{"as_of":"2026-08-22T02:59:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:821426c4b1bffb8531223fb8da226a9a13f0e7f5f6fb5cc7b2803018986e10b0","coverage":[{"denominator":57,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":57,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T04:19:16.525307Z","state":"measured"},{"denominator":57,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":57,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-21T06:32:19.484+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/2506.11757/citation-record","integrity":"/paper/2506.11757/integrity","json":"/paper/2506.11757/citation-record.json","paper":"/paper/2506.11757"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T04:19:32.591161Z","title":null,"venue":null,"work_id":"61f791b7-df05-4621-8c04-a26a637bd86a","year":2012},"citing_paper":{"arxiv_id":"2506.11757","last_updated":"2026-06-07T09:15:53Z","snapshot_observed_at":"2026-08-13T01:56:15.666139Z","submitted_at":"2025-06-13T13:12:33Z","title":"Hele-Shaw limit of chemotaxis-Navier-Stokes flows","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-07T04:19:09.027382Z"},"links":{"citing_paper":"/paper/2506.11757"},"observation_digest":"sha256:6d52f6c92621c21ab92087f6337f34527bc50405cfd4375f8ab39addcf5def2c","observation_id":"a4e61185-6dc0-4bf3-8c7a-3af7d9aba2ba","resolution":{"observed_at":"2026-08-07T04:19:32.670733Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-07T04:19:32.204295Z","title":null,"venue":null,"work_id":"96f6cfc0-784e-461b-966f-b1a6b9462a9d","year":2023},"citing_paper":{"arxiv_id":"2506.11757","last_updated":"2026-06-07T09:15:53Z","snapshot_observed_at":"2026-08-13T01:56:15.666139Z","submitted_at":"2025-06-13T13:12:33Z","title":"Hele-Shaw limit of chemotaxis-Navier-Stokes flows","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-07T04:19:09.148127Z"},"links":{"citing_paper":"/paper/2506.11757"},"observation_digest":"sha256:fbbd9d133d808e66883c9430f3311b5a896fc0fe0927d9ac6a051e465a5eb7db","observation_id":"93609f8d-e783-4ddd-903e-f79a3e5d2950","resolution":{"observed_at":"2026-08-07T04:19:32.378616Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-07T04:19:31.927245Z","title":null,"venue":null,"work_id":"910c68fe-09da-44fa-89a6-97d4d1ee5bc6","year":2013},"citing_paper":{"arxiv_id":"2506.11757","last_updated":"2026-06-07T09:15:53Z","snapshot_observed_at":"2026-08-13T01:56:15.666139Z","submitted_at":"2025-06-13T13:12:33Z","title":"Hele-Shaw limit of chemotaxis-Navier-Stokes flows","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-07T04:19:09.283202Z"},"links":{"citing_paper":"/paper/2506.11757"},"observation_digest":"sha256:f4225c944109279af8e861a3e336d800a6b7cad4071f6fa09cea4ff655d0f5a2","observation_id":"af41a4a2-b2e7-48f3-8417-427e77a50b38","resolution":{"observed_at":"2026-08-07T04:19:32.025826Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-07T04:19:31.803262Z","title":null,"venue":null,"work_id":"b82bbf02-fae1-4a64-be76-4239208922cd","year":2014},"citing_paper":{"arxiv_id":"2506.11757","last_updated":"2026-06-07T09:15:53Z","snapshot_observed_at":"2026-08-13T01:56:15.666139Z","submitted_at":"2025-06-13T13:12:33Z","title":"Hele-Shaw limit of chemotaxis-Navier-Stokes flows","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-07T04:19:09.354795Z"},"links":{"citing_paper":"/paper/2506.11757"},"observation_digest":"sha256:ee00c6ef1de1411b31b0c9161b44803fd9f203468700f65e69076350224df2a5","observation_id":"56126fbf-ced1-41e1-8642-c7b2438a4e05","resolution":{"observed_at":"2026-08-07T04:19:31.859118Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-07T04:19:31.627568Z","title":"Craig, I","venue":null,"work_id":"fbef2011-c165-4313-9289-cae177c6275f","year":2018},"citing_paper":{"arxiv_id":"2506.11757","last_updated":"2026-06-07T09:15:53Z","snapshot_observed_at":"2026-08-13T01:56:15.666139Z","submitted_at":"2025-06-13T13:12:33Z","title":"Hele-Shaw limit of chemotaxis-Navier-Stokes flows","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-07T04:19:09.436832Z"},"links":{"citing_paper":"/paper/2506.11757"},"observation_digest":"sha256:896990fa22eef3fead0e798c0fce3d303db532876649ce08de01e94ee5aef655","observation_id":"db17da69-4be2-48b5-86ef-fb4374693060","resolution":{"observed_at":"2026-08-07T04:19:31.733799Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-07T04:19:31.421082Z","title":null,"venue":null,"work_id":"32386f51-c976-4fff-ba6a-f71887bde2b8","year":2023},"citing_paper":{"arxiv_id":"2506.11757","last_updated":"2026-06-07T09:15:53Z","snapshot_observed_at":"2026-08-13T01:56:15.666139Z","submitted_at":"2025-06-13T13:12:33Z","title":"Hele-Shaw limit of chemotaxis-Navier-Stokes flows","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-07T04:19:09.528776Z"},"links":{"citing_paper":"/paper/2506.11757"},"observation_digest":"sha256:2d38516176c98b6230eeff0bee05b651715a088b2743c03120fb7ba50ded3c92","observation_id":"16e77398-1eaf-47ef-9ca1-0da13f42e3a0","resolution":{"observed_at":"2026-08-07T04:19:31.560532Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-07T04:19:31.257378Z","title":"David, T","venue":null,"work_id":"07ee1371-9da6-4eb6-bb2e-e303bd5da8db","year":2023},"citing_paper":{"arxiv_id":"2506.11757","last_updated":"2026-06-07T09:15:53Z","snapshot_observed_at":"2026-08-13T01:56:15.666139Z","submitted_at":"2025-06-13T13:12:33Z","title":"Hele-Shaw limit of chemotaxis-Navier-Stokes