","year":2004},"citing_paper":{"arxiv_id":"1908.07075","last_updated":"2020-08-21T10:58:56Z","snapshot_observed_at":"2026-08-14T12:24:58.755981Z","submitted_at":"2019-08-19T21:26:50Z","title":"Drift, stabilizing and destabilizing for a Patlak-Keller-Segel system with the short-wavelength external signal","version":3},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-14T12:36:00.153978Z"},"links":{"citing_paper":"/paper/1908.07075"},"observation_digest":"sha256:3087624509dcb37df3cd77a58ada553a524e8b3f89f81455f08d78939226952a","observation_id":"7765edf7-0077-49fb-abc3-f28764b0e177","resolution":{"observed_at":"2026-08-14T12:36:00.757811Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T12:36:00.738516Z","title":"Slow taxis in a predator-prey model","venue":null,"work_id":"9e986fd1-04b3-474a-8f68-b99c677cb998","year":2000},"citing_paper":{"arxiv_id":"1908.07075","last_updated":"2020-08-21T10:58:56Z","snapshot_observed_at":"2026-08-14T12:24:58.755981Z","submitted_at":"2019-08-19T21:26:50Z","title":"Drift, stabilizing and destabilizing for a Patlak-Keller-Segel system with the short-wavelength external signal","version":3},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-14T12:36:00.158167Z"},"links":{"citing_paper":"/paper/1908.07075"},"observation_digest":"sha256:309f0a394688e26e73819a91dace33874a0ec12c71cdbca40d12be0e2611243c","observation_id":"9b41e03a-30c2-4525-8ede-00337bf5cbd1","resolution":{"observed_at":"2026-08-14T12:36:00.745058Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T12:36:00.718449Z","title":"Directed movement of preda- tors and the emergence of density-dependence in predator–prey models","venue":null,"work_id":"66152fde-8ff2-4746-92ee-28c506bb5352","year":2001},"citing_paper":{"arxiv_id":"1908.07075","last_updated":"2020-08-21T10:58:56Z","snapshot_observed_at":"2026-08-14T12:24:58.755981Z","submitted_at":"2019-08-19T21:26:50Z","title":"Drift, stabilizing and destabilizing for a Patlak-Keller-Segel system with the short-wavelength external signal","version":3},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-14T12:36:00.162341Z"},"links":{"citing_paper":"/paper/1908.07075"},"observation_digest":"sha256:3d1846d8168f3ce0a91355c5be10a4edb3ee46947c2460c04a362f023be144e3","observation_id":"9d05d4df-2983-4dc5-997d-23ab04db17a8","resolution":{"observed_at":"2026-08-14T12:36:00.725111Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T12:36:00.698295Z","title":"Chemotaxis- induced spatio-temporal heterogeneity in multi-species host-parasitoid systems","venue":null,"work_id":"5f46bc74-0228-4e4b-8b30-5036043708f2","year":2007},"citing_paper":{"arxiv_id":"1908.07075","last_updated":"2020-08-21T10:58:56Z","snapshot_observed_at":"2026-08-14T12:24:58.755981Z","submitted_at":"2019-08-19T21:26:50Z","title":"Drift, stabilizing and destabilizing for a Patlak-Keller-Segel system with the short-wavelength external signal","version":3},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-14T12:36:00.166385Z"},"links":{"citing_paper":"/paper/1908.07075"},"observation_digest":"sha256:90fc9c6e3f38de54d748671d0ee7899a93b2593b41a0e021966803cc73327a96","observation_id":"b9cfaba2-a623-4e30-a4e2-2e623cfe4445","resolution":{"observed_at":"2026-08-14T12:36:00.703856Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T12:36:00.676005Z","title":"Toward a mathematical theory of Keller-Segel models of pattern formation in biological tissues","venue":null,"work_id":"73274373-0b78-401b-8c00-a728f9738d46","year":2015},"citing_paper":{"arxiv_id":"1908.07075","last_updated":"2020-08-21T10:58:56Z","snapshot_observed_at":"2026-08-14T12:24:58.755981Z","submitted_at":"2019-08-19T21:26:50Z","title":"Drift, stabilizing and destabilizing for a Patlak-Keller-Segel system with the short-wavelength external