{"as_of":"2026-08-17T15:35:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:292895ec499c18524c54782a3d4917ac1abfbc21710a5fd3bf987516eb8848d3","coverage":[{"denominator":27,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":27,"source":"paper_references, paper_reference_links","source_observed_at":"2026-07-14T12:08:40.947861Z","state":"measured"},{"denominator":28,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":28,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-17T06:30:58.91139+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-16T00:24:30.140289Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"pith","source_observed_at":"2026-08-16T00:24:30.679495Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2607.10384","last_updated":"2026-07-11T16:24:45Z","snapshot_observed_at":"2026-08-17T03:28:54.591116Z","submitted_at":"2026-07-11T16:24:45Z","title":"Stability and instability for the fully parabolic Keller-Segel system around constant equilibrium","version":1},"cited_work":{"arxiv_id":"2607.10384","doi":null,"metadata_source":"pith","pith_arxiv_id":"2607.10384","snapshot_observed_at":"2026-08-16T00:24:30.679495Z","title":"Stability and instability for the fully parabolic Keller-Segel system around constant equilibrium","venue":"math.AP","work_id":"c6b91a6b-e74c-42bb-9300-9b799f183445","year":2026},"citing_paper":{"arxiv_id":"2608.12226","last_updated":"2026-08-12T16:23:32Z","snapshot_observed_at":"2026-08-16T00:09:58.528511Z","submitted_at":"2026-08-12T16:23:32Z","title":"The traveling wave solutions of the 1D hyperbolic Keller-Segel equations","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-16T00:24:30.140289Z"},"links":{"cited_paper":"/paper/2607.10384","citing_paper":"/paper/2608.12226"},"observation_digest":"sha256:d9d386274e4336ae9dc7dcdaf693e0241bf26f8d081a582eac18277ec9d59b92","observation_id":"79744360-b27f-4057-be00-5d782e30397b","resolution":{"observed_at":"2026-08-16T00:24:30.686593Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2607.10384/citation-record","integrity":"/paper/2607.10384/integrity","json":"/paper/2607.10384/citation-record.json","paper":"/paper/2607.10384"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T12:08:40.947861Z","title":null,"venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2607.10384","last_updated":"2026-07-11T16:24:45Z","snapshot_observed_at":"2026-08-17T03:28:54.591116Z","submitted_at":"2026-07-11T16:24:45Z","title":"Stability and instability for the fully parabolic Keller-Segel system around constant equilibrium","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-07-14T12:08:40.947861Z"},"links":{"citing_paper":"/paper/2607.10384"},"observation_digest":"sha256:19f1968c51e4cb9da233bf88e3fd3b4bba1ace3e70f13e2d8ffe7b831f2ff9cd","observation_id":"7aa9dd86-81c2-49c8-908b-18bc123dd447","resolution":{"observed_at":"2026-07-14T12:08:40.947861Z","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":"2026-07-14T12:08:40.947861Z","title":"Bellomo, A","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2607.10384","last_updated":"2026-07-11T16:24:45Z","snapshot_observed_at":"2026-08-17T03:28:54.591116Z","submitted_at":"2026-07-11T16:24:45Z","title":"Stability and instability for the fully parabolic Keller-Segel system around constant equilibrium","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-07-14T12:08:40.947861Z"},"links":{"citing_paper":"/paper/2607.10384"},"observation_digest":"sha256:87787ab7e585ca0a488f55c98e6e170fc7067c39498c32c85001dc16c0292a7d","observation_id":"515a8f8d-95a9-47ce-819d-4f38ac3f1b83","resolution":{"observed_at":"2026-07-14T12:08:40.947861Z","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":"2026-07-14T12:08:40.947861Z","title":"Biler, Global solutions to some parabolic-elliptic systems of chemotaxis, Adv","venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2607.10384","last_updated":"2026-07-11T16:24:45Z","snapshot_observed_at":"2026-08-17T03:28:54.591116Z","submitted_at":"2026-07-11T16:24:45Z","title":"Stability