flows","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-07T04:19:09.619933Z"},"links":{"citing_paper":"/paper/2506.11757"},"observation_digest":"sha256:7cdf7fa7f21fc7b178be522c3152e4ca8d807e806ff533109ff99e257ef01f11","observation_id":"f913ebf2-4a20-42bb-9e88-01ed14840a1c","resolution":{"observed_at":"2026-08-07T04:19:31.330388Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2405.07227","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T04:19:18.228995Z","title":"David, A","venue":null,"work_id":"be67bb8f-71a5-41ed-a520-692fa1b7720c","year":2024},"citing_paper":{"arxiv_id":"2506.11757","last_updated":"2026-06-07T09:15:53Z","snapshot_observed_at":"2026-08-13T01:56:15.666139Z","submitted_at":"2025-06-13T13:12:33Z","title":"Hele-Shaw limit of chemotaxis-Navier-Stokes flows","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-07T04:19:09.679879Z"},"links":{"citing_paper":"/paper/2506.11757"},"observation_digest":"sha256:2586cc43ae7e43adc054f647adc35eba700e9fd6b4a2a89c12aa400e028b9da0","observation_id":"fb6527c8-dc9b-409c-845d-3bae197c0944","resolution":{"observed_at":"2026-08-07T04:19:18.323782Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-07T04:19:31.109936Z","title":"David and B","venue":null,"work_id":"0593c869-0b33-48fa-8f6a-e505a633d639","year":2021},"citing_paper":{"arxiv_id":"2506.11757","last_updated":"2026-06-07T09:15:53Z","snapshot_observed_at":"2026-08-13T01:56:15.666139Z","submitted_at":"2025-06-13T13:12:33Z","title":"Hele-Shaw limit of chemotaxis-Navier-Stokes flows","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-07T04:19:09.776048Z"},"links":{"citing_paper":"/paper/2506.11757"},"observation_digest":"sha256:3504a4a7ad19310f897002f510f04f45624632474c7a6d493004641e6d5f2449","observation_id":"e90bfae3-029b-4357-a6dd-d46a01d25b25","resolution":{"observed_at":"2026-08-07T04:19:31.172478Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-07T04:19:09.913439Z","title":"David and M","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2506.11757","last_updated":"2026-06-07T09:15:53Z","snapshot_observed_at":"2026-08-13T01:56:15.666139Z","submitted_at":"2025-06-13T13:12:33Z","title":"Hele-Shaw limit of chemotaxis-Navier-Stokes flows","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-07T04:19:09.913439Z"},"links":{"citing_paper":"/paper/2506.11757"},"observation_digest":"sha256:4c42ab3b8cd48cdab82ccc69256fcf04eae5ae5f1c9be2c6e753a333dcd7a8e6","observation_id":"7c2b3287-733d-4626-9b37-111274cf07c0","resolution":{"observed_at":"2026-08-07T04:19:09.913439Z","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":"2026-08-07T04:19:30.854375Z","title":"Debiec, B","venue":null,"work_id":"03f09e90-38f2-45c5-b899-2063b185415f","year":2021},"citing_paper":{"arxiv_id":"2506.11757","last_updated":"2026-06-07T09:15:53Z","snapshot_observed_at":"2026-08-13T01:56:15.666139Z","submitted_at":"2025-06-13T13:12:33Z","title":"Hele-Shaw limit of chemotaxis-Navier-Stokes flows","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-07T04:19:09.981012Z"},"links":{"citing_paper":"/paper/2506.11757"},"observation_digest":"sha256:947ce8952638097520c0a3a1f963a0c86034ab8908a9234126a8f7f3e2e87d9d","observation_id":"39d91e7b-2c73-4daf-a1f5-9368ec7f6043","resolution":{"observed_at":"2026-08-07T04:19:30.997173Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-07T04:19:30.551489Z","title":"Debiec and M","venue":null,"work_id":"8595f09f-0a80-4c0a-b14d-2c90bd5133d5","year":2020},"citing_paper":{"arxiv_id":"2506.11757","last_updated":"2026-06-07T09:15:53Z","snapshot_observed_at":"2026-08-13T01:56:15.666139Z","submitted_at":"2025-06-13T13:12:33Z","title":"Hele-Shaw limit of chemotaxis-Navier-Stokes flows","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-07T04:19:10.066344Z"},"links":{"citing_paper":"/paper/2506.11757"},"observation_digest":"sha256:65629167f54f1e0e33b7ef55c7b284d2a3301a2ff706326f4b70680a82f1ac94","observation_id":"ec91432d-d021-419b-9728-a444360f058e","resolution":{"observed_at":"2026-08-07T04:19:30.729246Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-07T04:19:30.242460Z","title":"Di Francesco, A","venue":null,"work_id":"a72fa40d-c284-440c-aeee-52f431413279","year":2010},"citing_paper":{"arxiv_id":"2506.11757","last_updated":"2026-06-07T09:15:53Z","snapshot_observed_at":"2026-08-13T01:56:15.666139Z","submitted_at":"2025-06-13T13:12:33Z","title":"Hele-Shaw limit of chemotaxis-Navier-Stokes flows","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-07T04:19:10.126017Z"},"links":{"citing_paper":"/paper/2506.11757"},"observation_digest":"sha256:ab2f36db4eba97222a4c3ed19dfe3ec59119ae50dac676ebdf8cc5df1fc5b9a0","observation_id":"c74e703a-dec0-4eed-80d9-976a8b224abc","resolution":{"observed_at":"2026-08-07T04:19:30.379083Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-07T04:19:29.959944Z","title":"Dolbeault and G","venue":null,"work_id":"8fef0eed-3b03-4a04-8094-72230799755f","year":2014},"citing_paper":{"arxiv_id":"2506.11757","last_updated":"2026-06-07T09:15:53Z","snapshot_observed_at":"2026-08-13T01:56:15.666139Z","submitted_at":"2025-06-13T13:12:33Z","title":"Hele-Shaw limit of chemotaxis-Navier-Stokes flows","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-07T04:19:10.216494Z"},"links":{"citing_paper":"/paper/2506.11757"},"observation_digest":"sha256:dcb7af68994b7937cdd1e06687a954bd1c9c3224331f4c62890ecca8fb784af0","observation_id":"e13471f9-a190-4ce4-b3ec-d6c22f8b805f","resolution":{"observed_at":"2026-08-07T04:19:30.109501Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-07T04:19:29.636955Z","title":null,"venue":null,"work_id":"0bde4ee0-70ce-4be9-a310-ebffb65d80af","year":2017},"citing_paper":{"arxiv_id":"2506.11757","last_updated":"2026-06-07T09:15:53Z","snapshot_observed_at":"2026-08-13T01:56:15.666139Z","submitted_at":"2025-06-13T13:12:33Z","title":"Hele-Shaw limit of chemotaxis-Navier-Stokes