signal","version":3},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-14T12:36:00.169859Z"},"links":{"citing_paper":"/paper/1908.07075"},"observation_digest":"sha256:d916ac2785cecebec073d4ed328e690a0386efb0c1804820cf61d07ec4157d2c","observation_id":"36e225d1-91a6-4e0e-9fb1-575612321a09","resolution":{"observed_at":"2026-08-14T12:36:00.688851Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T12:36:00.661308Z","title":"Steady states of a predator–prey model with prey-taxis","venue":null,"work_id":"441c86d7-d58c-4c05-a7b6-d59f7c58eef1","year":2014},"citing_paper":{"arxiv_id":"1908.07075","last_updated":"2020-08-21T10:58:56Z","snapshot_observed_at":"2026-08-14T12:24:58.755981Z","submitted_at":"2019-08-19T21:26:50Z","title":"Drift, stabilizing and destabilizing for a Patlak-Keller-Segel system with the short-wavelength external signal","version":3},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-14T12:36:00.173000Z"},"links":{"citing_paper":"/paper/1908.07075"},"observation_digest":"sha256:8822581de35dbf3254acf441bf3bf0bbf76f4c7b94aaf243b56fdd74bae67ff6","observation_id":"b898dfbd-32e7-4533-aabc-db54c1e21a20","resolution":{"observed_at":"2026-08-14T12:36:00.666430Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T12:36:00.642949Z","title":"Predator–prey model with diffusion and indirect prey-taxis","venue":null,"work_id":"8fca75ee-68c3-445a-962d-b580126a7b4f","year":2016},"citing_paper":{"arxiv_id":"1908.07075","last_updated":"2020-08-21T10:58:56Z","snapshot_observed_at":"2026-08-14T12:24:58.755981Z","submitted_at":"2019-08-19T21:26:50Z","title":"Drift, stabilizing and destabilizing for a Patlak-Keller-Segel system with the short-wavelength external signal","version":3},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-14T12:36:00.176060Z"},"links":{"citing_paper":"/paper/1908.07075"},"observation_digest":"sha256:b9adc648c310da1c1e665437b1c9be6d16eb559609dccb23a6b313636706084a","observation_id":"605feb7e-6aa9-406e-8368-b121bcd35384","resolution":{"observed_at":"2026-08-14T12:36:00.648482Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T12:36:00.623502Z","title":"Prey-taxis destabilizes homogeneous stationary state in spatial Gause–Kolmogorov-type model for predator–prey system","venue":null,"work_id":"a6e42e21-aa70-4397-b848-5e984ace17ed","year":2017},"citing_paper":{"arxiv_id":"1908.07075","last_updated":"2020-08-21T10:58:56Z","snapshot_observed_at":"2026-08-14T12:24:58.755981Z","submitted_at":"2019-08-19T21:26:50Z","title":"Drift, stabilizing and destabilizing for a Patlak-Keller-Segel system with the short-wavelength external signal","version":3},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-14T12:36:00.179325Z"},"links":{"citing_paper":"/paper/1908.07075"},"observation_digest":"sha256:eb331fa27701a0f2ddb0ec3483e6e957960b89a7dc671d9b48efd0cb6d2aa34d","observation_id":"b7d73314-b905-4305-af63-993da14bc317","resolution":{"observed_at":"2026-08-14T12:36:00.628951Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T12:36:00.490024Z","title":"Time-periodic and stable patterns of a two-competing-species Keller-Segel chemotaxis model: Effect of cellular growth","venue":null,"work_id":"311f245c-0ca4-450f-8283-21dd50bbd5be","year":2017},"citing_paper":{"arxiv_id":"1908.07075","last_updated":"2020-08-21T10:58:56Z","snapshot_observed_at":"2026-08-14T12:24:58.755981Z","submitted_at":"2019-08-19T21:26:50Z","title":"Drift, stabilizing and destabilizing for a Patlak-Keller-Segel system with the short-wavelength external signal","version":3},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-14T12:36:00.182893Z"},"links":{"citing_paper":"/paper/1908.07075"},"observation_digest":"sha256:3332a8491dd5beedf8875e83c4bcaf419bedb01b2fb0b37e52adde1ab8d66a1d","observation_id":"5b044bee-3ffc-4994-ae6f-80777a3269eb","resolution":{"observed_at":"2026-08-14T12:36:00.493742Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T12:36:00.476383Z","title":"Boundedness