{"as_of":"2026-08-21T14:15:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:e58558e6b90e72a00816f92c43dda16f000b8a81709976461b6835dd5a2f73fa","coverage":[{"denominator":37,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":37,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T16:44:51.861900Z","state":"measured"},{"denominator":38,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":38,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-21T06:32:19.484+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":"2026-08-04T22:27:18.533124Z","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":"2026-08-04T22:27:18.568074Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2507.13060","last_updated":"2025-07-17T12:29:04Z","snapshot_observed_at":"2026-08-21T07:56:50.311067Z","submitted_at":"2025-07-17T12:29:04Z","title":"Exponential convergence for ultrafast diffusion equations with log-concave weights","version":1},"cited_work":{"arxiv_id":"2507.13060","doi":null,"metadata_source":"pith","pith_arxiv_id":"2507.13060","snapshot_observed_at":"2026-08-04T22:27:18.568074Z","title":"Exponential convergence for ultrafast diffusion equations with log-concave weights","venue":"math.AP","work_id":"dfc4f5d7-a55d-4f46-be08-7e8903bacbea","year":2025},"citing_paper":{"arxiv_id":"2509.07382","last_updated":"2025-09-09T04:23:31Z","snapshot_observed_at":"2026-08-19T17:26:40.017852Z","submitted_at":"2025-09-09T04:23:31Z","title":"On the exponential convergence to equilibrium for ultrafast diffusion equations","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-04T22:27:18.533124Z"},"links":{"cited_paper":"/paper/2507.13060","citing_paper":"/paper/2509.07382"},"observation_digest":"sha256:ae30003836e3da068f241f86b59e89636fdaca6e02532d99b539c898d8a0902f","observation_id":"fb7368fd-3199-40ce-8f5c-901c482653f8","resolution":{"observed_at":"2026-08-04T22:27:18.574072Z","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"}}],"links":{"evidence":"/evidence","html":"/paper/2507.13060/citation-record","integrity":"/paper/2507.13060/integrity","json":"/paper/2507.13060/citation-record.json","paper":"/paper/2507.13060"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T16:44:57.449363Z","title":"Ambrosio, N","venue":null,"work_id":"ad245533-1a81-487c-957c-903a6ede224f","year":2008},"citing_paper":{"arxiv_id":"2507.13060","last_updated":"2025-07-17T12:29:04Z","snapshot_observed_at":"2026-08-21T07:56:50.311067Z","submitted_at":"2025-07-17T12:29:04Z","title":"Exponential convergence for ultrafast diffusion equations with log-concave weights","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-06T16:44:48.828113Z"},"links":{"citing_paper":"/paper/2507.13060"},"observation_digest":"sha256:366be4c1a2a155b96b2276fde38426aba3d2927967c78d71fbd0e66ec9338ebb","observation_id":"cf25ae83-7960-450a-8b2d-8612899506d3","resolution":{"observed_at":"2026-08-06T16:44:57.518475Z","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":"2026-08-06T16:44:57.261024Z","title":"Blanchet, M","venue":null,"work_id":"7b959005-4ea0-43c1-abe8-0db1352bba6e","year":2009},"citing_paper":{"arxiv_id":"2507.13060","last_updated":"2025-07-17T12:29:04Z","snapshot_observed_at":"2026-08-21T07:56:50.311067Z","submitted_at":"2025-07-17T12:29:04Z","title":"Exponential convergence for ultrafast diffusion equations with log-concave weights","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-06T16:44:48.887698Z"},"links":{"citing_paper":"/paper/2507.13060"},"observation_digest":"sha256:4e164cf83d4945f7092254da76db7d91d1a043e729427563801e2021342f7c01","observation_id":"eeb91477-cfb0-4336-ae36-f5b1c2bb857b","resolution":{"observed_at":"2026-08-06T16:44:57.353428Z","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":"2026-08-06T16:44:57.088326Z","title":null,"venue":null,"work_id":"d73c90b6-d994-4294-aa83-72def3404d0d","year":1999},"citing_paper":{"arxiv_id":"2507.13060","last_updated":"2025-07-17T12:29:04Z","snapshot_observed_at":"2026-08-21T07:56:50.311067Z","submitted_at":"2025-07-17T12:29:04Z","title":"Exponential