flows","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-07T04:19:10.312940Z"},"links":{"citing_paper":"/paper/2506.11757"},"observation_digest":"sha256:c42dece5928c615663328df5b3805f06b82d138cbd300726748af117ff92719f","observation_id":"18c9103b-6359-47e4-ae50-e834ec4a6fb0","resolution":{"observed_at":"2026-08-07T04:19:29.763600Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-07T04:19:29.448124Z","title":null,"venue":null,"work_id":"10e22d25-ecfe-4cda-b169-db48c08637c5","year":2010},"citing_paper":{"arxiv_id":"2506.11757","last_updated":"2026-06-07T09:15:53Z","snapshot_observed_at":"2026-08-13T01:56:15.666139Z","submitted_at":"2025-06-13T13:12:33Z","title":"Hele-Shaw limit of chemotaxis-Navier-Stokes flows","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-07T04:19:10.413649Z"},"links":{"citing_paper":"/paper/2506.11757"},"observation_digest":"sha256:c9b7339734af8a8d13a43e4c3526a28bcc4438caafdfcfff292b6bb3f66a31e5","observation_id":"a45e9c48-b4c3-4180-8704-586c24a90c37","resolution":{"observed_at":"2026-08-07T04:19:29.520356Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-07T04:19:29.248828Z","title":"Duan and Z","venue":null,"work_id":"db10f9b5-df54-4013-a400-59627bb38043","year":2014},"citing_paper":{"arxiv_id":"2506.11757","last_updated":"2026-06-07T09:15:53Z","snapshot_observed_at":"2026-08-13T01:56:15.666139Z","submitted_at":"2025-06-13T13:12:33Z","title":"Hele-Shaw limit of chemotaxis-Navier-Stokes flows","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-07T04:19:10.503868Z"},"links":{"citing_paper":"/paper/2506.11757"},"observation_digest":"sha256:06efe208eb0571dd90a18a8fd0db75566b4ee06ee0f5f6d631c95ce38fe58c45","observation_id":"a41ec3d0-5acd-421b-a203-fe761cefae77","resolution":{"observed_at":"2026-08-07T04:19:29.327547Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-07T04:19:29.024030Z","title":null,"venue":null,"work_id":"c1342113-b3bc-465a-8e0a-3c1f8e2431c9","year":1965},"citing_paper":{"arxiv_id":"2506.11757","last_updated":"2026-06-07T09:15:53Z","snapshot_observed_at":"2026-08-13T01:56:15.666139Z","submitted_at":"2025-06-13T13:12:33Z","title":"Hele-Shaw limit of chemotaxis-Navier-Stokes flows","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-07T04:19:10.585714Z"},"links":{"citing_paper":"/paper/2506.11757"},"observation_digest":"sha256:490e05585a4c013e2e28c29533b7ccaa392cc8d6d29af39d6b907555ee11cd64","observation_id":"775d3cd0-0e33-43d7-aa38-8d1a8e0dbb27","resolution":{"observed_at":"2026-08-07T04:19:29.101308Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2404.16353","last_updated":"2025-05-10T12:45:20Z","snapshot_observed_at":"2026-08-18T14:45:41.307464Z","submitted_at":"2024-04-25T06:11:59Z","title":"Nonsymmetric traveling wave solution to a Hele-Shaw type tumor growth model","version":2},"cited_work":{"arxiv_id":"2404.16353","doi":null,"metadata_source":"pith","pith_arxiv_id":"2404.16353","snapshot_observed_at":"2026-08-07T04:19:17.754827Z","title":"Nonsymmetric traveling wave solution to a Hele-Shaw type tumor growth model","venue":"math.AP","work_id":"2d9b51ec-dcf1-4466-808a-9e36ef7a993d","year":2024},"citing_paper":{"arxiv_id":"2506.11757","last_updated":"2026-06-07T09:15:53Z","snapshot_observed_at":"2026-08-13T01:56:15.666139Z","submitted_at":"2025-06-13T13:12:33Z","title":"Hele-Shaw limit of chemotaxis-Navier-Stokes flows","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-07T04:19:10.662841Z"},"links":{"cited_paper":"/paper/2404.16353","citing_paper":"/paper/2506.11757"},"observation_digest":"sha256:594fbafb2723a7bf84e7025dd2f51f6146ff80997651f4b8be1c21c3d07925a3","observation_id":"4478fd0a-bac4-4116-8c37-df960dee06fd","resolution":{"observed_at":"2026-08-07T04:19:17.985678Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-07T04:19:28.740097Z","title":"Gilbarg and N","venue":null,"work_id":"9d73d383-bf21-46af-b3a0-b1773468db05","year":1983},"citing_paper":{"arxiv_id":"2506.11757","last_updated":"2026-06-07T09:15:53Z","snapshot_observed_at":"2026-08-13T01:56:15.666139Z","submitted_at":"2025-06-13T13:12:33Z","title":"Hele-Shaw limit of chemotaxis-Navier-Stokes flows","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-07T04:19:10.758560Z"},"links":{"citing_paper":"/paper/2506.11757"},"observation_digest":"sha256:742c4d19d656503466f509ccc9c59617fcc36865a3200f9aa5818a6a609d0365","observation_id":"ee994219-30f8-4bff-bc4f-a6324630b078","resolution":{"observed_at":"2026-08-07T04:19:28.914519Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-07T04:19:28.438779Z","title":"Guillen, I","venue":null,"work_id":"55e6b4bb-52a7-4992-bf1e-ce33ab1fc13f","year":2022},"citing_paper":{"arxiv_id":"2506.11757","last_updated":"2026-06-07T09:15:53Z","snapshot_observed_at":"2026-08-13T01:56:15.666139Z","submitted_at":"2025-06-13T13:12:33Z","title":"Hele-Shaw limit of chemotaxis-Navier-Stokes flows","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-07T04:19:10.857652Z"},"links":{"citing_paper":"/paper/2506.11757"},"observation_digest":"sha256:1f6fbf83368890f0daca441e26a7e060f553161ea5c3e31494cc97e46361a938","observation_id":"a0a528f8-5fef-46dd-8dff-758587936e7a","resolution":{"observed_at":"2026-08-07T04:19:28.585794Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2312.16869","last_updated":"2023-12-28T07:39:06Z","snapshot_observed_at":"2026-08-21T14:51:01.446002Z","submitted_at":"2023-12-28T07:39:06Z","title":"Incompressible limit of porous media equation with chemotaxis and growth","version":1},"cited_work":{"arxiv_id":"2312.16869","doi":null,"metadata_source":"pith","pith_arxiv_id":"2312.16869","snapshot_observed_at":"2026-08-07T04:19:17.437870Z","title":"Incompressible limit of porous media equation with chemotaxis and growth","venue":"math.AP","work_id":"b2df974e-cc56-41cc-866c-3655bda454e3","year":2023},"citing_paper":{"arxiv_id":"2506.11757","last_updated":"2026-06-07T09:15:53Z","snapshot_observed_at":"2026-08-13T01:56:15.666139Z","submitted_at":"2025-06-13T13:12:33Z","title":"Hele-Shaw limit of chemotaxis-Navier-Stokes flows","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-07T04:19:10.944660Z"},"links":{"cited_paper":"/paper/2312.16869","citing_paper":"/paper/2506.11757"},"observation_digest":"sha256:91059dbc8e527ff19465d8ded250426914972a264face79292fccbffc3c53557","observation_id":"e110a467-3af9-4d3f-8f5c-c3d2f7b00f81","resolution":{"observed_at":"2026-08-07T04:19:17.578453Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-07T04:19:28.073909Z","title":"He, H.