and instability for the fully parabolic Keller-Segel system around constant equilibrium","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-07-14T12:08:40.947861Z"},"links":{"citing_paper":"/paper/2607.10384"},"observation_digest":"sha256:119d39bb8b285735055ae425639b27502fa1095b27541f89763df2571b060c1f","observation_id":"f95ddcdc-db09-42ae-8860-53d3cac53d0d","resolution":{"observed_at":"2026-07-14T12:08:40.947861Z","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":"2026-07-14T12:08:40.947861Z","title":"Biler, G","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2607.10384","last_updated":"2026-07-11T16:24:45Z","snapshot_observed_at":"2026-08-17T03:28:54.591116Z","submitted_at":"2026-07-11T16:24:45Z","title":"Stability and instability for the fully parabolic Keller-Segel system around constant equilibrium","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-07-14T12:08:40.947861Z"},"links":{"citing_paper":"/paper/2607.10384"},"observation_digest":"sha256:5cfcd95c3f575727169997617a179cebac045cf7111c6331a75928714c4bfc9d","observation_id":"e1ed3e3c-ee5c-41ac-893b-0fbe7e914a27","resolution":{"observed_at":"2026-07-14T12:08:40.947861Z","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":"2026-07-14T12:08:40.947861Z","title":"Blanchet, J.A","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2607.10384","last_updated":"2026-07-11T16:24:45Z","snapshot_observed_at":"2026-08-17T03:28:54.591116Z","submitted_at":"2026-07-11T16:24:45Z","title":"Stability and instability for the fully parabolic Keller-Segel system around constant equilibrium","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-07-14T12:08:40.947861Z"},"links":{"citing_paper":"/paper/2607.10384"},"observation_digest":"sha256:65b2a3382d56fa0ba163c55d7f29ef062159d996900b06b61ddfdefc208d41d9","observation_id":"745354bb-4231-455c-9a47-3a666ed84789","resolution":{"observed_at":"2026-07-14T12:08:40.947861Z","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":"2026-07-14T12:08:40.947861Z","title":"Blanchet, E","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2607.10384","last_updated":"2026-07-11T16:24:45Z","snapshot_observed_at":"2026-08-17T03:28:54.591116Z","submitted_at":"2026-07-11T16:24:45Z","title":"Stability and instability for the fully parabolic Keller-Segel system around constant equilibrium","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-07-14T12:08:40.947861Z"},"links":{"citing_paper":"/paper/2607.10384"},"observation_digest":"sha256:1e8de6ead4acfb56a83c70408d3cadcc5c7365a5fd1617010529b08ffd49372f","observation_id":"a533b2ba-9951-4eeb-9895-10e1b2824689","resolution":{"observed_at":"2026-07-14T12:08:40.947861Z","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":"2026-07-14T12:08:40.947861Z","title":"Blanchet, J","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2607.10384","last_updated":"2026-07-11T16:24:45Z","snapshot_observed_at":"2026-08-17T03:28:54.591116Z","submitted_at":"2026-07-11T16:24:45Z","title":"Stability and instability for the fully parabolic Keller-Segel system around constant equilibrium","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-07-14T12:08:40.947861Z"},"links":{"citing_paper":"/paper/2607.10384"},"observation_digest":"sha256:44dcb7428260ae997704872e633c3dccac5197872e4a775d1586fa0c103f3eba","observation_id":"c032ac42-dc39-49b0-a899-4299fe8d3e20","resolution":{"observed_at":"2026-07-14T12:08:40.947861Z","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":"2026-07-14T12:08:40.947861Z","title":null,"venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2607.10384","last_updated":"2026-07-11T16:24:45Z","snapshot_observed_at":"2026-08-17T03:28:54.591116Z","submitted_at":"2026-07-11T16:24:45Z","title":"Stability and instability for the fully parabolic Keller-Segel system around constant equilibrium","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-07-14T12:08:40.947861Z"},"links":{"citing_paper":"/paper/2607.10384"},"observation_digest":"sha256:c13309f07f2ae7938a6d9f804bc4dc22a4147e9c6a38d0e5bf850bcd0edde11a","observation_id":"af546093-3506-4c93-b4f2-b3803c8de099","resolution":{"observed_at":"2026-07-14T12:08:40.947861Z","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":"2026-07-14T12:08:40.947861Z","title":"Collot, T.