convergence for ultrafast diffusion equations with log-concave weights","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-06T16:44:48.958858Z"},"links":{"citing_paper":"/paper/2507.13060"},"observation_digest":"sha256:05ef79f3294d7735ab5c975bded31c8d3fddcfaa54e2557f23f6b5f43afba49e","observation_id":"f2c250e9-f875-43da-9a36-d164493f4aab","resolution":{"observed_at":"2026-08-06T16:44:57.134408Z","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":"2026-08-06T16:44:56.965930Z","title":"Bonforte and J","venue":null,"work_id":"17785a82-8c51-4d29-9327-0a0ef2ec1e28","year":2006},"citing_paper":{"arxiv_id":"2507.13060","last_updated":"2025-07-17T12:29:04Z","snapshot_observed_at":"2026-08-21T07:56:50.311067Z","submitted_at":"2025-07-17T12:29:04Z","title":"Exponential convergence for ultrafast diffusion equations with log-concave weights","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-06T16:44:49.038425Z"},"links":{"citing_paper":"/paper/2507.13060"},"observation_digest":"sha256:deffdf2ea4dfb9860ed5ddb5dc84dca650e5555a26efa01f4e10008ca0f4e427","observation_id":"94cba34f-b7ec-4669-99af-8d068eed350c","resolution":{"observed_at":"2026-08-06T16:44:57.034154Z","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":"2026-08-06T16:44:56.824955Z","title":"Bonforte and J","venue":null,"work_id":"e15b7a1d-88eb-46f6-822f-ac5c0aa77a0a","year":2007},"citing_paper":{"arxiv_id":"2507.13060","last_updated":"2025-07-17T12:29:04Z","snapshot_observed_at":"2026-08-21T07:56:50.311067Z","submitted_at":"2025-07-17T12:29:04Z","title":"Exponential convergence for ultrafast diffusion equations with log-concave weights","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-06T16:44:49.154422Z"},"links":{"citing_paper":"/paper/2507.13060"},"observation_digest":"sha256:cf5b43f25ba92f6d3e3d36eae8bdb5b209887f97e97b7397bc05d9114e26c732","observation_id":"10a34b18-0845-4f3d-9a75-47128e77004b","resolution":{"observed_at":"2026-08-06T16:44:56.884359Z","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":"2026-08-06T16:44:56.697177Z","title":"Bonforte and J","venue":null,"work_id":"d427c021-a57d-489d-8f7b-21e0f900a93b","year":2010},"citing_paper":{"arxiv_id":"2507.13060","last_updated":"2025-07-17T12:29:04Z","snapshot_observed_at":"2026-08-21T07:56:50.311067Z","submitted_at":"2025-07-17T12:29:04Z","title":"Exponential convergence for ultrafast diffusion equations with log-concave weights","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-06T16:44:49.223388Z"},"links":{"citing_paper":"/paper/2507.13060"},"observation_digest":"sha256:53cb2cc63cf95d694be25f3e4b53bc42afb4d50136f9a060d0be1707ef3f6321","observation_id":"dbed8dd0-97a6-4ac9-a60e-51771c36a08c","resolution":{"observed_at":"2026-08-06T16:44:56.775271Z","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":"2026-08-06T16:44:56.570388Z","title":"Bonforte, J","venue":null,"work_id":"5e03bf7b-25e9-49bc-b05b-edd7d7a68d6a","year":2017},"citing_paper":{"arxiv_id":"2507.13060","last_updated":"2025-07-17T12:29:04Z","snapshot_observed_at":"2026-08-21T07:56:50.311067Z","submitted_at":"2025-07-17T12:29:04Z","title":"Exponential convergence for ultrafast diffusion equations with log-concave weights","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-06T16:44:49.293272Z"},"links":{"citing_paper":"/paper/2507.13060"},"observation_digest":"sha256:372f442b111887ecb8c91626aba49953b745fee27148ada17e29ec9b62430ddb","observation_id":"cf079c23-8870-4a5b-9c67-bb3adc2897db","resolution":{"observed_at":"2026-08-06T16:44:56.617443Z","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":"2026-08-06T16:44:56.419415Z","title":"Bonforte, J","venue":null,"work_id":"fec8b738-9d68-40b6-a205-cfa5e345ef51","year":2017},"citing_paper":{"arxiv_id":"2507.13060","last_updated":"2025-07-17T12:29:04Z","snapshot_observed_at":"2026-08-21T07:56:50.311067Z","submitted_at":"2025-07-17T12:29:04Z","title":"Exponential convergence for ultrafast diffusion equations with log-concave