-L","venue":null,"work_id":"69b3eb74-f146-4c16-b6f0-a6d8d5f4cc44","year":2023},"citing_paper":{"arxiv_id":"2506.11757","last_updated":"2026-06-07T09:15:53Z","snapshot_observed_at":"2026-08-13T01:56:15.666139Z","submitted_at":"2025-06-13T13:12:33Z","title":"Hele-Shaw limit of chemotaxis-Navier-Stokes flows","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-07T04:19:11.036362Z"},"links":{"citing_paper":"/paper/2506.11757"},"observation_digest":"sha256:952c5547578463bdca684c900866f2ba530de3e8dd4d90e79853a8b0e6f20c0f","observation_id":"bd5e4ed2-54a2-4327-ade2-0040ab266275","resolution":{"observed_at":"2026-08-07T04:19:28.256136Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-07T04:19:27.835391Z","title":"He, L.-Y","venue":null,"work_id":"0fc729d7-3561-44fb-980d-fc706b59fca3","year":2025},"citing_paper":{"arxiv_id":"2506.11757","last_updated":"2026-06-07T09:15:53Z","snapshot_observed_at":"2026-08-13T01:56:15.666139Z","submitted_at":"2025-06-13T13:12:33Z","title":"Hele-Shaw limit of chemotaxis-Navier-Stokes flows","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-07T04:19:11.203595Z"},"links":{"citing_paper":"/paper/2506.11757"},"observation_digest":"sha256:a336be71b8a044dc5cb3f9549563f3d1c604adc11f56cc33ec4cd816ce9ada5b","observation_id":"8c317fe8-68f7-4085-bebf-30429375f1a7","resolution":{"observed_at":"2026-08-07T04:19:27.969260Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2412.05884","last_updated":"2024-12-08T10:25:52Z","snapshot_observed_at":"2026-08-12T14:21:04.056549Z","submitted_at":"2024-12-08T10:25:52Z","title":"On the incompressible limit of Keller-Segel system with volume-filling effects","version":1},"cited_work":{"arxiv_id":"2412.05884","doi":null,"metadata_source":"pith","pith_arxiv_id":"2412.05884","snapshot_observed_at":"2026-08-07T04:19:17.101471Z","title":"On the incompressible limit of Keller-Segel system with volume-filling effects","venue":"math.AP","work_id":"55f2e51d-3ea3-40cf-aa45-aab71319abdc","year":2024},"citing_paper":{"arxiv_id":"2506.11757","last_updated":"2026-06-07T09:15:53Z","snapshot_observed_at":"2026-08-13T01:56:15.666139Z","submitted_at":"2025-06-13T13:12:33Z","title":"Hele-Shaw limit of chemotaxis-Navier-Stokes flows","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-07T04:19:11.368899Z"},"links":{"cited_paper":"/paper/2412.05884","citing_paper":"/paper/2506.11757"},"observation_digest":"sha256:03a23364bdb0903cc3e52327a02e753ad5257a20cc04825385ad7c2a385eb038","observation_id":"80503121-dd06-4d1b-ba57-720d18e4bf29","resolution":{"observed_at":"2026-08-07T04:19:17.270035Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-07T04:19:11.583061Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2506.11757","last_updated":"2026-06-07T09:15:53Z","snapshot_observed_at":"2026-08-13T01:56:15.666139Z","submitted_at":"2025-06-13T13:12:33Z","title":"Hele-Shaw limit of chemotaxis-Navier-Stokes flows","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-07T04:19:11.583061Z"},"links":{"citing_paper":"/paper/2506.11757"},"observation_digest":"sha256:bf4326e509394e2b70e388c36b76b2ce96d14bf07575255ffe86987285461278","observation_id":"3f7aaa47-1ccf-4324-bbce-c6dd0e4d5270","resolution":{"observed_at":"2026-08-07T04:19:11.583061Z","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":"2026-08-07T04:19:27.624173Z","title":null,"venue":null,"work_id":"93f31ab2-5dff-4280-a8c8-884bb14305eb","year":2025},"citing_paper":{"arxiv_id":"2506.11757","last_updated":"2026-06-07T09:15:53Z","snapshot_observed_at":"2026-08-13T01:56:15.666139Z","submitted_at":"2025-06-13T13:12:33Z","title":"Hele-Shaw limit of chemotaxis-Navier-Stokes flows","version":2},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-07T04:19:11.756734Z"},"links":{"citing_paper":"/paper/2506.11757"},"observation_digest":"sha256:4a6aeb1b45f4258f2f42011c5ee9f578d94c9d90c29bc8e7d8fd865fd2674bc0","observation_id":"1c6a5561-e572-4863-b040-76168107c170","resolution":{"observed_at":"2026-08-07T04:19:27.711302Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-07T04:19:27.406693Z","title":"Kim and A","venue":null,"work_id":"89e3fa39-316e-4a14-b383-398a74f0079e","year":2023},"citing_paper":{"arxiv_id":"2506.11757","last_updated":"2026-06-07T09:15:53Z","snapshot_observed_at":"2026-08-13T01:56:15.666139Z","submitted_at":"2025-06-13T13:12:33Z","title":"Hele-Shaw limit of chemotaxis-Navier-Stokes flows","version":2},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-07T04:19:11.911380Z"},"links":{"citing_paper":"/paper/2506.11757"},"observation_digest":"sha256:6a2e90e5d984557346273c863de34d96d3ecae5b6548e33d3dcb4f2b150e30c6","observation_id":"ce195616-6020-4982-98e5-20560f8f28c6","resolution":{"observed_at":"2026-08-07T04:19:27.522856Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-07T04:19:27.163213Z","title":null,"venue":null,"work_id":"6c64cea8-9e29-4971-b589-21e3c366370b","year":2019},"citing_paper":{"arxiv_id":"2506.11757","last_updated":"2026-06-07T09:15:53Z","snapshot_observed_at":"2026-08-13T01:56:15.666139Z","submitted_at":"2025-06-13T13:12:33Z","title":"Hele-Shaw