-E","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.10384","last_updated":"2026-07-11T16:24:45Z","snapshot_observed_at":"2026-08-17T03:28:54.591116Z","submitted_at":"2026-07-11T16:24:45Z","title":"Stability and instability for the fully parabolic Keller-Segel system around constant equilibrium","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-07-14T12:08:40.947861Z"},"links":{"citing_paper":"/paper/2607.10384"},"observation_digest":"sha256:ee8b61b3ecd290853733429a9183ee4185dc252894c14bb58881b3fab8cfd447","observation_id":"db500bd5-e395-4558-b555-fc555939487e","resolution":{"observed_at":"2026-07-14T12:08:40.947861Z","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":"2026-07-14T12:08:40.947861Z","title":"Cygan, G","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.10384","last_updated":"2026-07-11T16:24:45Z","snapshot_observed_at":"2026-08-17T03:28:54.591116Z","submitted_at":"2026-07-11T16:24:45Z","title":"Stability and instability for the fully parabolic Keller-Segel system around constant equilibrium","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-07-14T12:08:40.947861Z"},"links":{"citing_paper":"/paper/2607.10384"},"observation_digest":"sha256:9c2fc3fd902d6cfc8ceef78616eb9389f568a4bc9476635a4ed65718ca48604c","observation_id":"142caa8f-e539-404e-8608-fe317b989a46","resolution":{"observed_at":"2026-07-14T12:08:40.947861Z","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":"2026-07-14T12:08:40.947861Z","title":"D´ avila, M","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.10384","last_updated":"2026-07-11T16:24:45Z","snapshot_observed_at":"2026-08-17T03:28:54.591116Z","submitted_at":"2026-07-11T16:24:45Z","title":"Stability and instability for the fully parabolic Keller-Segel system around constant equilibrium","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-07-14T12:08:40.947861Z"},"links":{"citing_paper":"/paper/2607.10384"},"observation_digest":"sha256:8889e17eae73102185feaf014152e359a86f8abff0e93a939fa78db3f030a1f2","observation_id":"d885b32b-7474-416b-85b1-94a5f9155c0d","resolution":{"observed_at":"2026-07-14T12:08:40.947861Z","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":"2026-07-14T12:08:40.947861Z","title":"Friedlander, N","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2607.10384","last_updated":"2026-07-11T16:24:45Z","snapshot_observed_at":"2026-08-17T03:28:54.591116Z","submitted_at":"2026-07-11T16:24:45Z","title":"Stability and instability for the fully parabolic Keller-Segel system around constant equilibrium","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-07-14T12:08:40.947861Z"},"links":{"citing_paper":"/paper/2607.10384"},"observation_digest":"sha256:3c6a53fc0fa160c62f60f6776d9b3be7de95056e6dc05ae9efa07c321712b571","observation_id":"0c3f2922-c057-4986-b757-158b5738c5fe","resolution":{"observed_at":"2026-07-14T12:08:40.947861Z","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":"2026-07-14T12:08:40.947861Z","title":"Glogi´ c, B","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.10384","last_updated":"2026-07-11T16:24:45Z","snapshot_observed_at":"2026-08-17T03:28:54.591116Z","submitted_at":"2026-07-11T16:24:45Z","title":"Stability and instability for the fully parabolic Keller-Segel system around constant equilibrium","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-07-14T12:08:40.947861Z"},"links":{"citing_paper":"/paper/2607.10384"},"observation_digest":"sha256:8b95795bd07b777cd1a90cea36f5d4f51af9f0df2df04405c0b4fc584c14a3d6","observation_id":"c6beb2aa-d0bf-4d48-9dac-44c7d19b509f","resolution":{"observed_at":"2026-07-14T12:08:40.947861Z","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":"2026-07-14T12:08:40.947861Z","title":"Guo, H.