{"as_of":"2026-08-16T09:23:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:32be4ad8a2e2394a90325edbd26dafcb481445a8e0ae0e5ff4fc2bc5e1695188","coverage":[{"denominator":60,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":60,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-14T13:41:41.091823Z","state":"measured"},{"denominator":60,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":60,"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/1908.05026/citation-record","integrity":"/paper/1908.05026/integrity","json":"/paper/1908.05026/citation-record.json","paper":"/paper/1908.05026"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:41:43.823621Z","title":"Achdou, G","venue":null,"work_id":"b817389a-3a6e-47da-b6ef-94d29ed2ef37","year":2013},"citing_paper":{"arxiv_id":"1908.05026","last_updated":"2020-05-04T07:29:31Z","snapshot_observed_at":"2026-08-16T03:36:51.392763Z","submitted_at":"2019-08-14T09:05:57Z","title":"Asymptotic spreading of interacting species with multiple fronts II: Exponentially decaying initial data","version":3},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-14T13:41:40.682337Z"},"links":{"citing_paper":"/paper/1908.05026"},"observation_digest":"sha256:2a291eb52cb5876476e7d512c968542d2192fa2086585642d97791bfe8a762ef","observation_id":"d97dc705-1297-4a58-b2f5-fc643076ff89","resolution":{"observed_at":"2026-08-14T13:41:43.828719Z","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":"2026-08-14T13:41:43.807217Z","title":"Alvarez, Bounded-from-below viscosity solutions of Hamilton-Jacobi equa- tions","venue":null,"work_id":"c6d9b683-48f3-4c4b-b84d-52982f48ed61","year":1997},"citing_paper":{"arxiv_id":"1908.05026","last_updated":"2020-05-04T07:29:31Z","snapshot_observed_at":"2026-08-16T03:36:51.392763Z","submitted_at":"2019-08-14T09:05:57Z","title":"Asymptotic spreading of interacting species with multiple fronts II: Exponentially decaying initial data","version":3},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-14T13:41:40.690994Z"},"links":{"citing_paper":"/paper/1908.05026"},"observation_digest":"sha256:500375c54f40cacb4a423289b8ea21f52f07993065b43bfb311f5029f215af6f","observation_id":"14bf1f57-bf3f-4758-aada-0b9820c3933b","resolution":{"observed_at":"2026-08-14T13:41:43.812546Z","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":"2026-08-14T13:41:40.697274Z","title":"Aronson, H.F","venue":null,"work_id":null,"year":1975},"citing_paper":{"arxiv_id":"1908.05026","last_updated":"2020-05-04T07:29:31Z","snapshot_observed_at":"2026-08-16T03:36:51.392763Z","submitted_at":"2019-08-14T09:05:57Z","title":"Asymptotic spreading of interacting species with multiple fronts II: Exponentially decaying initial data","version":3},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-14T13:41:40.697274Z"},"links":{"citing_paper":"/paper/1908.05026"},"observation_digest":"sha256:ff07cf318247513791a2fe827b5c03e96530adbaf57595d26da740c1ff6a2761","observation_id":"d20afb62-0549-4525-b62f-41e8b4403cb7","resolution":{"observed_at":"2026-08-14T13:41:40.697274Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:41:40.703804Z","title":"Barles, B","venue":null,"work_id":null,"year":1987},"citing_paper":{"arxiv_id":"1908.05026","last_updated":"2020-05-04T07:29:31Z","snapshot_observed_at":"2026-08-16T03:36:51.392763Z","submitted_at":"2019-08-14T09:05:57Z","title":"Asymptotic spreading of interacting species with multiple fronts II: Exponentially decaying initial data","version":3},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-14T13:41:40.703804Z"},"links":{"citing_paper":"/paper/1908.05026"},"observation_digest":"sha256:4bb87ad8260bbd5aa9db4eb5f7939515254c5ff7003133a263ca1a905c5a327c","observation_id":"c158fd9b-3524-45bc-9897-cf1f8616b200","resolution":{"observed_at":"2026-08-14T13:41:40.703804Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.jde.2017.10.016","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:41:41.968904Z","title":"Berestycki, J","venue":null,"work_id":"eb5f3f8a-a31a-463b-b20f-4593c30c2604","year":2018},"citing_paper":{"arxiv_id":"1908.05026","last_updated":"2020-05-04T07:29:31Z","snapshot_observed_at":"2026-08-16T03:36:51.392763Z","submitted_at":"2019-08-14T09:05:57Z","title":"Asymptotic spreading of interacting species with multiple fronts II: Exponentially decaying initial data","version":3},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-14T13:41:40.709817Z"},"links":{"citing_paper":"/paper/1908.05026"},"observation_digest":"sha256:a770df73688f0f649f0af708ce8d9e384f793111036dcef0759c212243bb01ab","observation_id":"c40a810e-1884-498f-839f-c6364b2d29e9","resolution":{"observed_at":"2026-08-14T13:41:41.975165Z","resolver_source":"doi","status":"verified_exact"},"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":"2026-08-14T13:41:40.715837Z","title":"Berestycki, F","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"1908.05026","last_updated":"2020-05-04T07:29:31Z","snapshot_observed_at":"2026-08-16T03:36:51.392763Z","submitted_at":"2019-08-14T09:05:57Z","title":"Asymptotic spreading of interacting species with multiple fronts II: Exponentially decaying initial data","version":3},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-14T13:41:40.715837Z"},"links":{"citing_paper":"/paper/1908.05026"},"observation_digest":"sha256:bb6886dca57e6c37ebe4f8f9a20c70e745d1a51074dab8f8959528ad3ae5ba17","observation_id":"3e566f89-19f0-46b2-82d4-feb6528d174b","resolution":{"observed_at":"2026-08-14T13:41:40.715837Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:41:40.723473Z","title":"Berestycki, G","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"1908.05026","last_updated":"2020-05-04T07:29:31Z","snapshot_observed_at":"2026-08-16T03:36:51.392763Z","submitted_at":"2019-08-14T09:05:57Z","title":"Asymptotic spreading of interacting species with multiple fronts II: Exponentially decaying initial data","version":3},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-14T13:41:40.723473Z"},"links":{"citing_paper":"/paper/1908.05026"},"observation_digest":"sha256:414cca50dc548314bb5ee0f235c86b82292ed0a889664a85926203fdecc45dde","observation_id":"894a9a21-331b-4ffb-81ad-b07e299c84cc","resolution":{"observed_at":"2026-08-14T13:41:40.723473Z","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":"2026-08-14T13:41:43.790330Z","title":"Berestycki, G","venue":null,"work_id":"6dbce10d-36dd-44f3-b0de-868070c42d7e","year":null},"citing_paper":{"arxiv_id":"1908.05026","last_updated":"2020-05-04T07:29:31Z","snapshot_observed_at":"2026-08-16T03:36:51.392763Z","submitted_at":"2019-08-14T09:05:57Z","title":"Asymptotic spreading of interacting species with multiple fronts II: Exponentially decaying initial