limit of chemotaxis-Navier-Stokes flows","version":2},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-07T04:19:12.115713Z"},"links":{"citing_paper":"/paper/2506.11757"},"observation_digest":"sha256:669ded4d9e3a89fce5659aac394f298b17276e5af3bde5a4a546e95b35d05146","observation_id":"8a4203fd-30dc-4777-93b8-9fc2804a3dac","resolution":{"observed_at":"2026-08-07T04:19:27.277844Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-07T04:19:26.852095Z","title":"Kim and O","venue":null,"work_id":"52e57973-5ed9-4b48-91ef-788730af59ac","year":2018},"citing_paper":{"arxiv_id":"2506.11757","last_updated":"2026-06-07T09:15:53Z","snapshot_observed_at":"2026-08-13T01:56:15.666139Z","submitted_at":"2025-06-13T13:12:33Z","title":"Hele-Shaw limit of chemotaxis-Navier-Stokes flows","version":2},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-07T04:19:12.312194Z"},"links":{"citing_paper":"/paper/2506.11757"},"observation_digest":"sha256:d09ef3698c3c69dbc709695667db98079d6bc60c4a2df7db3e2493b6a228ffd2","observation_id":"f9df767b-9364-4661-b86c-2070030c2d6f","resolution":{"observed_at":"2026-08-07T04:19:26.979280Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-07T04:19:26.566251Z","title":"Kiselev and L","venue":null,"work_id":"1b725f9f-cf42-4793-8f86-4f022d19e584","year":2012},"citing_paper":{"arxiv_id":"2506.11757","last_updated":"2026-06-07T09:15:53Z","snapshot_observed_at":"2026-08-13T01:56:15.666139Z","submitted_at":"2025-06-13T13:12:33Z","title":"Hele-Shaw limit of chemotaxis-Navier-Stokes flows","version":2},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-07T04:19:12.460187Z"},"links":{"citing_paper":"/paper/2506.11757"},"observation_digest":"sha256:585d7955e8f98b4d119b6786c3b7f3607d682f22027d60cc63d8f1103352729f","observation_id":"bd005a00-126a-4696-bce9-e790a37135d4","resolution":{"observed_at":"2026-08-07T04:19:26.723348Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-07T04:19:26.244681Z","title":"Kiselev and X","venue":null,"work_id":"0201d9d8-68fd-4285-bc46-e52e15d78fff","year":2016},"citing_paper":{"arxiv_id":"2506.11757","last_updated":"2026-06-07T09:15:53Z","snapshot_observed_at":"2026-08-13T01:56:15.666139Z","submitted_at":"2025-06-13T13:12:33Z","title":"Hele-Shaw limit of chemotaxis-Navier-Stokes flows","version":2},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-07T04:19:12.616539Z"},"links":{"citing_paper":"/paper/2506.11757"},"observation_digest":"sha256:1d5875d732a8e60ef60aa7a3e2c32b3b23efd026eb6b4e1d9c7fc5a541bd8bb7","observation_id":"9a5a5bc1-36ab-4567-b3ac-0398996c1aae","resolution":{"observed_at":"2026-08-07T04:19:26.413222Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-07T04:19:25.904436Z","title":null,"venue":null,"work_id":"05bb8519-b08d-4194-b63e-e4159b6279ff","year":2023},"citing_paper":{"arxiv_id":"2506.11757","last_updated":"2026-06-07T09:15:53Z","snapshot_observed_at":"2026-08-13T01:56:15.666139Z","submitted_at":"2025-06-13T13:12:33Z","title":"Hele-Shaw limit of chemotaxis-Navier-Stokes flows","version":2},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-07T04:19:12.760664Z"},"links":{"citing_paper":"/paper/2506.11757"},"observation_digest":"sha256:74563919df648eadd2846b976ee507a5652f03cee6169cdf60e96d14e310102c","observation_id":"627641fe-1e4c-4e70-b6b7-86a1d06325f0","resolution":{"observed_at":"2026-08-07T04:19:26.064719Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-07T04:19:25.554945Z","title":"Liu and A","venue":null,"work_id":"81913879-7202-44af-bf56-c85449ae22a0","year":2011},"citing_paper":{"arxiv_id":"2506.11757","last_updated":"2026-06-07T09:15:53Z","snapshot_observed_at":"2026-08-13T01:56:15.666139Z","submitted_at":"2025-06-13T13:12:33Z","title":"Hele-Shaw limit of chemotaxis-Navier-Stokes flows","version":2},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-07T04:19:12.915799Z"},"links":{"citing_paper":"/paper/2506.11757"},"observation_digest":"sha256:2e2e6fa2c9173e1a20b5ece676641e4c5b2ac0dc31db8d2bfad39e1cf61ca97d","observation_id":"39c7c277-5b90-4eb4-8fa1-1390afae20f8","resolution":{"observed_at":"2026-08-07T04:19:25.737654Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-07T04:19:25.212157Z","title":"Liu and X","venue":null,"work_id":"951b5971-0b2f-4f24-9690-e1ea5ad3e87c","year":2021},"citing_paper":{"arxiv_id":"2506.11757","last_updated":"2026-06-07T09:15:53Z","snapshot_observed_at":"2026-08-13T01:56:15.666139Z","submitted_at":"2025-06-13T13:12:33Z","title":"Hele-Shaw limit of chemotaxis-Navier-Stokes flows","version":2},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-07T04:19:13.055226Z"},"links":{"citing_paper":"/paper/2506.11757"},"observation_digest":"sha256:6e82671567db0c7faf3c33f5be9e8a6de4a4ee9b9652eb7088063fd2d7e8af69","observation_id":"331d58cd-a5b3-46a1-820a-3ec2a6168c9f","resolution":{"observed_at":"2026-08-07T04:19:25.393253Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-07T04:19:24.976680Z","title":null,"venue":null,"work_id":"21631d41-f66d-4053-b5fe-fba1e589d4d8","year":2010},"citing_paper":{"arxiv_id":"2506.11757","last_updated":"2026-06-07T09:15:53Z","snapshot_observed_at":"2026-08-13T01:56:15.666139Z","submitted_at":"2025-06-13T13:12:33Z","title":"Hele-Shaw limit of chemotaxis-Navier-Stokes