-J","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2607.10384","last_updated":"2026-07-11T16:24:45Z","snapshot_observed_at":"2026-08-17T03:28:54.591116Z","submitted_at":"2026-07-11T16:24:45Z","title":"Stability and instability for the fully parabolic Keller-Segel system around constant equilibrium","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-07-14T12:08:40.947861Z"},"links":{"citing_paper":"/paper/2607.10384"},"observation_digest":"sha256:ecbffff48d6c654d0bb5b5e65b632fe4706988346969035b23082661ce6d96e5","observation_id":"3da21979-8b65-43ee-842d-712bac78994d","resolution":{"observed_at":"2026-07-14T12:08:40.947861Z","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":"2026-07-14T12:08:40.947861Z","title":null,"venue":null,"work_id":null,"year":1970},"citing_paper":{"arxiv_id":"2607.10384","last_updated":"2026-07-11T16:24:45Z","snapshot_observed_at":"2026-08-17T03:28:54.591116Z","submitted_at":"2026-07-11T16:24:45Z","title":"Stability and instability for the fully parabolic Keller-Segel system around constant equilibrium","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-07-14T12:08:40.947861Z"},"links":{"citing_paper":"/paper/2607.10384"},"observation_digest":"sha256:cf5b06582c2392963aad1138e33185b73b3902738f1097f44f63863f849f25b5","observation_id":"852efcae-470f-4dd0-becf-872486bf2c9e","resolution":{"observed_at":"2026-07-14T12:08:40.947861Z","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":"2026-07-14T12:08:40.947861Z","title":"L´ opez-G´ omez, T","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2607.10384","last_updated":"2026-07-11T16:24:45Z","snapshot_observed_at":"2026-08-17T03:28:54.591116Z","submitted_at":"2026-07-11T16:24:45Z","title":"Stability and instability for the fully parabolic Keller-Segel system around constant equilibrium","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-07-14T12:08:40.947861Z"},"links":{"citing_paper":"/paper/2607.10384"},"observation_digest":"sha256:ed2645f12bd2f10ef2305c7c821b17b4a18442c0d3982b190878a74c2b742853","observation_id":"56d31475-92e6-4c14-9d47-fd959eb06278","resolution":{"observed_at":"2026-07-14T12:08:40.947861Z","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":"2026-07-14T12:08:40.947861Z","title":"Majda, A","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2607.10384","last_updated":"2026-07-11T16:24:45Z","snapshot_observed_at":"2026-08-17T03:28:54.591116Z","submitted_at":"2026-07-11T16:24:45Z","title":"Stability and instability for the fully parabolic Keller-Segel system around constant equilibrium","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-07-14T12:08:40.947861Z"},"links":{"citing_paper":"/paper/2607.10384"},"observation_digest":"sha256:c3134ff77ebde9709ba3a1a50e17fccb136543508791e782ec532288c03cbace","observation_id":"045c8c40-94c5-45ce-9e64-071dad78b95b","resolution":{"observed_at":"2026-07-14T12:08:40.947861Z","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":"2026-07-14T12:08:40.947861Z","title":"Mizoguchi, Type II blowup in a doubly parabolic Keller–Segel system in two dimensions, J","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2607.10384","last_updated":"2026-07-11T16:24:45Z","snapshot_observed_at":"2026-08-17T03:28:54.591116Z","submitted_at":"2026-07-11T16:24:45Z","title":"Stability and instability for the fully parabolic Keller-Segel system around constant equilibrium","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-07-14T12:08:40.947861Z"},"links":{"citing_paper":"/paper/2607.10384"},"observation_digest":"sha256:c98442295d01d3b1daaba85a837bbf082697239b2d6f5f29e4e03e6a8b8391dd","observation_id":"4d382dc5-95b5-4ea5-8812-306fbe1ba7dc","resolution":{"observed_at":"2026-07-14T12:08:40.947861Z","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":"2026-07-14T12:08:40.947861Z","title":"Mizoguchi, Determination