data","version":3},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-14T13:41:40.729083Z"},"links":{"citing_paper":"/paper/1908.05026"},"observation_digest":"sha256:41f5ccedf9874ed1ea064098683420c541419ef239335b2ce26e7226cbee7f9f","observation_id":"e5971fe3-b513-4e5d-aaaa-2da1c9ee8bb8","resolution":{"observed_at":"2026-08-14T13:41:43.795984Z","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":"10.1137/0153050","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:41:41.914377Z","title":"Booty, R","venue":null,"work_id":"a0a8f0d0-de49-45d1-a223-29fc6b43c782","year":1993},"citing_paper":{"arxiv_id":"1908.05026","last_updated":"2020-05-04T07:29:31Z","snapshot_observed_at":"2026-08-16T03:36:51.392763Z","submitted_at":"2019-08-14T09:05:57Z","title":"Asymptotic spreading of interacting species with multiple fronts II: Exponentially decaying initial data","version":3},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-14T13:41:40.735991Z"},"links":{"citing_paper":"/paper/1908.05026"},"observation_digest":"sha256:e964dc3061a8f003498e0430cd574424a47f77c142a85b794755356711bec039","observation_id":"f8bd2379-9a23-4667-9364-41311aba17c6","resolution":{"observed_at":"2026-08-14T13:41:41.920642Z","resolver_source":"doi","status":"verified_exact"},"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":"10.1016/j.jde.2017.10.017","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:41:41.895065Z","title":"Carrère, Spreading speeds for a two-species competi tion- diffusion system, J","venue":null,"work_id":"6d0a4aaa-390f-44cd-b383-b7adc953f761","year":2018},"citing_paper":{"arxiv_id":"1908.05026","last_updated":"2020-05-04T07:29:31Z","snapshot_observed_at":"2026-08-16T03:36:51.392763Z","submitted_at":"2019-08-14T09:05:57Z","title":"Asymptotic spreading of interacting species with multiple fronts II: Exponentially decaying initial data","version":3},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-14T13:41:40.741863Z"},"links":{"citing_paper":"/paper/1908.05026"},"observation_digest":"sha256:692bed46cb923af5cb15f659795d20ffaea0d3cdf550e9b54cc1c784ab72eea9","observation_id":"6f0f03b6-a145-4249-b89c-11cf65a92a02","resolution":{"observed_at":"2026-08-14T13:41:41.901780Z","resolver_source":"doi","status":"verified_exact"},"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":"2026-08-14T13:41:43.772923Z","title":null,"venue":null,"work_id":"b0eca0a6-e670-4cd2-b640-fe6a17c0d2ca","year":2008},"citing_paper":{"arxiv_id":"1908.05026","last_updated":"2020-05-04T07:29:31Z","snapshot_observed_at":"2026-08-16T03:36:51.392763Z","submitted_at":"2019-08-14T09:05:57Z","title":"Asymptotic spreading of interacting species with multiple fronts II: Exponentially decaying initial data","version":3},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-14T13:41:40.748011Z"},"links":{"citing_paper":"/paper/1908.05026"},"observation_digest":"sha256:297129f6e1df8b924aef23aa4bab07a8fc32fcf7ad335d8ca5bb8ce5d272fcb2","observation_id":"55ecf0ca-7180-41a7-bbd0-20d2b9cee217","resolution":{"observed_at":"2026-08-14T13:41:43.778196Z","resolver_source":"raw_fallback","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:41:40.754379Z","title":"Crandall, P.L","venue":null,"work_id":null,"year":1983},"citing_paper":{"arxiv_id":"1908.05026","last_updated":"2020-05-04T07:29:31Z","snapshot_observed_at":"2026-08-16T03:36:51.392763Z","submitted_at":"2019-08-14T09:05:57Z","title":"Asymptotic spreading of interacting species with multiple fronts II: Exponentially decaying initial data","version":3},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-14T13:41:40.754379Z"},"links":{"citing_paper":"/paper/1908.05026"},"observation_digest":"sha256:de50983edcb6e95a23d9fe9134633c8c758a59213e89a9001aaed98f11d9ac78","observation_id":"1e48cb4d-fcf9-489e-941c-523014aad556","resolution":{"observed_at":"2026-08-14T13:41:40.754379Z","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":"jmsj/0394058","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:41:43.407722Z","title":"Crandall, P.L","venue":null,"work_id":"98acbfd4-5567-4801-819f-719ffdd9917a","year":1987},"citing_paper":{"arxiv_id":"1908.05026","last_updated":"2020-05-04T07:29:31Z","snapshot_observed_at":"2026-08-16T03:36:51.392763Z","submitted_at":"2019-08-14T09:05:57Z","title":"Asymptotic spreading of interacting species with multiple fronts II: Exponentially decaying initial data","version":3},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-14T13:41:40.761371Z"},"links":{"citing_paper":"/paper/1908.05026"},"observation_digest":"sha256:e99ddcb515393dcfdcda879530a51ba5d31be1f6af692385387a9ab33c9ee2aa","observation_id":"1304b9b3-0c4a-4dd4-8829-67e481d308d6","resolution":{"observed_at":"2026-08-14T13:41:43.416001Z","resolver_source":"raw_fallback","status":"verified_exact"},"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/s00526-018-1339-5","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:41:41.859551Z","title":null,"venue":null,"work_id":"a19e5dd7-f47b-41ac-922e-8c618bb2b725","year":2018},"citing_paper":{"arxiv_id":"1908.05026","last_updated":"2020-05-04T07:29:31Z","snapshot_observed_at":"2026-08-16T03:36:51.392763Z","submitted_at":"2019-08-14T09:05:57Z","title":"Asymptotic spreading of interacting species with multiple fronts II: Exponentially decaying initial data","version":3},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-14T13:41:40.769642Z"},"links":{"citing_paper":"/paper/1908.05026"},"observation_digest":"sha256:d2e1174e14eb3c1016e7473a07f71a8498327eb762f6e77220d1ee3d719c700b","observation_id":"301ccba0-49de-45f4-bea6-f07c6e988221","resolution":{"observed_at":"2026-08-14T13:41:41.865191Z","resolver_source":"doi","status":"verified_exact"},"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/s00526-019-1576-2","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:41:41.840390Z","title":"Ducrot, T","venue":null,"work_id":"22a2501a-84c7-437c-bd40-5c41b3cdfec1","year":2019},"citing_paper":{"arxiv_id":"1908.05026","last_updated":"2020-05-04T07:29:31Z","snapshot_observed_at":"2026-08-16T03:36:51.392763Z","submitted_at":"2019-08-14T09:05:57Z","title":"Asymptotic spreading of interacting species with multiple fronts II: Exponentially decaying initial data","version":3},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-14T13:41:40.777136Z"},"links":{"citing_paper":"/paper/1908.05026"},"observation_digest":"sha256:d4bd426e29e0ddd3567d2e7c3e4f7d23c43c258278a21cc420f1e02ab9e2ed41","observation_id":"c669c17e-5c9f-4c8c-8404-aec3a3ce5a3c","resolution":{"observed_at":"2026-08-14T13:41:41.846091Z","resolver_source":"doi","status":"verified_exact"},"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":"2026-08-14T13:41:40.786553Z","title":"Ebert, W.V","venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"1908.05026","last_updated":"2020-05-04T07:29:31Z","snapshot_observed_at":"2026-08-16T03:36:51.392763Z","submitted_at":"2019-08-14T09:05:57Z","title":"Asymptotic