flows","version":2},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-07T04:19:13.226216Z"},"links":{"citing_paper":"/paper/2506.11757"},"observation_digest":"sha256:c6d18cb1bbfc9ca020f5cdb71c64dd72b3328f87edff8a852b53226ee3ddd771","observation_id":"733300c3-8da6-4660-a362-d1817d70238e","resolution":{"observed_at":"2026-08-07T04:19:25.099270Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-07T04:19:24.720692Z","title":null,"venue":null,"work_id":"2521bc4f-3921-423a-99a9-677cb0843f0b","year":2012},"citing_paper":{"arxiv_id":"2506.11757","last_updated":"2026-06-07T09:15:53Z","snapshot_observed_at":"2026-08-13T01:56:15.666139Z","submitted_at":"2025-06-13T13:12:33Z","title":"Hele-Shaw limit of chemotaxis-Navier-Stokes flows","version":2},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-07T04:19:13.474668Z"},"links":{"citing_paper":"/paper/2506.11757"},"observation_digest":"sha256:2d22f3d51140f92b4439fc83526aadd57f68ab6fab613b51d172e5a851380ec4","observation_id":"6d27281d-edb0-46ea-9fcb-4ad388bf7ca0","resolution":{"observed_at":"2026-08-07T04:19:24.816842Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-07T04:19:24.437814Z","title":"Nirenberg","venue":null,"work_id":"2dec29ff-0916-4bda-9e8b-6239e8a63f5d","year":1959},"citing_paper":{"arxiv_id":"2506.11757","last_updated":"2026-06-07T09:15:53Z","snapshot_observed_at":"2026-08-13T01:56:15.666139Z","submitted_at":"2025-06-13T13:12:33Z","title":"Hele-Shaw limit of chemotaxis-Navier-Stokes flows","version":2},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-07T04:19:13.693600Z"},"links":{"citing_paper":"/paper/2506.11757"},"observation_digest":"sha256:7309450b0a3ab09cc27ff7fa8e5d24c6cd286051885e72ca7ec79d44674a516c","observation_id":"174de87f-3fb6-4845-9f48-8d7087286233","resolution":{"observed_at":"2026-08-07T04:19:24.559330Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-07T04:19:24.082066Z","title":"Peng and Z","venue":null,"work_id":"d6321968-b991-4315-b9ed-f0008b231ab9","year":2018},"citing_paper":{"arxiv_id":"2506.11757","last_updated":"2026-06-07T09:15:53Z","snapshot_observed_at":"2026-08-13T01:56:15.666139Z","submitted_at":"2025-06-13T13:12:33Z","title":"Hele-Shaw limit of chemotaxis-Navier-Stokes flows","version":2},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-07T04:19:13.846638Z"},"links":{"citing_paper":"/paper/2506.11757"},"observation_digest":"sha256:8171f6835ff63185212550e5e954edb8b28cacea314094951ea4d11506a20430","observation_id":"68b39c43-3d84-454d-8d95-23042dd99fa3","resolution":{"observed_at":"2026-08-07T04:19:24.248377Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-07T04:19:23.791989Z","title":"Peng and Z","venue":null,"work_id":"926898ef-7cfa-40f0-97a0-867d9ed34907","year":2019},"citing_paper":{"arxiv_id":"2506.11757","last_updated":"2026-06-07T09:15:53Z","snapshot_observed_at":"2026-08-13T01:56:15.666139Z","submitted_at":"2025-06-13T13:12:33Z","title":"Hele-Shaw limit of chemotaxis-Navier-Stokes flows","version":2},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-07T04:19:14.071257Z"},"links":{"citing_paper":"/paper/2506.11757"},"observation_digest":"sha256:70ebecf47fc1386fefc172fbadb9c627545c2e63aa145f6414899adad4f9bb6b","observation_id":"e35f7802-87bd-4709-9168-58f06596ed05","resolution":{"observed_at":"2026-08-07T04:19:23.973974Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-07T04:19:23.481475Z","title":"Perthame, F","venue":null,"work_id":"ca8cf3f3-6bd0-45fb-8ee9-a45386a8f16b","year":2014},"citing_paper":{"arxiv_id":"2506.11757","last_updated":"2026-06-07T09:15:53Z","snapshot_observed_at":"2026-08-13T01:56:15.666139Z","submitted_at":"2025-06-13T13:12:33Z","title":"Hele-Shaw limit of chemotaxis-Navier-Stokes flows","version":2},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-07T04:19:14.226732Z"},"links":{"citing_paper":"/paper/2506.11757"},"observation_digest":"sha256:18a25fe302b86f2471a7bd190e7a7c50c62e49d1315b6e41e43cbe1378143d22","observation_id":"4195b105-207c-4981-a1ba-76780564fa13","resolution":{"observed_at":"2026-08-07T04:19:23.630144Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-07T04:19:23.133255Z","title":"Perthame, F","venue":null,"work_id":"c553910d-2cec-4eec-b27d-59b05996a340","year":2014},"citing_paper":{"arxiv_id":"2506.11757","last_updated":"2026-06-07T09:15:53Z","snapshot_observed_at":"2026-08-13T01:56:15.666139Z","submitted_at":"2025-06-13T13:12:33Z","title":"Hele-Shaw limit of chemotaxis-Navier-Stokes flows","version":2},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-07T04:19:14.373396Z"},"links":{"citing_paper":"/paper/2506.11757"},"observation_digest":"sha256:de6562aa5b9ca88f91ff56aec8bc918ca73e7cf2d0989ddf935473ee73c0cdeb","observation_id":"a26e2d24-fde1-43cc-8034-0f824a7c3354","resolution":{"observed_at":"2026-08-07T04:19:23.275607Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-07T04:19:22.789709Z","title":"Perthame and N","venue":null,"work_id":"774c7071-7926-49ee-a21a-a9e075097a1f","year":2015},"citing_paper":{"arxiv_id":"2506.11757","last_updated":"2026-06-07T09:15:53Z","snapshot_observed_at":"2026-08-13T01:56:15.666139Z","submitted_at":"2025-06-13T13:12:33Z","title":"Hele-Shaw limit of chemotaxis-Navier-Stokes flows","version":2},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-07T04:19:14.532600Z"},"links":{"citing_paper":"/paper/2506.11757"},"observation_digest":"sha256:65244b782c33bff81a828122e4d041001f72aa1013580979f8e20a2a294219ff","observation_id":"04c24094-dd25-4c1f-a852-147dae397229","resolution":{"observed_at":"2026-08-07T04:19:22.980134Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-07T04:19:14.683982Z","title":null,"venue":null,"work_id":null,"year":1987},"citing_paper":{"arxiv_id":"2506.11757","last_updated":"2026-06-07T09:15:53Z","snapshot_observed_at":"2026-08-13T01:56:15.666139Z","submitted_at":"2025-06-13T13:12:33Z","title":"Hele-Shaw