in a chemotaxis system with indirect signal production and generalized logistic source","venue":null,"work_id":"7858eefe-0ff5-4d34-a590-98a5bce26bdf","year":2018},"citing_paper":{"arxiv_id":"1908.07075","last_updated":"2020-08-21T10:58:56Z","snapshot_observed_at":"2026-08-14T12:24:58.755981Z","submitted_at":"2019-08-19T21:26:50Z","title":"Drift, stabilizing and destabilizing for a Patlak-Keller-Segel system with the short-wavelength external signal","version":3},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-14T12:36:00.186162Z"},"links":{"citing_paper":"/paper/1908.07075"},"observation_digest":"sha256:4644b4c187586d17946f3f6a908cfe7a09009065283b5b9079881c0042090b97","observation_id":"011c2678-72cc-4708-9209-2bc08c15ef39","resolution":{"observed_at":"2026-08-14T12:36:00.481169Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T12:36:00.462182Z","title":"Homogenization techniques for population dynamics in strongly heterogeneous landscapes","venue":null,"work_id":"4ef05508-4c88-42ff-bdbc-4fae65c2b4f5","year":2018},"citing_paper":{"arxiv_id":"1908.07075","last_updated":"2020-08-21T10:58:56Z","snapshot_observed_at":"2026-08-14T12:24:58.755981Z","submitted_at":"2019-08-19T21:26:50Z","title":"Drift, stabilizing and destabilizing for a Patlak-Keller-Segel system with the short-wavelength external signal","version":3},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-14T12:36:00.189373Z"},"links":{"citing_paper":"/paper/1908.07075"},"observation_digest":"sha256:8fdb949bf3c92b905e329ac098789944b846c1590ac06ba38df74311fe13ca20","observation_id":"3f511132-851b-4125-8e03-f8342807e296","resolution":{"observed_at":"2026-08-14T12:36:00.467367Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T12:36:00.450724Z","title":"Boundedness in a Keller–Segel system with external signal production","venue":null,"work_id":"de8df5a9-62e8-4f6a-9fcc-809c3fd92ae2","year":2017},"citing_paper":{"arxiv_id":"1908.07075","last_updated":"2020-08-21T10:58:56Z","snapshot_observed_at":"2026-08-14T12:24:58.755981Z","submitted_at":"2019-08-19T21:26:50Z","title":"Drift, stabilizing and destabilizing for a Patlak-Keller-Segel system with the short-wavelength external signal","version":3},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-14T12:36:00.193003Z"},"links":{"citing_paper":"/paper/1908.07075"},"observation_digest":"sha256:ad972250257f92c2be1e5424e1eaf0c23be57abbe430650e40cfa3eabce33e3f","observation_id":"a71ed3ce-e649-4d3f-89a9-17dc2785e567","resolution":{"observed_at":"2026-08-14T12:36:00.455143Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s10884-018-","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T12:36:00.287322Z","title":"& Shen, W","venue":null,"work_id":"c2512c16-7246-4141-bfcc-4638cc1d9203","year":2018},"citing_paper":{"arxiv_id":"1908.07075","last_updated":"2020-08-21T10:58:56Z","snapshot_observed_at":"2026-08-14T12:24:58.755981Z","submitted_at":"2019-08-19T21:26:50Z","title":"Drift, stabilizing and destabilizing for a Patlak-Keller-Segel system with the short-wavelength external signal","version":3},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-14T12:36:00.196109Z"},"links":{"citing_paper":"/paper/1908.07075"},"observation_digest":"sha256:bd7378d0d5a12b0dc158147ec1f567e2533f763be8c25ab895f244d836f2cb56","observation_id":"a99f36a4-7d91-4f64-bd40-913ed1a1c187","resolution":{"observed_at":"2026-08-14T12:36:00.292456Z","resolver_source":"doi_truncated","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T12:36:00.438730Z","title":null,"venue":null,"work_id":"c68804dc-3910-4504-852f-38005123f1f3","year":2012},"citing_paper":{"arxiv_id":"1908.07075","last_updated":"2020-08-21T10:58:56Z","snapshot_observed_at":"2026-08-14T12:24:58.755981Z","submitted_at":"2019-08-19T21:26:50Z","title":"Drift, stabilizing