spreading of interacting species with multiple fronts II: Exponentially decaying initial data","version":3},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-14T13:41:40.786553Z"},"links":{"citing_paper":"/paper/1908.05026"},"observation_digest":"sha256:97cdb5b9119efc9ba60593cc35f30d995105f9c00f6dda147dd41af2c2508bf0","observation_id":"8def9e93-3ea6-4c09-9170-4d7f82b110d1","resolution":{"observed_at":"2026-08-14T13:41:40.786553Z","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":"stable/2489534","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:41:43.317638Z","title":"Evans, P.E","venue":null,"work_id":"6071ad72-a7e0-4cd0-8408-4a5e2a4776f0","year":1989},"citing_paper":{"arxiv_id":"1908.05026","last_updated":"2020-05-04T07:29:31Z","snapshot_observed_at":"2026-08-16T03:36:51.392763Z","submitted_at":"2019-08-14T09:05:57Z","title":"Asymptotic spreading of interacting species with multiple fronts II: Exponentially decaying initial data","version":3},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-14T13:41:40.792375Z"},"links":{"citing_paper":"/paper/1908.05026"},"observation_digest":"sha256:059922a3dfc3f6ca079115deb1707c89a97a37aa9c22d50a4b322807e2e4c5af","observation_id":"ee704559-a360-4f66-8c4b-36a05315163b","resolution":{"observed_at":"2026-08-14T13:41:43.325625Z","resolver_source":"raw_fallback","status":"verified_exact"},"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":"2026-08-14T13:41:43.756981Z","title":"Evans, P.E","venue":null,"work_id":"71cfeca3-e5d6-4460-811e-1944a68d5211","year":1989},"citing_paper":{"arxiv_id":"1908.05026","last_updated":"2020-05-04T07:29:31Z","snapshot_observed_at":"2026-08-16T03:36:51.392763Z","submitted_at":"2019-08-14T09:05:57Z","title":"Asymptotic spreading of interacting species with multiple fronts II: Exponentially decaying initial data","version":3},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-14T13:41:40.798446Z"},"links":{"citing_paper":"/paper/1908.05026"},"observation_digest":"sha256:2d1599c89f12fb3e4d5f96275cf518fb80d3d6efbf2f9501c0155adfefa41c07","observation_id":"c1575be6-6914-41f1-97c5-b5f07a0add9c","resolution":{"observed_at":"2026-08-14T13:41:43.761917Z","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":"10.1137/15m1029564","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:41:41.788957Z","title":"Fang, Y.J","venue":null,"work_id":"f4c37b79-719d-4746-96ec-29f45bab1c07","year":2016},"citing_paper":{"arxiv_id":"1908.05026","last_updated":"2020-05-04T07:29:31Z","snapshot_observed_at":"2026-08-16T03:36:51.392763Z","submitted_at":"2019-08-14T09:05:57Z","title":"Asymptotic spreading of interacting species with multiple fronts II: Exponentially decaying initial data","version":3},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-14T13:41:40.805396Z"},"links":{"citing_paper":"/paper/1908.05026"},"observation_digest":"sha256:24a2aef4dde476e4989dd2b5ff519dec1e39aae646542daaf0e34177894743d5","observation_id":"71363820-8cc3-4860-8187-8d708a98371a","resolution":{"observed_at":"2026-08-14T13:41:41.800973Z","resolver_source":"doi","status":"verified_exact"},"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":"10.1137/140953939","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:41:41.763878Z","title":"Fang, X.Q","venue":null,"work_id":"b2721b76-38f4-45ab-b508-39fc16456d7f","year":2014},"citing_paper":{"arxiv_id":"1908.05026","last_updated":"2020-05-04T07:29:31Z","snapshot_observed_at":"2026-08-16T03:36:51.392763Z","submitted_at":"2019-08-14T09:05:57Z","title":"Asymptotic spreading of interacting species with multiple fronts II: Exponentially decaying initial data","version":3},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-14T13:41:40.811130Z"},"links":{"citing_paper":"/paper/1908.05026"},"observation_digest":"sha256:993cd6a3ecf976a31c260b189c5e933c52def668a87f222ee952aa2895dd8fc9","observation_id":"0f64e24f-d4de-4cd9-9932-98a60edcec50","resolution":{"observed_at":"2026-08-14T13:41:41.772176Z","resolver_source":"doi","status":"verified_exact"},"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":"2026-08-14T13:41:40.817270Z","title":"Fisher, The wave of advance of advantageous genes, Ann","venue":null,"work_id":null,"year":1937},"citing_paper":{"arxiv_id":"1908.05026","last_updated":"2020-05-04T07:29:31Z","snapshot_observed_at":"2026-08-16T03:36:51.392763Z","submitted_at":"2019-08-14T09:05:57Z","title":"Asymptotic spreading of interacting species with multiple fronts II: Exponentially decaying initial data","version":3},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-14T13:41:40.817270Z"},"links":{"citing_paper":"/paper/1908.05026"},"observation_digest":"sha256:1f1f4cba062af3dd326c7db8b7f18646c77dd015d3b087cb87d42bf4a35bac6c","observation_id":"8eb842c3-6624-4607-8aae-c9a1ea81c268","resolution":{"observed_at":"2026-08-14T13:41:40.817270Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:41:40.823087Z","title":"Freidlin, Limit theorems for large deviations and reaction-diffusion equation, Ann","venue":null,"work_id":null,"year":1985},"citing_paper":{"arxiv_id":"1908.05026","last_updated":"2020-05-04T07:29:31Z","snapshot_observed_at":"2026-08-16T03:36:51.392763Z","submitted_at":"2019-08-14T09:05:57Z","title":"Asymptotic spreading of interacting species with multiple fronts II: Exponentially decaying initial data","version":3},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-14T13:41:40.823087Z"},"links":{"citing_paper":"/paper/1908.05026"},"observation_digest":"sha256:cb2e571544c9bb30af311337e218275e659fc7b6b9e512526aa442cd230ced16","observation_id":"b4cbfed6-27fa-4976-9b54-3dff802c98a3","resolution":{"observed_at":"2026-08-14T13:41:40.823087Z","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":"stable/2244251","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:41:42.572084Z","title":"Freidlin, Coupled reaction-diffusion equations","venue":null,"work_id":"d477c905-934c-4c31-abf3-14844badae7a","year":1991},"citing_paper":{"arxiv_id":"1908.05026","last_updated":"2020-05-04T07:29:31Z","snapshot_observed_at":"2026-08-16T03:36:51.392763Z","submitted_at":"2019-08-14T09:05:57Z","title":"Asymptotic spreading of interacting species with multiple fronts II: Exponentially decaying initial data","version":3},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-14T13:41:40.829031Z"},"links":{"citing_paper":"/paper/1908.05026"},"observation_digest":"sha256:9c89c47292c343becb26f3e34383b5f9748c45f823c28f7ddd4e9a5a8045c97c","observation_id":"0c7eab29-94b6-4469-8675-c336180e43d5","resolution":{"observed_at":"2026-08-14T13:41:42.581974Z","resolver_source":"raw_fallback","status":"verified_exact"},"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/s10884-012-9254-5","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:41:41.736821Z","title":"Garnier, T","venue":null,"work_id":"d839729b-cb13-47e7-98cc-0b9161ff0cf2","year":2012},"citing_paper":{"arxiv_id":"1908.05026","last_updated":"2020-05-04T07:29:31Z","snapshot_observed_at":"2026-08-16T03:36:51.392763Z","submitted_at":"2019-08-14T09:05:57Z","title":"Asymptotic