limit of chemotaxis-Navier-Stokes flows","version":2},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-07T04:19:14.683982Z"},"links":{"citing_paper":"/paper/2506.11757"},"observation_digest":"sha256:dd33e91f4c8c2bef5be06748d54473996b1f596c882cc513f635b8d0864bb056","observation_id":"1ffad80c-2288-4784-ab9a-a34bfa0136c1","resolution":{"observed_at":"2026-08-07T04:19:14.683982Z","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":"2026-08-07T04:19:22.475328Z","title":"Tao and M","venue":null,"work_id":"8829135a-8721-4ecc-8e1f-e65f18d4d03f","year":1901},"citing_paper":{"arxiv_id":"2506.11757","last_updated":"2026-06-07T09:15:53Z","snapshot_observed_at":"2026-08-13T01:56:15.666139Z","submitted_at":"2025-06-13T13:12:33Z","title":"Hele-Shaw limit of chemotaxis-Navier-Stokes flows","version":2},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-07T04:19:14.862177Z"},"links":{"citing_paper":"/paper/2506.11757"},"observation_digest":"sha256:3c9b67fa96b84805885821fbddae294293e2f0eb6872bf3314f5956605eaaade","observation_id":"f4e199b3-0bb9-4e64-89ed-31de9185993e","resolution":{"observed_at":"2026-08-07T04:19:22.621994Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-07T04:19:22.154492Z","title":"Tao and M","venue":null,"work_id":"9b34acf3-30cf-4964-afa4-6f9f702d910d","year":2013},"citing_paper":{"arxiv_id":"2506.11757","last_updated":"2026-06-07T09:15:53Z","snapshot_observed_at":"2026-08-13T01:56:15.666139Z","submitted_at":"2025-06-13T13:12:33Z","title":"Hele-Shaw limit of chemotaxis-Navier-Stokes flows","version":2},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-07T04:19:15.010644Z"},"links":{"citing_paper":"/paper/2506.11757"},"observation_digest":"sha256:9657da74f31fdac0cfa5d8389c223ab5675fa46d1b6bcdcaae4405a1f47ebafa","observation_id":"fcf590ef-006b-4b24-a3b0-b95aa0aa61d2","resolution":{"observed_at":"2026-08-07T04:19:22.287342Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2403.05804","last_updated":"2024-03-09T05:45:26Z","snapshot_observed_at":"2026-08-16T14:11:25.136474Z","submitted_at":"2024-03-09T05:45:26Z","title":"Convergence of Free Boundaries in the Incompressible Limit of Tumor Growth Models","version":1},"cited_work":{"arxiv_id":"2403.05804","doi":null,"metadata_source":"pith","pith_arxiv_id":"2403.05804","snapshot_observed_at":"2026-08-07T04:19:16.665043Z","title":"Convergence of Free Boundaries in the Incompressible Limit of Tumor Growth Models","venue":"math.AP","work_id":"3beaa005-353b-486e-9f32-11c98c752ebf","year":2024},"citing_paper":{"arxiv_id":"2506.11757","last_updated":"2026-06-07T09:15:53Z","snapshot_observed_at":"2026-08-13T01:56:15.666139Z","submitted_at":"2025-06-13T13:12:33Z","title":"Hele-Shaw limit of chemotaxis-Navier-Stokes flows","version":2},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-07T04:19:15.223130Z"},"links":{"cited_paper":"/paper/2403.05804","citing_paper":"/paper/2506.11757"},"observation_digest":"sha256:2ca904407c1595d4a3e797a2931f01f1077dbb9446fb5de003fe311d50503085","observation_id":"2adb0969-8427-4a8d-abf5-fc54cca717e2","resolution":{"observed_at":"2026-08-07T04:19:16.862466Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-07T04:19:21.725778Z","title":"Tuval, L","venue":null,"work_id":"791190b1-206a-4514-913a-89fe570d0cd5","year":2005},"citing_paper":{"arxiv_id":"2506.11757","last_updated":"2026-06-07T09:15:53Z","snapshot_observed_at":"2026-08-13T01:56:15.666139Z","submitted_at":"2025-06-13T13:12:33Z","title":"Hele-Shaw limit of chemotaxis-Navier-Stokes flows","version":2},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-07T04:19:15.321103Z"},"links":{"citing_paper":"/paper/2506.11757"},"observation_digest":"sha256:aa01326f4dd1323b6de83ab00c017059986bfd00303b51c43583bcabb738ee89","observation_id":"bad8be5c-c2c0-4a1f-b94c-d8f2192ab02f","resolution":{"observed_at":"2026-08-07T04:19:21.950377Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-07T04:19:21.357583Z","title":null,"venue":null,"work_id":"5c9f97c5-4edd-4f9f-8369-c6d264c4d22b","year":2012},"citing_paper":{"arxiv_id":"2506.11757","last_updated":"2026-06-07T09:15:53Z","snapshot_observed_at":"2026-08-13T01:56:15.666139Z","submitted_at":"2025-06-13T13:12:33Z","title":"Hele-Shaw limit of chemotaxis-Navier-Stokes flows","version":2},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-07T04:19:15.434606Z"},"links":{"citing_paper":"/paper/2506.11757"},"observation_digest":"sha256:c21a4f416277d4d2ca231dafbe7d32da04eb71e1c3223ecc3f86f3b80e8d5034","observation_id":"fe5b5411-0b65-4b43-b5e5-fd67e7c3f686","resolution":{"observed_at":"2026-08-07T04:19:21.542535Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-07T04:19:21.053619Z","title":null,"venue":null,"work_id":"8ecb7e07-2678-4a7e-9954-a9e464f2611a","year":2014},"citing_paper":{"arxiv_id":"2506.11757","last_updated":"2026-06-07T09:15:53Z","snapshot_observed_at":"2026-08-13T01:56:15.666139Z","submitted_at":"2025-06-13T13:12:33Z","title":"Hele-Shaw limit of chemotaxis-Navier-Stokes flows","version":2},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-07T04:19:15.590321Z"},"links":{"citing_paper":"/paper/2506.11757"},"observation_digest":"sha256:d581b2555afb054a964cec5175f0c4429a90fa8b9def3d4f1404498c3f10a61a","observation_id":"0bae8a11-4636-4d53-8e94-3672c6eda75f","resolution":{"observed_at":"2026-08-07T04:19:21.204986Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-07T04:19:20.625465Z","title":null,"venue":null,"work_id":"a69c4547-e0c4-4168-b0b0-2eb1c34eb8d6","year":2015},"citing_paper":{"arxiv_id":"2506.11757","last_updated":"2026-06-07T09:15:53Z","snapshot_observed_at":"2026-08-13T01:56:15.666139Z","submitted_at":"2025-06-13T13:12:33Z","title":"Hele-Shaw