and destabilizing for a Patlak-Keller-Segel system with the short-wavelength external signal","version":3},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-14T12:36:00.199548Z"},"links":{"citing_paper":"/paper/1908.07075"},"observation_digest":"sha256:491af0db5e201c2fd96e407ee82d5d83b03143e77e79ecdb70f1f2e333c3b241","observation_id":"75234906-5b61-4d4d-97bc-cd4343414135","resolution":{"observed_at":"2026-08-14T12:36:00.442396Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T12:36:00.426095Z","title":"I., Afrajmovich, V","venue":null,"work_id":"ab8ff9af-1919-4136-aec7-9ce9d7852bb0","year":2013},"citing_paper":{"arxiv_id":"1908.07075","last_updated":"2020-08-21T10:58:56Z","snapshot_observed_at":"2026-08-14T12:24:58.755981Z","submitted_at":"2019-08-19T21:26:50Z","title":"Drift, stabilizing and destabilizing for a Patlak-Keller-Segel system with the short-wavelength external signal","version":3},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-14T12:36:00.203515Z"},"links":{"citing_paper":"/paper/1908.07075"},"observation_digest":"sha256:27dd9648b022ce355db4871c23c0550370f91445df762e9875c0c0754efd3d1a","observation_id":"b8e45035-4f27-416e-997a-059725e74c78","resolution":{"observed_at":"2026-08-14T12:36:00.430379Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T12:36:00.414259Z","title":null,"venue":null,"work_id":"3ccfd6c9-8814-4260-aadc-45989f660567","year":2010},"citing_paper":{"arxiv_id":"1908.07075","last_updated":"2020-08-21T10:58:56Z","snapshot_observed_at":"2026-08-14T12:24:58.755981Z","submitted_at":"2019-08-19T21:26:50Z","title":"Drift, stabilizing and destabilizing for a Patlak-Keller-Segel system with the short-wavelength external signal","version":3},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-14T12:36:00.207194Z"},"links":{"citing_paper":"/paper/1908.07075"},"observation_digest":"sha256:17b2eae462dd99073d3987b1fd0b5a142c13863239934df65db1c0bde73d0752","observation_id":"d539097c-b7a2-42c9-b9ae-d085e6d43bca","resolution":{"observed_at":"2026-08-14T12:36:00.418426Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T12:36:00.400375Z","title":"The dynamics of vibrations in systems with constraints","venue":null,"work_id":"273b2181-98e1-447c-9a90-1d587019e90b","year":1997},"citing_paper":{"arxiv_id":"1908.07075","last_updated":"2020-08-21T10:58:56Z","snapshot_observed_at":"2026-08-14T12:24:58.755981Z","submitted_at":"2019-08-19T21:26:50Z","title":"Drift, stabilizing and destabilizing for a Patlak-Keller-Segel system with the short-wavelength external signal","version":3},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-14T12:36:00.210985Z"},"links":{"citing_paper":"/paper/1908.07075"},"observation_digest":"sha256:81c45c3ba2502eff1d0e62d0b00b27bf97936789d176a33c34b50302732cccf6","observation_id":"d3ee1874-2622-4c5a-b5ea-75f2ef26efe3","resolution":{"observed_at":"2026-08-14T12:36:00.404579Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T12:36:00.387412Z","title":"On vibrodynamics of pendulum and submerged solid","venue":null,"work_id":"f56fcccd-9923-4557-b5c3-0393084f97b8","year":2005},"citing_paper":{"arxiv_id":"1908.07075","last_updated":"2020-08-21T10:58:56Z","snapshot_observed_at":"2026-08-14T12:24:58.755981Z","submitted_at":"2019-08-19T21:26:50Z","title":"Drift, stabilizing and destabilizing for a Patlak-Keller-Segel system with the short-wavelength external signal","version":3},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-14T12:36:00.214767Z"},"links":{"citing_paper":"/paper/1908.07075"},"observation_digest":"sha256:08922ea6b765db80979f6a6bf5233692c7261d40a1915b8cf7adb72a4ca2ec56","observation_id":"a3b80738-bfa6-460f-b3d2-03e9a681a935","resolution":{"observed_at":"2026-08-14T12:36:00.391755Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T12:36:00.375063Z","title":"Two-Timing