spreading of interacting species with multiple fronts II: Exponentially decaying initial data","version":3},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-14T13:41:40.834508Z"},"links":{"citing_paper":"/paper/1908.05026"},"observation_digest":"sha256:6047bacfbf3bed2267c8e7cfe2ed8bd791fa44a19e2fb4a0f30e48c435a32875","observation_id":"12cf708a-eb5b-4695-9d06-471743343709","resolution":{"observed_at":"2026-08-14T13:41:41.744446Z","resolver_source":"doi","status":"verified_exact"},"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":"2026-08-14T13:41:43.739369Z","title":null,"venue":null,"work_id":"2cbe53a8-3a24-419b-8cdf-2a57f4399185","year":2011},"citing_paper":{"arxiv_id":"1908.05026","last_updated":"2020-05-04T07:29:31Z","snapshot_observed_at":"2026-08-16T03:36:51.392763Z","submitted_at":"2019-08-14T09:05:57Z","title":"Asymptotic spreading of interacting species with multiple fronts II: Exponentially decaying initial data","version":3},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-14T13:41:40.839910Z"},"links":{"citing_paper":"/paper/1908.05026"},"observation_digest":"sha256:1ee48b50e215da03a43331e9984416328267dca3f7f0607fd4a1fd578adbdbde","observation_id":"0f5d939f-853e-426e-bcc0-8e14c23cf3ff","resolution":{"observed_at":"2026-08-14T13:41:43.744593Z","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":"10.1112/plms.12270","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:41:41.695339Z","title":"Girardin, K.Y","venue":null,"work_id":"676089a4-0f96-424b-9143-0c6654286604","year":2019},"citing_paper":{"arxiv_id":"1908.05026","last_updated":"2020-05-04T07:29:31Z","snapshot_observed_at":"2026-08-16T03:36:51.392763Z","submitted_at":"2019-08-14T09:05:57Z","title":"Asymptotic spreading of interacting species with multiple fronts II: Exponentially decaying initial data","version":3},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-14T13:41:40.852354Z"},"links":{"citing_paper":"/paper/1908.05026"},"observation_digest":"sha256:7eeba163354a35def224a45b274c81709077c0eeaf14f55bf90d73dd8055ee6a","observation_id":"1d087a35-0949-498f-8b78-28716602da47","resolution":{"observed_at":"2026-08-14T13:41:41.707245Z","resolver_source":"doi","status":"verified_exact"},"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":"10.1088/0951-7715/28/1/1","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:41:41.672043Z","title":"Guo, C.H","venue":null,"work_id":"4a08cd7f-5130-4811-a7d0-80744140bec3","year":2015},"citing_paper":{"arxiv_id":"1908.05026","last_updated":"2020-05-04T07:29:31Z","snapshot_observed_at":"2026-08-16T03:36:51.392763Z","submitted_at":"2019-08-14T09:05:57Z","title":"Asymptotic spreading of interacting species with multiple fronts II: Exponentially decaying initial data","version":3},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-14T13:41:40.859235Z"},"links":{"citing_paper":"/paper/1908.05026"},"observation_digest":"sha256:57c939aa37613b52f4b3afc43cd09c826f8c009ffb13e12590440823a99b5cd0","observation_id":"1b6b2fc6-316a-4da1-935e-7a71d596cbf2","resolution":{"observed_at":"2026-08-14T13:41:41.680980Z","resolver_source":"doi","status":"verified_exact"},"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":"2026-08-14T13:41:43.723414Z","title":"Hamel, G","venue":null,"work_id":"301b5a2b-eb7c-41a7-b4a0-fa8b15d0b091","year":2012},"citing_paper":{"arxiv_id":"1908.05026","last_updated":"2020-05-04T07:29:31Z","snapshot_observed_at":"2026-08-16T03:36:51.392763Z","submitted_at":"2019-08-14T09:05:57Z","title":"Asymptotic spreading of interacting species with multiple fronts II: Exponentially decaying initial data","version":3},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-14T13:41:40.865245Z"},"links":{"citing_paper":"/paper/1908.05026"},"observation_digest":"sha256:c0a1ef734b92e1d5b98756863e69341f87bf54b64f3885572c98d87c4b93be37","observation_id":"00ae52cd-5818-4390-b49b-53ed3e661f06","resolution":{"observed_at":"2026-08-14T13:41:43.728580Z","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":"10.1137/120887746","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:41:41.652075Z","title":"Holzer, A","venue":null,"work_id":"342258e7-81e6-42b7-94af-d3061205b367","year":2014},"citing_paper":{"arxiv_id":"1908.05026","last_updated":"2020-05-04T07:29:31Z","snapshot_observed_at":"2026-08-16T03:36:51.392763Z","submitted_at":"2019-08-14T09:05:57Z","title":"Asymptotic spreading of interacting species with multiple fronts II: Exponentially decaying initial data","version":3},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-14T13:41:40.880887Z"},"links":{"citing_paper":"/paper/1908.05026"},"observation_digest":"sha256:30d312f446c2662234198856851a060606226547772ff439e5a82994051d6a4d","observation_id":"393c961b-ee5e-4a57-acb1-066f141ad403","resolution":{"observed_at":"2026-08-14T13:41:41.658024Z","resolver_source":"doi","status":"verified_exact"},"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":"10.1137/1.9781611970487","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:41:41.631497Z","title":"Hoppensteadt, Mathematical theories of populati ons: demographics, genet- ics, and epidemics, CBMS-NSF Regional Conf","venue":null,"work_id":"ad098258-70ad-477d-86ac-d9911dbec601","year":1975},"citing_paper":{"arxiv_id":"1908.05026","last_updated":"2020-05-04T07:29:31Z","snapshot_observed_at":"2026-08-16T03:36:51.392763Z","submitted_at":"2019-08-14T09:05:57Z","title":"Asymptotic spreading of interacting species with multiple fronts II: Exponentially decaying initial data","version":3},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-14T13:41:40.887314Z"},"links":{"citing_paper":"/paper/1908.05026"},"observation_digest":"sha256:aa8e5c858e26782b0daf827885d34afd149719e15f73b1e234e475bfc5f6ee6c","observation_id":"e7542d11-a306-4004-8666-f9c21a6231e6","resolution":{"observed_at":"2026-08-14T13:41:41.637643Z","resolver_source":"doi","status":"verified_exact"},"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":"10.1137/100792846","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:41:41.606534Z","title":null,"venue":null,"work_id":"7f3723c4-418d-4338-8fb0-4b2ef873463b","year":2011},"citing_paper":{"arxiv_id":"1908.05026","last_updated":"2020-05-04T07:29:31Z","snapshot_observed_at":"2026-08-16T03:36:51.392763Z","submitted_at":"2019-08-14T09:05:57Z","title":"Asymptotic spreading of interacting species with multiple fronts II: Exponentially decaying initial