limit of chemotaxis-Navier-Stokes flows","version":2},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-07T04:19:15.727429Z"},"links":{"citing_paper":"/paper/2506.11757"},"observation_digest":"sha256:ac376aa94237151c1d7d507acd45b209860841037c0e5ced8ab804222c9b3b7e","observation_id":"ce5bacfa-71a0-48d4-b82c-b033c8a31fe5","resolution":{"observed_at":"2026-08-07T04:19:20.852293Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-07T04:19:20.316345Z","title":null,"venue":null,"work_id":"f7a57d20-e8aa-4a4a-a19f-e667645d7b18","year":2016},"citing_paper":{"arxiv_id":"2506.11757","last_updated":"2026-06-07T09:15:53Z","snapshot_observed_at":"2026-08-13T01:56:15.666139Z","submitted_at":"2025-06-13T13:12:33Z","title":"Hele-Shaw limit of chemotaxis-Navier-Stokes flows","version":2},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-07T04:19:15.880944Z"},"links":{"citing_paper":"/paper/2506.11757"},"observation_digest":"sha256:1b15d964729c5a960f47775cfe51868a6ed09fdd6bf6b3d1ad967602124f477d","observation_id":"a7e51288-cac9-44ad-a8b9-bd52786f445b","resolution":{"observed_at":"2026-08-07T04:19:20.487842Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-07T04:19:19.970680Z","title":null,"venue":null,"work_id":"dffac89e-1016-4125-bd78-eb551999dfa4","year":2017},"citing_paper":{"arxiv_id":"2506.11757","last_updated":"2026-06-07T09:15:53Z","snapshot_observed_at":"2026-08-13T01:56:15.666139Z","submitted_at":"2025-06-13T13:12:33Z","title":"Hele-Shaw limit of chemotaxis-Navier-Stokes flows","version":2},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-07T04:19:16.013244Z"},"links":{"citing_paper":"/paper/2506.11757"},"observation_digest":"sha256:194835e46c42941f311a37fdafd875157fd75d6af6d65693abf1516fe48abd5c","observation_id":"c71b04e6-8bb9-4c3c-b9ec-24460d345213","resolution":{"observed_at":"2026-08-07T04:19:20.122219Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-07T04:19:19.650110Z","title":null,"venue":null,"work_id":"3e7a7d13-d083-406e-bfe6-c79f963b33ec","year":2023},"citing_paper":{"arxiv_id":"2506.11757","last_updated":"2026-06-07T09:15:53Z","snapshot_observed_at":"2026-08-13T01:56:15.666139Z","submitted_at":"2025-06-13T13:12:33Z","title":"Hele-Shaw limit of chemotaxis-Navier-Stokes flows","version":2},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-07T04:19:16.155750Z"},"links":{"citing_paper":"/paper/2506.11757"},"observation_digest":"sha256:4eff1d2986bf9ba9f7126e9673be67884ad73a6228a6762db46beea26578a3a5","observation_id":"45229849-cca6-49df-a969-82013d835072","resolution":{"observed_at":"2026-08-07T04:19:19.814926Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-07T04:19:19.340488Z","title":null,"venue":null,"work_id":"71f79027-947b-4e65-8bdd-75f86bf26c6e","year":2021},"citing_paper":{"arxiv_id":"2506.11757","last_updated":"2026-06-07T09:15:53Z","snapshot_observed_at":"2026-08-13T01:56:15.666139Z","submitted_at":"2025-06-13T13:12:33Z","title":"Hele-Shaw limit of chemotaxis-Navier-Stokes flows","version":2},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-07T04:19:16.283826Z"},"links":{"citing_paper":"/paper/2506.11757"},"observation_digest":"sha256:61029ed4ef5e7ecd06e4d53d6a9b56476b54aa213342d9d35e9580b37dac223d","observation_id":"a53e0a06-9058-463a-b884-26dce8452b2c","resolution":{"observed_at":"2026-08-07T04:19:19.494297Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-07T04:19:18.883163Z","title":"Zhang and Y","venue":null,"work_id":"5fc188ed-6fee-4682-9ea1-42fcd5f63da1","year":2015},"citing_paper":{"arxiv_id":"2506.11757","last_updated":"2026-06-07T09:15:53Z","snapshot_observed_at":"2026-08-13T01:56:15.666139Z","submitted_at":"2025-06-13T13:12:33Z","title":"Hele-Shaw limit of chemotaxis-Navier-Stokes flows","version":2},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-08-07T04:19:16.417931Z"},"links":{"citing_paper":"/paper/2506.11757"},"observation_digest":"sha256:e28b373c0e6e61763dd79d79379c19152a9d939cdc78e1639c9e97baebf577d2","observation_id":"350ac486-e127-49a1-88d4-b9b89d00877e","resolution":{"observed_at":"2026-08-07T04:19:19.116795Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-07T04:19:18.479950Z","title":"Zhang and X","venue":null,"work_id":"38240726-770d-4b8d-a35a-532f8ca9bfc1","year":2014},"citing_paper":{"arxiv_id":"2506.11757","last_updated":"2026-06-07T09:15:53Z","snapshot_observed_at":"2026-08-13T01:56:15.666139Z","submitted_at":"2025-06-13T13:12:33Z","title":"Hele-Shaw limit of chemotaxis-Navier-Stokes flows","version":2},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-08-07T04:19:16.525307Z"},"links":{"citing_paper":"/paper/2506.11757"},"observation_digest":"sha256:a6e003b557ca297bd763db33a0cf488f9091de66f6a0ffacaa85e9d7072c4055","observation_id":"072a8300-90b1-43ae-a638-ebddc0296827","resolution":{"observed_at":"2026-08-07T04:19:18.684970Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2506.11757","last_updated":"2026-06-07T09:15:53Z","latest_version":2,"primary_category":"math.AP","snapshot_observed_at":"2026-08-13T01:56:15.666139Z","submitted_at":"2025-06-13T13:12:33Z","title":"Hele-Shaw limit of chemotaxis-Navier-Stokes flows"},"reference_resolution":{"displayed":57,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":23,"verified_exact":5,"verified_fuzzy":29},"total_outbound_references":57},"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":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"thesis":"As of 22 August 2026, this Paper Citation Record lists 57 of 57 outbound references and 0 inbound Pith citation observations for arXiv:2506.11757."}