of blowup type in the parabolic–parabolic Keller–Segel system, Math","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.10384","last_updated":"2026-07-11T16:24:45Z","snapshot_observed_at":"2026-08-17T03:28:54.591116Z","submitted_at":"2026-07-11T16:24:45Z","title":"Stability and instability for the fully parabolic Keller-Segel system around constant equilibrium","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-07-14T12:08:40.947861Z"},"links":{"citing_paper":"/paper/2607.10384"},"observation_digest":"sha256:e367061e4ee7ead441a5b4ec2bb5d9917caa3ae8086938825accdd281b30214e","observation_id":"34446b4c-9dfc-4fc3-bf7b-179d144e166b","resolution":{"observed_at":"2026-07-14T12:08:40.947861Z","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":"2026-07-14T12:08:40.947861Z","title":"Mizoguchi, Finite-time blowup in Cauchy problem of parabolic-parabolic chemotaxis system, J","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.10384","last_updated":"2026-07-11T16:24:45Z","snapshot_observed_at":"2026-08-17T03:28:54.591116Z","submitted_at":"2026-07-11T16:24:45Z","title":"Stability and instability for the fully parabolic Keller-Segel system around constant equilibrium","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-07-14T12:08:40.947861Z"},"links":{"citing_paper":"/paper/2607.10384"},"observation_digest":"sha256:97d38d6427b5685a07fa931e2990b8618951330f100ade938a62e202678bbc49","observation_id":"77961f8b-6058-46e3-a1e1-96cec2e047cc","resolution":{"observed_at":"2026-07-14T12:08:40.947861Z","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":"2026-07-14T12:08:40.947861Z","title":"Osaki, A","venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2607.10384","last_updated":"2026-07-11T16:24:45Z","snapshot_observed_at":"2026-08-17T03:28:54.591116Z","submitted_at":"2026-07-11T16:24:45Z","title":"Stability and instability for the fully parabolic Keller-Segel system around constant equilibrium","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-07-14T12:08:40.947861Z"},"links":{"citing_paper":"/paper/2607.10384"},"observation_digest":"sha256:9bdd4e28c04431fb6546b068cfc67f6ddbdbcd280f610f15e6bb97cba031c96e","observation_id":"6913a7ec-01d9-4bd9-aaf8-c5055e20db0f","resolution":{"observed_at":"2026-07-14T12:08:40.947861Z","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":"2026-07-14T12:08:40.947861Z","title":"Rapha¨ el, R","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2607.10384","last_updated":"2026-07-11T16:24:45Z","snapshot_observed_at":"2026-08-17T03:28:54.591116Z","submitted_at":"2026-07-11T16:24:45Z","title":"Stability and instability for the fully parabolic Keller-Segel system around constant equilibrium","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-07-14T12:08:40.947861Z"},"links":{"citing_paper":"/paper/2607.10384"},"observation_digest":"sha256:5234ee13c38a92b3d069cd92f14cad6269d9d4c9d0c1cf631a5dfa48da767f51","observation_id":"2b9de251-5cc1-4f04-925a-09e174c6a4d1","resolution":{"observed_at":"2026-07-14T12:08:40.947861Z","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":"2026-07-14T12:08:40.947861Z","title":"Schaaf, Stationary solutions of chemotaxis systems, Trans","venue":null,"work_id":null,"year":1985},"citing_paper":{"arxiv_id":"2607.10384","last_updated":"2026-07-11T16:24:45Z","snapshot_observed_at":"2026-08-17T03:28:54.591116Z","submitted_at":"2026-07-11T16:24:45Z","title":"Stability and instability for the fully parabolic Keller-Segel system around constant equilibrium","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-07-14T12:08:40.947861Z"},"links":{"citing_paper":"/paper/2607.10384"},"observation_digest":"sha256:f8b63b0483c3b0e563c518b69217e0603ecc14a80c9d88e63a3463ab4a3e2f46","observation_id":"fb76cf32-f787-4c9e-918b-d6093926344a","resolution":{"observed_at":"2026-07-14T12:08:40.947861Z","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":"2026-07-14T12:08:40.947861Z","title":null,"venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2607.10384","last_updated":"2026-07-11T16:24:45Z","snapshot_observed_at":"2026-08-17T03:28:54.591116Z","submitted_at":"2026-07-11T16:24:45Z","title":"Stability