data","version":3},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-14T13:41:40.894821Z"},"links":{"citing_paper":"/paper/1908.05026"},"observation_digest":"sha256:d6edf691e1e94aeed6176139d1e3a667323be375943696c70a43014af3efe50b","observation_id":"5d7f9c5a-438e-4341-8784-df63d13a3a5c","resolution":{"observed_at":"2026-08-14T13:41:41.613881Z","resolver_source":"doi","status":"verified_exact"},"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":"2026-08-14T13:41:43.705718Z","title":"Ishii, Hamilton-Jacobi equations with discontinuo us Hamiltonians on arbitrary open Sets, Bull","venue":null,"work_id":"0d7a8d3c-cf77-415d-b012-20db97e60ffd","year":1985},"citing_paper":{"arxiv_id":"1908.05026","last_updated":"2020-05-04T07:29:31Z","snapshot_observed_at":"2026-08-16T03:36:51.392763Z","submitted_at":"2019-08-14T09:05:57Z","title":"Asymptotic spreading of interacting species with multiple fronts II: Exponentially decaying initial data","version":3},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-14T13:41:40.901000Z"},"links":{"citing_paper":"/paper/1908.05026"},"observation_digest":"sha256:c7b5f09639c071a123d9cf136c341908b6f8c31ab14d78f41b80adcce9af7ec5","observation_id":"6d79f92e-abc5-4f2a-98ef-50505a71c064","resolution":{"observed_at":"2026-08-14T13:41:43.711836Z","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":"10.1080/00036819708840617","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:41:41.573690Z","title":"Ishii, Comparison results for hamilton-jacobi equa tions without growth condition on solutions from above, Appl","venue":null,"work_id":"0ca6457d-94e3-4654-979a-537e18c69a90","year":1997},"citing_paper":{"arxiv_id":"1908.05026","last_updated":"2020-05-04T07:29:31Z","snapshot_observed_at":"2026-08-16T03:36:51.392763Z","submitted_at":"2019-08-14T09:05:57Z","title":"Asymptotic spreading of interacting species with multiple fronts II: Exponentially decaying initial data","version":3},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-14T13:41:40.906742Z"},"links":{"citing_paper":"/paper/1908.05026"},"observation_digest":"sha256:36e9b709532da73e14c321a74dc2e257f373f5e0f208ad5fba885e43d2a0d623","observation_id":"04579cd5-e811-4a8e-9145-24bcbeffeb69","resolution":{"observed_at":"2026-08-14T13:41:41.585181Z","resolver_source":"doi","status":"verified_exact"},"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":"10.18910/9093","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:41:41.552886Z","title":"Kametaka, On the nonlinear diffusion equation of Kolm ogorov- Petrovski-Piskunov type, Osaka J","venue":null,"work_id":"c6d7d916-c6b3-4dbb-8349-165490939691","year":1976},"citing_paper":{"arxiv_id":"1908.05026","last_updated":"2020-05-04T07:29:31Z","snapshot_observed_at":"2026-08-16T03:36:51.392763Z","submitted_at":"2019-08-14T09:05:57Z","title":"Asymptotic spreading of interacting species with multiple fronts II: Exponentially decaying initial data","version":3},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-14T13:41:40.913779Z"},"links":{"citing_paper":"/paper/1908.05026"},"observation_digest":"sha256:7a3cb16b3263dd9296af1b0c116c968a2fbc43b1f73104f9bdba5ec980921b9c","observation_id":"2bc5f763-75d7-4046-aff4-4603e82e9057","resolution":{"observed_at":"2026-08-14T13:41:41.558596Z","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":"2026-08-14T13:41:43.686633Z","title":"Kolmogorov, I.G","venue":null,"work_id":"e000caa5-7ab3-42eb-b3fc-0ff655509f21","year":1937},"citing_paper":{"arxiv_id":"1908.05026","last_updated":"2020-05-04T07:29:31Z","snapshot_observed_at":"2026-08-16T03:36:51.392763Z","submitted_at":"2019-08-14T09:05:57Z","title":"Asymptotic spreading of interacting species with multiple fronts II: Exponentially decaying initial data","version":3},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-14T13:41:40.920839Z"},"links":{"citing_paper":"/paper/1908.05026"},"observation_digest":"sha256:ec387dc0a195b8a7e0bcdde95ae9a476d3ce87341d0cd59dad22c7662e96000b","observation_id":"8cc71839-c03a-4424-ac95-f2b195f88c76","resolution":{"observed_at":"2026-08-14T13:41:43.692203Z","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/s002850200144","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:41:41.527925Z","title":"Lewis, B.T","venue":null,"work_id":"1ada7b3c-1aa0-407f-9ce8-4f8757b00386","year":2002},"citing_paper":{"arxiv_id":"1908.05026","last_updated":"2020-05-04T07:29:31Z","snapshot_observed_at":"2026-08-16T03:36:51.392763Z","submitted_at":"2019-08-14T09:05:57Z","title":"Asymptotic spreading of interacting species with multiple fronts II: Exponentially decaying initial data","version":3},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-14T13:41:40.928124Z"},"links":{"citing_paper":"/paper/1908.05026"},"observation_digest":"sha256:6830aace50259225823b0d879fc93519daf7bcc132ab5e12e48144f69d377df0","observation_id":"7a9e693b-5c01-4fba-a9ea-e3745bade6e2","resolution":{"observed_at":"2026-08-14T13:41:41.534952Z","resolver_source":"doi","status":"verified_exact"},"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/s00285-017-1200-z","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:41:41.506516Z","title":"Li, Multiple invasion speeds in a two-species inte gro- difference competition model, J","venue":null,"work_id":"e23452d8-b727-47b6-89e7-f6297ba92189","year":2018},"citing_paper":{"arxiv_id":"1908.05026","last_updated":"2020-05-04T07:29:31Z","snapshot_observed_at":"2026-08-16T03:36:51.392763Z","submitted_at":"2019-08-14T09:05:57Z","title":"Asymptotic spreading of interacting species with multiple fronts II: Exponentially decaying initial data","version":3},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-14T13:41:40.936087Z"},"links":{"citing_paper":"/paper/1908.05026"},"observation_digest":"sha256:1a60692f5c0615622886603c2efaac08446befebdd369e5880e8bd2dcd1c8631","observation_id":"e7f3bd8a-916b-46d3-9656-a86ef3a33b62","resolution":{"observed_at":"2026-08-14T13:41:41.513883Z","resolver_source":"doi","status":"verified_exact"},"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":"10.1016/j.mbs.2005.03.008","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:41:41.483287Z","title":null,"venue":null,"work_id":"1ad6238d-6e06-43f0-9208-5218a69f13cb","year":2005},"citing_paper":{"arxiv_id":"1908.05026","last_updated":"2020-05-04T07:29:31Z","snapshot_observed_at":"2026-08-16T03:36:51.392763Z","submitted_at":"2019-08-14T09:05:57Z","title":"Asymptotic spreading of interacting species with multiple fronts II: Exponentially decaying initial