weights","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-06T16:44:49.382558Z"},"links":{"citing_paper":"/paper/2507.13060"},"observation_digest":"sha256:49a095ea9076ce65f658aa7d687019ec3654ebe3c482f13ee28ce40b878afe06","observation_id":"cd407f2c-f7db-44d6-99a4-781678cea7ca","resolution":{"observed_at":"2026-08-06T16:44:56.479400Z","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":"2026-08-06T16:44:56.311712Z","title":"Bonforte and A","venue":null,"work_id":"f5ed6017-ea63-45c7-b8c1-7fe7aef94b1e","year":2024},"citing_paper":{"arxiv_id":"2507.13060","last_updated":"2025-07-17T12:29:04Z","snapshot_observed_at":"2026-08-21T07:56:50.311067Z","submitted_at":"2025-07-17T12:29:04Z","title":"Exponential convergence for ultrafast diffusion equations with log-concave weights","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-06T16:44:49.510883Z"},"links":{"citing_paper":"/paper/2507.13060"},"observation_digest":"sha256:e23dd576fde86cc6140fa31ea993eeedc830e75292e83150efa2c1b9f1a27ae8","observation_id":"4d80a1eb-7e32-4c8a-a98c-bb07bb10dd4e","resolution":{"observed_at":"2026-08-06T16:44:56.362292Z","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":"2026-08-06T16:44:56.221338Z","title":null,"venue":null,"work_id":"0b88da67-a099-4b0a-a98a-52bff1a40956","year":2000},"citing_paper":{"arxiv_id":"2507.13060","last_updated":"2025-07-17T12:29:04Z","snapshot_observed_at":"2026-08-21T07:56:50.311067Z","submitted_at":"2025-07-17T12:29:04Z","title":"Exponential convergence for ultrafast diffusion equations with log-concave weights","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-06T16:44:49.603643Z"},"links":{"citing_paper":"/paper/2507.13060"},"observation_digest":"sha256:9a3daeb12f6c9bf0e14ac133a25e7acf0f4f614aa76d2497e0da12cd49cd712f","observation_id":"1744bdf4-ea09-4328-8712-429b9820e963","resolution":{"observed_at":"2026-08-06T16:44:56.249229Z","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":"2026-08-06T16:44:56.076559Z","title":"Caglioti, F","venue":null,"work_id":"dba07c2a-3923-4b63-bb5b-c0948493bc3d","year":2015},"citing_paper":{"arxiv_id":"2507.13060","last_updated":"2025-07-17T12:29:04Z","snapshot_observed_at":"2026-08-21T07:56:50.311067Z","submitted_at":"2025-07-17T12:29:04Z","title":"Exponential convergence for ultrafast diffusion equations with log-concave weights","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-06T16:44:49.675802Z"},"links":{"citing_paper":"/paper/2507.13060"},"observation_digest":"sha256:2fcbd83a2341a8b1478f08963fddba2a1b8c6442d5de1d9aff337cfb4356077d","observation_id":"0649cd5f-b64c-437b-b9f7-94c9d618f6be","resolution":{"observed_at":"2026-08-06T16:44:56.164798Z","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":"2026-08-06T16:44:55.960372Z","title":"Caglioti, F","venue":null,"work_id":"fc51ce91-3cbe-48d3-8fa3-a018d204dea4","year":null},"citing_paper":{"arxiv_id":"2507.13060","last_updated":"2025-07-17T12:29:04Z","snapshot_observed_at":"2026-08-21T07:56:50.311067Z","submitted_at":"2025-07-17T12:29:04Z","title":"Exponential convergence for ultrafast diffusion equations with log-concave weights","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-06T16:44:49.768141Z"},"links":{"citing_paper":"/paper/2507.13060"},"observation_digest":"sha256:f7d55e7c0da125dd8f85a8e475feaa72518d5059b850efdd4f6909f4fa1c5891","observation_id":"f24ed812-4804-4a15-b76f-45470ebc67ad","resolution":{"observed_at":"2026-08-06T16:44:56.008549Z","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":"2404.05456","last_updated":"2024-04-08T12:39:35Z","snapshot_observed_at":"2026-08-19T17:26:07.938229Z","submitted_at":"2024-04-08T12:39:35Z","title":"On Optimal Transport Maps Between 1 /d-Concave Densities","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2404.05456","snapshot_observed_at":"2026-08-06T16:44:49.845020Z","title":"Carlier, A","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.13060","last_updated":"2025-07-17T12:29:04Z","snapshot_observed_at":"2026-08-21T07:56:50.311067Z","submitted_at":"2025-07-17T12:29:04Z","title":"Exponential