Hypothesis, Distinguished Limits, Drifts, and Pseudo-Diffusion for Oscillating Flows","venue":null,"work_id":"db271dad-55b5-48c3-bbf9-035ff91919c8","year":2017},"citing_paper":{"arxiv_id":"1908.07075","last_updated":"2020-08-21T10:58:56Z","snapshot_observed_at":"2026-08-14T12:24:58.755981Z","submitted_at":"2019-08-19T21:26:50Z","title":"Drift, stabilizing and destabilizing for a Patlak-Keller-Segel system with the short-wavelength external signal","version":3},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-14T12:36:00.219198Z"},"links":{"citing_paper":"/paper/1908.07075"},"observation_digest":"sha256:d968fc244dfae6b91ffa9fb2dc0d609b04b127c968de521e6da1310e72a00225","observation_id":"77906f94-dbdb-490d-99e7-9d5d29f3e442","resolution":{"observed_at":"2026-08-14T12:36:00.379445Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T12:36:00.361974Z","title":null,"venue":null,"work_id":"e2813908-ead2-410c-a720-8abf50556a57","year":2012},"citing_paper":{"arxiv_id":"1908.07075","last_updated":"2020-08-21T10:58:56Z","snapshot_observed_at":"2026-08-14T12:24:58.755981Z","submitted_at":"2019-08-19T21:26:50Z","title":"Drift, stabilizing and destabilizing for a Patlak-Keller-Segel system with the short-wavelength external signal","version":3},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-14T12:36:00.223084Z"},"links":{"citing_paper":"/paper/1908.07075"},"observation_digest":"sha256:be1def0acdf2d4db0581b8facc73fbf0cda320bf1175db0a46d3f8e12c1589df","observation_id":"e16dd62e-a5e1-4948-90d6-c5433e50f7d5","resolution":{"observed_at":"2026-08-14T12:36:00.366187Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T12:36:00.349448Z","title":"Homogenization and two-scale convergence","venue":null,"work_id":"1b451b6f-de73-497c-b8b6-38203987929f","year":1992},"citing_paper":{"arxiv_id":"1908.07075","last_updated":"2020-08-21T10:58:56Z","snapshot_observed_at":"2026-08-14T12:24:58.755981Z","submitted_at":"2019-08-19T21:26:50Z","title":"Drift, stabilizing and destabilizing for a Patlak-Keller-Segel system with the short-wavelength external signal","version":3},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-14T12:36:00.227642Z"},"links":{"citing_paper":"/paper/1908.07075"},"observation_digest":"sha256:9d46cfe875e10e44603eb136056ce7e5c3c956f771304abf644c425523c724d8","observation_id":"36904420-8033-4332-8005-cecad5e76fe2","resolution":{"observed_at":"2026-08-14T12:36:00.353401Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T12:36:00.338433Z","title":null,"venue":null,"work_id":"184c57fb-e273-4f13-9b35-72ece94c932c","year":2012},"citing_paper":{"arxiv_id":"1908.07075","last_updated":"2020-08-21T10:58:56Z","snapshot_observed_at":"2026-08-14T12:24:58.755981Z","submitted_at":"2019-08-19T21:26:50Z","title":"Drift, stabilizing and destabilizing for a Patlak-Keller-Segel system with the short-wavelength external signal","version":3},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-14T12:36:00.231982Z"},"links":{"citing_paper":"/paper/1908.07075"},"observation_digest":"sha256:9726ef04f2738f06f0b7d88a77e6971ebd64c12382c22f8460c366b4a8d31b2c","observation_id":"947076b8-0a88-4e4f-b6fb-6095bbf89741","resolution":{"observed_at":"2026-08-14T12:36:00.342083Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T12:36:00.326626Z","title":"& Yudovich, V","venue":null,"work_id":"ed20415e-1088-4842-b36b-447cd1c19175","year":1985},"citing_paper":{"arxiv_id":"1908.07075","last_updated":"2020-08-21T10:58:56Z","snapshot_observed_at":"2026-08-14T12:24:58.755981Z","submitted_at":"2019-08-19T21:26:50Z","title":"Drift, stabilizing and destabilizing