data","version":3},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-14T13:41:40.941834Z"},"links":{"citing_paper":"/paper/1908.05026"},"observation_digest":"sha256:9de3c8a7d1c038ca6c18b6c4fb6e4fa37588d7cd361bbfda1d43858fb6118378","observation_id":"18ef22eb-6d2b-4950-9ae4-e9040081d4a1","resolution":{"observed_at":"2026-08-14T13:41:41.491404Z","resolver_source":"doi","status":"verified_exact"},"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":"10.1002/cpa.20154","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:41:41.458830Z","title":"Liang, X.Q","venue":null,"work_id":"de56cafd-86ee-4a10-9724-7ec053c04c8b","year":2007},"citing_paper":{"arxiv_id":"1908.05026","last_updated":"2020-05-04T07:29:31Z","snapshot_observed_at":"2026-08-16T03:36:51.392763Z","submitted_at":"2019-08-14T09:05:57Z","title":"Asymptotic spreading of interacting species with multiple fronts II: Exponentially decaying initial data","version":3},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-14T13:41:40.948550Z"},"links":{"citing_paper":"/paper/1908.05026"},"observation_digest":"sha256:5495c32464163b82fe7baf7aaacca0b22aea9d1ec48b3bd87916e132f70395bf","observation_id":"8e69eb15-cbf0-474a-84b6-1dc4d3ccb635","resolution":{"observed_at":"2026-08-14T13:41:41.465440Z","resolver_source":"doi","status":"verified_exact"},"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":"10.1017/s0956792512000198","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:41:41.435113Z","title":"Lin, W.T","venue":null,"work_id":"a177a14f-b111-4b0f-8b21-6f9aa87e4a4f","year":2012},"citing_paper":{"arxiv_id":"1908.05026","last_updated":"2020-05-04T07:29:31Z","snapshot_observed_at":"2026-08-16T03:36:51.392763Z","submitted_at":"2019-08-14T09:05:57Z","title":"Asymptotic spreading of interacting species with multiple fronts II: Exponentially decaying initial data","version":3},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-14T13:41:40.956691Z"},"links":{"citing_paper":"/paper/1908.05026"},"observation_digest":"sha256:a89b342bed2209b30c7d2776840e7f32a528be7590e901f95cf672994a81821a","observation_id":"3055ad62-8033-4352-a05b-f51b2f3fb230","resolution":{"observed_at":"2026-08-14T13:41:41.442232Z","resolver_source":"doi","status":"verified_exact"},"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":"2026-08-14T13:41:43.666773Z","title":null,"venue":null,"work_id":"d8e29561-f88a-4fe6-8790-8196b62f21ac","year":1908},"citing_paper":{"arxiv_id":"1908.05026","last_updated":"2020-05-04T07:29:31Z","snapshot_observed_at":"2026-08-16T03:36:51.392763Z","submitted_at":"2019-08-14T09:05:57Z","title":"Asymptotic spreading of interacting species with multiple fronts II: Exponentially decaying initial data","version":3},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-14T13:41:40.964974Z"},"links":{"citing_paper":"/paper/1908.05026"},"observation_digest":"sha256:79b8a6e962767dadc487afc24b8eb0e36aeba9a653c8f80f8e446e3d1659606d","observation_id":"f3739ac5-5496-48d4-839c-18bc54353ac1","resolution":{"observed_at":"2026-08-14T13:41:43.673545Z","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":"10.1016/j.jde.2018.10.009","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:41:41.409040Z","title":"Liu, H.M","venue":null,"work_id":"757135c2-228f-498e-929f-baa849675c78","year":2019},"citing_paper":{"arxiv_id":"1908.05026","last_updated":"2020-05-04T07:29:31Z","snapshot_observed_at":"2026-08-16T03:36:51.392763Z","submitted_at":"2019-08-14T09:05:57Z","title":"Asymptotic spreading of interacting species with multiple fronts II: Exponentially decaying initial data","version":3},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-14T13:41:40.973940Z"},"links":{"citing_paper":"/paper/1908.05026"},"observation_digest":"sha256:322246ff3ee7ccbd515ec2a7454dfee8b31fba53ffc19cbf13947a0e412d7840","observation_id":"fb9ee8f4-db51-489a-a83c-ae0193d99493","resolution":{"observed_at":"2026-08-14T13:41:41.417679Z","resolver_source":"doi","status":"verified_exact"},"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":"2026-08-14T13:41:40.981956Z","title":"Lui, Biological growth and spread modeled by sys- tems of recursions, Math","venue":null,"work_id":null,"year":1989},"citing_paper":{"arxiv_id":"1908.05026","last_updated":"2020-05-04T07:29:31Z","snapshot_observed_at":"2026-08-16T03:36:51.392763Z","submitted_at":"2019-08-14T09:05:57Z","title":"Asymptotic spreading of interacting species with multiple fronts II: Exponentially decaying initial data","version":3},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-14T13:41:40.981956Z"},"links":{"citing_paper":"/paper/1908.05026"},"observation_digest":"sha256:98a0a8e5d130f8ffc4a0df190712aa010b26e48ac5451d4d4252bc486e8fa314","observation_id":"97e97a13-c884-4fa3-879b-d415da09a5e3","resolution":{"observed_at":"2026-08-14T13:41:40.981956Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:41:40.988562Z","title":"Mckean, Application of Brownian motion to the equa tion of Kolmogorov- Petrovskii-Piskunov, Commun","venue":null,"work_id":null,"year":1975},"citing_paper":{"arxiv_id":"1908.05026","last_updated":"2020-05-04T07:29:31Z","snapshot_observed_at":"2026-08-16T03:36:51.392763Z","submitted_at":"2019-08-14T09:05:57Z","title":"Asymptotic spreading of interacting species with multiple fronts II: Exponentially decaying initial data","version":3},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-14T13:41:40.988562Z"},"links":{"citing_paper":"/paper/1908.05026"},"observation_digest":"sha256:a88b3e02c29a8092c015a52e713435a9689913778bbabb2b44c7a1b252b79424","observation_id":"a9cc6e47-f47a-4aea-b99e-76848fc1b033","resolution":{"observed_at":"2026-08-14T13:41:40.988562Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.anihpc.2008.02.005","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:41:41.350951Z","title":"Nolen, J","venue":null,"work_id":"f8edd806-884b-4082-a519-13135b6fbe07","year":2008},"citing_paper":{"arxiv_id":"1908.05026","last_updated":"2020-05-04T07:29:31Z","snapshot_observed_at":"2026-08-16T03:36:51.392763Z","submitted_at":"2019-08-14T09:05:57Z","title":"Asymptotic spreading of interacting species with multiple fronts II: Exponentially decaying initial data","version":3},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-14T13:41:40.994261Z"},"links":{"citing_paper":"/paper/1908.05026"},"observation_digest":"sha256:496ae0cfdb55d312de8663e45fd8fe05992babfb936bdf7016dd881e81ef1c7f","observation_id":"73027db8-172a-4087-9f5b-36585b9a2176","resolution":{"observed_at":"2026-08-14T13:41:41.357850Z","resolver_source":"doi","status":"verified_exact"},"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":"2001.4088","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:41:42.371410Z","title":"Ostrov, Solutions of Hamilton-Jacobi equations a nd scalar conservation laws with discontinuous space-time dependence, J","venue":null,"work_id":"29b8dd01-ce38-4b0d-a8dc-7fee450b0642","year":2002},"citing_paper":{"arxiv_id":"1908.05026","last_updated":"2020-05-04T07:29:31Z","snapshot_observed_at":"2026-08-16T03:36:51.392763Z","submitted_at":"2019-08-14T09:05:57Z","title":"Asymptotic spreading of interacting species with multiple fronts II: Exponentially decaying initial