and instability for the fully parabolic Keller-Segel system around constant equilibrium","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-07-14T12:08:40.947861Z"},"links":{"citing_paper":"/paper/2607.10384"},"observation_digest":"sha256:a1b46de29e36de5e8f3dd413dedb210086d59ec8d3420f6d145d6047ad3597c9","observation_id":"13d8b01f-7ade-4188-a8b7-ca6a746ac836","resolution":{"observed_at":"2026-07-14T12:08:40.947861Z","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":"2026-07-14T12:08:40.947861Z","title":"Winkler, Aggregation vs","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2607.10384","last_updated":"2026-07-11T16:24:45Z","snapshot_observed_at":"2026-08-17T03:28:54.591116Z","submitted_at":"2026-07-11T16:24:45Z","title":"Stability and instability for the fully parabolic Keller-Segel system around constant equilibrium","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-07-14T12:08:40.947861Z"},"links":{"citing_paper":"/paper/2607.10384"},"observation_digest":"sha256:5418c6daf1931483811c49e91e0072b0f5e4e5c080e3d71fbd302f399417e752","observation_id":"1de1c34e-8b55-4326-b74c-5387d5a4dd4a","resolution":{"observed_at":"2026-07-14T12:08:40.947861Z","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":"2026-07-14T12:08:40.947861Z","title":"Winkler, Finite-time blow-up in the higher-dimensional parabolic-parabolic Keller-Segel system","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2607.10384","last_updated":"2026-07-11T16:24:45Z","snapshot_observed_at":"2026-08-17T03:28:54.591116Z","submitted_at":"2026-07-11T16:24:45Z","title":"Stability and instability for the fully parabolic Keller-Segel system around constant equilibrium","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-07-14T12:08:40.947861Z"},"links":{"citing_paper":"/paper/2607.10384"},"observation_digest":"sha256:9364b5d837c120803c7a6151c2f64bb1e3a26a5e398e4fe787754539e030bca1","observation_id":"f347f78f-cba6-48f4-8b9b-e2ac477d2c70","resolution":{"observed_at":"2026-07-14T12:08:40.947861Z","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":"2026-07-14T12:08:40.947861Z","title":"Winkler, How unstable is spatial homogeneity in Keller-Segel systems? A new critical mass phe- nomenon in two- and higher-dimensional parabolic-elliptic cases","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.10384","last_updated":"2026-07-11T16:24:45Z","snapshot_observed_at":"2026-08-17T03:28:54.591116Z","submitted_at":"2026-07-11T16:24:45Z","title":"Stability and instability for the fully parabolic Keller-Segel system around constant equilibrium","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-07-14T12:08:40.947861Z"},"links":{"citing_paper":"/paper/2607.10384"},"observation_digest":"sha256:290f6d722bc789011530e3854023e8e4f1e269dba86de484ae517e1fa96ff2d8","observation_id":"add6882c-f27a-48d7-961c-ab74ab4a5229","resolution":{"observed_at":"2026-07-14T12:08:40.947861Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.10384","last_updated":"2026-07-11T16:24:45Z","latest_version":1,"primary_category":"math.AP","snapshot_observed_at":"2026-08-17T03:28:54.591116Z","submitted_at":"2026-07-11T16:24:45Z","title":"Stability and instability for the fully parabolic Keller-Segel system around constant equilibrium"},"reference_resolution":{"displayed":27,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":27,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":27},"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":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"thesis":"As of 17 August 2026, this Paper Citation Record lists 27 of 27 outbound references and 1 inbound Pith citation observation for arXiv:2607.10384."}