for a Patlak-Keller-Segel system with the short-wavelength external signal","version":3},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-14T12:36:00.235822Z"},"links":{"citing_paper":"/paper/1908.07075"},"observation_digest":"sha256:7d3b46f3c9f97af76f4c0842200b6f74fa90f53c7d82e6caecc9780153a146b6","observation_id":"6f9dbeeb-811a-4a22-8d62-6ee15ba6f2a5","resolution":{"observed_at":"2026-08-14T12:36:00.330377Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T12:36:00.239860Z","title":"Cycle-creating bifurcation from a family of equilibria of a dynamical system and its delay, J","venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"1908.07075","last_updated":"2020-08-21T10:58:56Z","snapshot_observed_at":"2026-08-14T12:24:58.755981Z","submitted_at":"2019-08-19T21:26:50Z","title":"Drift, stabilizing and destabilizing for a Patlak-Keller-Segel system with the short-wavelength external signal","version":3},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-14T12:36:00.239860Z"},"links":{"citing_paper":"/paper/1908.07075"},"observation_digest":"sha256:f09080f6ee6ed73008e221faf8242fec711cfe6795378628c29908e8819a6141","observation_id":"3ae7b0ee-13c7-443c-8717-510b1bdd1208","resolution":{"observed_at":"2026-08-14T12:36:00.239860Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T12:36:00.314182Z","title":"A strong maximum principle for parabolic equations","venue":null,"work_id":"929ec05d-06bf-45cf-83ea-fb04f56e20f3","year":1953},"citing_paper":{"arxiv_id":"1908.07075","last_updated":"2020-08-21T10:58:56Z","snapshot_observed_at":"2026-08-14T12:24:58.755981Z","submitted_at":"2019-08-19T21:26:50Z","title":"Drift, stabilizing and destabilizing for a Patlak-Keller-Segel system with the short-wavelength external signal","version":3},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-14T12:36:00.243511Z"},"links":{"citing_paper":"/paper/1908.07075"},"observation_digest":"sha256:060bb5ff60bfe44bbffa412f49b981d9e90cda806eb62304b8bb5350451c2a56","observation_id":"839fe276-ef61-4a44-9c19-b06feb9f656d","resolution":{"observed_at":"2026-08-14T12:36:00.318340Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T12:36:00.300886Z","title":"Second order equations of elliptic and parabolic type","venue":null,"work_id":"28a95a91-0232-4aba-9fc6-f7d49f36cb2f","year":1997},"citing_paper":{"arxiv_id":"1908.07075","last_updated":"2020-08-21T10:58:56Z","snapshot_observed_at":"2026-08-14T12:24:58.755981Z","submitted_at":"2019-08-19T21:26:50Z","title":"Drift, stabilizing and destabilizing for a Patlak-Keller-Segel system with the short-wavelength external signal","version":3},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-14T12:36:00.247478Z"},"links":{"citing_paper":"/paper/1908.07075"},"observation_digest":"sha256:161f8acd6e1aae08881eb294321204b61efbbdccd11c2d43e68b81a0275d4cce","observation_id":"fed38d88-93f6-47c2-9281-ee9f925d03ac","resolution":{"observed_at":"2026-08-14T12:36:00.306118Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"1908.07075","last_updated":"2020-08-21T10:58:56Z","latest_version":3,"primary_category":"q-bio.PE","snapshot_observed_at":"2026-08-14T12:24:58.755981Z","submitted_at":"2019-08-19T21:26:50Z","title":"Drift, stabilizing and destabilizing for a Patlak-Keller-Segel system with the short-wavelength external signal"},"reference_resolution":{"displayed":29,"state_counts":{"malformed_identifier":2,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":5,"verified_exact":0,"verified_fuzzy":22},"total_outbound_references":29},"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":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"thesis":"As of 17 August 2026, this Paper Citation Record lists 29 of 29 outbound references and 0 inbound Pith citation observations for arXiv:1908.07075."}