data","version":3},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-14T13:41:41.001934Z"},"links":{"citing_paper":"/paper/1908.05026"},"observation_digest":"sha256:2fe1162ed1e6a93d442b7316084e2379fc5b49c1598f7d3893a83b9d65cd35df","observation_id":"b094a2ff-ff1f-4953-b9e5-e37c9d228faf","resolution":{"observed_at":"2026-08-14T13:41:42.380137Z","resolver_source":"raw_fallback","status":"verified_exact"},"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":"2026-08-14T13:41:41.007337Z","title":null,"venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"1908.05026","last_updated":"2020-05-04T07:29:31Z","snapshot_observed_at":"2026-08-16T03:36:51.392763Z","submitted_at":"2019-08-14T09:05:57Z","title":"Asymptotic spreading of interacting species with multiple fronts II: Exponentially decaying initial data","version":3},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-14T13:41:41.007337Z"},"links":{"citing_paper":"/paper/1908.05026"},"observation_digest":"sha256:c502df0a0c61016637fb8622974c23751960fdb6e41b4a7415162f9f3d6e45f0","observation_id":"9321f48d-2309-4a7a-a410-dd0bcf749ff6","resolution":{"observed_at":"2026-08-14T13:41:41.007337Z","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":"2026-08-14T13:41:43.649166Z","title":"Shigesada, K","venue":null,"work_id":"dc9bb242-900a-4d74-a511-92afba115ca1","year":1997},"citing_paper":{"arxiv_id":"1908.05026","last_updated":"2020-05-04T07:29:31Z","snapshot_observed_at":"2026-08-16T03:36:51.392763Z","submitted_at":"2019-08-14T09:05:57Z","title":"Asymptotic spreading of interacting species with multiple fronts II: Exponentially decaying initial data","version":3},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-14T13:41:41.013903Z"},"links":{"citing_paper":"/paper/1908.05026"},"observation_digest":"sha256:2ca952958b484114e5c7f291f62d018dd5e1e07f5b4af6a425eea251c129f73d","observation_id":"e9cf2dec-476d-4891-830d-055e680f8f09","resolution":{"observed_at":"2026-08-14T13:41:43.654621Z","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":"2026-08-14T13:41:43.632444Z","title":"Smith, Monotone Dynamical Systems: An Introducti on to the Theory of Competitive and Cooperative Systems, AMS, Providence, RI 1 995","venue":null,"work_id":"40c72b8f-8bb0-476f-9e86-3e66ec6d655e","year":null},"citing_paper":{"arxiv_id":"1908.05026","last_updated":"2020-05-04T07:29:31Z","snapshot_observed_at":"2026-08-16T03:36:51.392763Z","submitted_at":"2019-08-14T09:05:57Z","title":"Asymptotic spreading of interacting species with multiple fronts II: Exponentially decaying initial data","version":3},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-14T13:41:41.023674Z"},"links":{"citing_paper":"/paper/1908.05026"},"observation_digest":"sha256:828f9353c35ac4365f1f09b0dfc157e6b3c748053c874e098d2753695cebf9d4","observation_id":"8c515acc-10e7-4d92-8775-b64697ea6c88","resolution":{"observed_at":"2026-08-14T13:41:43.637969Z","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/bf00283257","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:41:41.306757Z","title":"Tang, P.C","venue":null,"work_id":"356500f1-c7ed-4fe3-b732-062499035991","year":1980},"citing_paper":{"arxiv_id":"1908.05026","last_updated":"2020-05-04T07:29:31Z","snapshot_observed_at":"2026-08-16T03:36:51.392763Z","submitted_at":"2019-08-14T09:05:57Z","title":"Asymptotic spreading of interacting species with multiple fronts II: Exponentially decaying initial data","version":3},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-14T13:41:41.032760Z"},"links":{"citing_paper":"/paper/1908.05026"},"observation_digest":"sha256:eedf82f176ba5f369f92221af69e2f2432f21f84b673cc7017b18601c9e4c534","observation_id":"a8ad889c-96f3-4d42-a9c8-47318085d769","resolution":{"observed_at":"2026-08-14T13:41:41.314135Z","resolver_source":"doi","status":"verified_exact"},"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/bf01396221","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:41:41.281732Z","title":"Tourin, A comparison theorem for a piecewise Lipschi tz continuous Hamilto- nian and application to Shape-from-Shading problems, Nume r","venue":null,"work_id":"579b9b07-efca-4537-85ff-e2eadacfeac7","year":1992},"citing_paper":{"arxiv_id":"1908.05026","last_updated":"2020-05-04T07:29:31Z","snapshot_observed_at":"2026-08-16T03:36:51.392763Z","submitted_at":"2019-08-14T09:05:57Z","title":"Asymptotic spreading of interacting species with multiple fronts II: Exponentially decaying initial data","version":3},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-14T13:41:41.041930Z"},"links":{"citing_paper":"/paper/1908.05026"},"observation_digest":"sha256:d1bbb3c17ec114183df20ea83b7c4c723b62e879226477f702fe3582a8137e24","observation_id":"1674448d-ed71-4e4c-af21-20cfbe9812e7","resolution":{"observed_at":"2026-08-14T13:41:41.288467Z","resolver_source":"doi","status":"verified_exact"},"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":"2026-08-14T13:41:43.613738Z","title":"Volpert, V.A","venue":null,"work_id":"aa2cea35-5c6f-476c-ad1a-04f2528f2d33","year":1994},"citing_paper":{"arxiv_id":"1908.05026","last_updated":"2020-05-04T07:29:31Z","snapshot_observed_at":"2026-08-16T03:36:51.392763Z","submitted_at":"2019-08-14T09:05:57Z","title":"Asymptotic spreading of interacting species with multiple fronts II: Exponentially decaying initial data","version":3},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-14T13:41:41.049293Z"},"links":{"citing_paper":"/paper/1908.05026"},"observation_digest":"sha256:3b7c24d05e527f8b80785395006816f065de5a41b333c52f232aa67afddb997c","observation_id":"0e0ce48f-033a-46dc-9691-f0a5b2482956","resolution":{"observed_at":"2026-08-14T13:41:43.619305Z","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":"10.1016/j.na.2017.01.005","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:41:41.257664Z","title":null,"venue":null,"work_id":"5ef907e4-8f60-4754-bff5-0233fe3c04e4","year":2017},"citing_paper":{"arxiv_id":"1908.05026","last_updated":"2020-05-04T07:29:31Z","snapshot_observed_at":"2026-08-16T03:36:51.392763Z","submitted_at":"2019-08-14T09:05:57Z","title":"Asymptotic spreading of interacting species with multiple fronts II: Exponentially decaying initial data","version":3},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-14T13:41:41.054663Z"},"links":{"citing_paper":"/paper/1908.05026"},"observation_digest":"sha256:1f4f9d3f898ee4da050e75ad4ad9d39174f9e1161290635b89023cb067d1700f","observation_id":"beb797ad-e5a2-41f0-9f15-4e4d32a0aba9","resolution":{"observed_at":"2026-08-14T13:41:41.265219Z","resolver_source":"doi","status":"verified_exact"},"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":"10.1016/j.jde.2017.11.027","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:41:41.235484Z","title":null,"venue":null,"work_id":"c2e98170-1190-4a8e-8e08-ccb88e20a701","year":2017},"citing_paper":{"arxiv_id":"1908.05026","last_updated":"2020-05-04T07:29:31Z","snapshot_observed_at":"2026-08-16T03:36:51.392763Z","submitted_at":"2019-08-14T09:05:57Z","title":"Asymptotic spreading of interacting species with multiple fronts II: Exponentially decaying initial data","version":3},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-14T13:41:41.062064Z"},"links":{"citing_paper":"/paper/1908.05026"},"observation_digest":"sha256:42de3f5f627b09bf7fe703510de16dd575fb6da74722f2687db748468d16ac14","observation_id":"9d84617a-1c04-4306-86cf-95033cfbcfe2","resolution":{"observed_at":"2026-08-14T13:41:41.242117Z","resolver_source":"doi","status":"verified_exact"},"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":"2026-08-14T13:41:41.067632Z","title":"Weinberger, Long-time behavior of a class of biolo gical models, SIAM J","venue":null,"work_id":null,"year":1982},"citing_paper":{"arxiv_id":"1908.05026","last_updated":"2020-05-04T07:29:31Z","snapshot_observed_at":"2026-08-16T03:36:51.392763Z","submitted_at":"2019-08-14T09:05:57Z","title":"Asymptotic spreading of interacting species with multiple fronts II: Exponentially decaying initial data","version":3},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-14T13:41:41.067632Z"},"links":{"citing_paper":"/paper/1908.05026"},"observation_digest":"sha256:48268447d71c18534308d466f3d6f5c98cc69f4d790468ca27f87567cbc1beb3","observation_id":"3005ef99-0217-4e20-870e-4acd09cec27f","resolution":{"observed_at":"2026-08-14T13:41:41.067632Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s00285-002-0169-3","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:41:41.194375Z","title":"Weinberger, On spreading speed and traveling wave s for growth and migration models in a periodic habitat, J","venue":null,"work_id":"3a42deb4-8383-4a19-a6ee-40378d8e25ba","year":null},"citing_paper":{"arxiv_id":"1908.05026","last_updated":"2020-05-04T07:29:31Z","snapshot_observed_at":"2026-08-16T03:36:51.392763Z","submitted_at":"2019-08-14T09:05:57Z","title":"Asymptotic spreading of interacting species with multiple fronts II: Exponentially decaying initial data","version":3},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-08-14T13:41:41.074520Z"},"links":{"citing_paper":"/paper/1908.05026"},"observation_digest":"sha256:ef84355a018f51eec900161918fc5a5c2fa7a92ed529e8c308711179a5a394c4","observation_id":"84dff25f-93a4-4a98-8b78-8a8db97f317a","resolution":{"observed_at":"2026-08-14T13:41:41.200809Z","resolver_source":"doi","status":"verified_exact"},"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/s002850200145","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:41:41.172473Z","title":"Weinberger, M.A","venue":null,"work_id":"0d9ef1ad-1776-4298-9dbe-b7f1f8bf7a0b","year":null},"citing_paper":{"arxiv_id":"1908.05026","last_updated":"2020-05-04T07:29:31Z","snapshot_observed_at":"2026-08-16T03:36:51.392763Z","submitted_at":"2019-08-14T09:05:57Z","title":"Asymptotic spreading of interacting species with multiple fronts II: Exponentially decaying initial data","version":3},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-08-14T13:41:41.083454Z"},"links":{"citing_paper":"/paper/1908.05026"},"observation_digest":"sha256:2e34a8faa508f83b7a54bb2b5e0308ecd6763f514423ba1408b59871333e918f","observation_id":"972eddfa-0ba5-4179-8348-09af5d88e94c","resolution":{"observed_at":"2026-08-14T13:41:41.179063Z","resolver_source":"doi","status":"verified_exact"},"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":"10.1016/j.jde.2015.02.021","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:41:41.142948Z","title":"Wu, The minimal habitat size for spreading in a weak competition sys- tem with two free boundaries, J","venue":null,"work_id":"b29e955d-c479-43b0-ad02-d10ae2775a9f","year":2015},"citing_paper":{"arxiv_id":"1908.05026","last_updated":"2020-05-04T07:29:31Z","snapshot_observed_at":"2026-08-16T03:36:51.392763Z","submitted_at":"2019-08-14T09:05:57Z","title":"Asymptotic spreading of interacting species with multiple fronts II: Exponentially decaying initial data","version":3},"reference_index":58,"source":"pdf_text","source_observed_at":"2026-08-14T13:41:41.091823Z"},"links":{"citing_paper":"/paper/1908.05026"},"observation_digest":"sha256:95129363a219d4d86520b17255574bd75464078c1254cafcb18c3c772a716208","observation_id":"4e22c6f2-7eb1-4211-af83-b57ccffae219","resolution":{"observed_at":"2026-08-14T13:41:41.151587Z","resolver_source":"doi","status":"verified_exact"},"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":"2026-08-14T13:41:40.873631Z","title":null,"venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"1908.05026","last_updated":"2020-05-04T07:29:31Z","snapshot_observed_at":"2026-08-16T03:36:51.392763Z","submitted_at":"2019-08-14T09:05:57Z","title":"Asymptotic spreading of interacting species with multiple fronts II: Exponentially decaying initial data","version":3},"reference_index":537,"source":"pdf_text","source_observed_at":"2026-08-14T13:41:40.873631Z"},"links":{"citing_paper":"/paper/1908.05026"},"observation_digest":"sha256:12db92e0aaecd3dc30a7323a2b1f29a7d155b8e7afca2b884d50be91300c6cb1","observation_id":"210389f0-bc55-46e0-8b78-8620bd9d4b65","resolution":{"observed_at":"2026-08-14T13:41:40.873631Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:41:40.846525Z","title":null,"venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"1908.05026","last_updated":"2020-05-04T07:29:31Z","snapshot_observed_at":"2026-08-16T03:36:51.392763Z","submitted_at":"2019-08-14T09:05:57Z","title":"Asymptotic spreading of interacting species with multiple fronts II: Exponentially decaying initial data","version":3},"reference_index":1785,"source":"pdf_text","source_observed_at":"2026-08-14T13:41:40.846525Z"},"links":{"citing_paper":"/paper/1908.05026"},"observation_digest":"sha256:16e4165fa237c6b6244b19adf6982e73686c77eeefb61216117f080ba48cfbcf","observation_id":"d6a7c49f-3605-4469-8372-14299e6fb9f2","resolution":{"observed_at":"2026-08-14T13:41:40.846525Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"1908.05026","last_updated":"2020-05-04T07:29:31Z","latest_version":3,"primary_category":"math.AP","snapshot_observed_at":"2026-08-16T03:36:51.392763Z","submitted_at":"2019-08-14T09:05:57Z","title":"Asymptotic spreading of interacting species with multiple fronts II: Exponentially decaying initial data"},"reference_resolution":{"displayed":60,"state_counts":{"malformed_identifier":2,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":16,"verified_exact":32,"verified_fuzzy":10},"total_outbound_references":60},"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 16 August 2026, this Paper Citation Record lists 60 of 60 outbound references and 0 inbound Pith citation observations for arXiv:1908.05026."}