convergence for ultrafast diffusion equations with log-concave weights","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-06T16:44:49.845020Z"},"links":{"cited_paper":"/paper/2404.05456","citing_paper":"/paper/2507.13060"},"observation_digest":"sha256:e3be84e070cf4ad426465c422634ec43ce63af48f414009daf0c018695116d44","observation_id":"01d879a2-6b09-4ad7-bbc3-2b9a1434f58c","resolution":{"observed_at":"2026-08-06T16:44:49.845020Z","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":"2026-08-06T16:44:55.845134Z","title":null,"venue":null,"work_id":"543c230d-9af4-4f17-a82f-bb147d3caae6","year":2002},"citing_paper":{"arxiv_id":"2507.13060","last_updated":"2025-07-17T12:29:04Z","snapshot_observed_at":"2026-08-21T07:56:50.311067Z","submitted_at":"2025-07-17T12:29:04Z","title":"Exponential convergence for ultrafast diffusion equations with log-concave weights","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-06T16:44:49.901374Z"},"links":{"citing_paper":"/paper/2507.13060"},"observation_digest":"sha256:05961b66f3231b8efe10e87d4ce83f3643c9b43db0474d8ab18e32fa4c4c37a2","observation_id":"629ff8b3-62e6-49b7-9a2b-bf65caea34e8","resolution":{"observed_at":"2026-08-06T16:44:55.905358Z","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":"2026-08-06T16:44:55.710686Z","title":null,"venue":null,"work_id":"17b7f94b-ead4-4ba1-bbb7-796421f7b8d5","year":2009},"citing_paper":{"arxiv_id":"2507.13060","last_updated":"2025-07-17T12:29:04Z","snapshot_observed_at":"2026-08-21T07:56:50.311067Z","submitted_at":"2025-07-17T12:29:04Z","title":"Exponential convergence for ultrafast diffusion equations with log-concave weights","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-06T16:44:49.994583Z"},"links":{"citing_paper":"/paper/2507.13060"},"observation_digest":"sha256:1286d17aeb75e269ac70ad026fb40ed182c65dedc3d65f32986a5d7ca65817f7","observation_id":"6269c540-ed3b-477e-b928-c396fd599f75","resolution":{"observed_at":"2026-08-06T16:44:55.777829Z","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":"2026-08-06T16:44:55.502537Z","title":"Colombo, A","venue":null,"work_id":"c6a53ddc-761b-4676-a2d7-5eed50a4c19a","year":2017},"citing_paper":{"arxiv_id":"2507.13060","last_updated":"2025-07-17T12:29:04Z","snapshot_observed_at":"2026-08-21T07:56:50.311067Z","submitted_at":"2025-07-17T12:29:04Z","title":"Exponential convergence for ultrafast diffusion equations with log-concave weights","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-06T16:44:50.086428Z"},"links":{"citing_paper":"/paper/2507.13060"},"observation_digest":"sha256:f2a1d789219e54546844d4fae91fe6f2f95fff827fb0edb059fe6a595edf2335","observation_id":"92c4ef08-ee92-4b7e-be1f-e821782c3927","resolution":{"observed_at":"2026-08-06T16:44:55.593598Z","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":"2026-08-06T16:44:55.355284Z","title":"Daskalopoulos and M","venue":null,"work_id":"8eb60dd6-ac66-4c56-bd81-5e76ebcfab7a","year":1997},"citing_paper":{"arxiv_id":"2507.13060","last_updated":"2025-07-17T12:29:04Z","snapshot_observed_at":"2026-08-21T07:56:50.311067Z","submitted_at":"2025-07-17T12:29:04Z","title":"Exponential convergence for ultrafast diffusion equations with log-concave weights","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-06T16:44:50.161326Z"},"links":{"citing_paper":"/paper/2507.13060"},"observation_digest":"sha256:92033ca67ad49e905c7cf5cd7c37aee6205acc29c556a3f8f85666018c0491d4","observation_id":"2a86428b-98de-443e-b4c6-f2139d153ee9","resolution":{"observed_at":"2026-08-06T16:44:55.420032Z","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":"2026-08-06T16:44:55.137095Z","title":null,"venue":null,"work_id":"7244816a-3350-40a9-b5b4-f0484f6b2ea5","year":1988},"citing_paper":{"arxiv_id":"2507.13060","last_updated":"2025-07-17T12:29:04Z","snapshot_observed_at":"2026-08-21T07:56:50.311067Z","submitted_at":"2025-07-17T12:29:04Z","title":"Exponential convergence for ultrafast diffusion equations with log-concave weights","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-06T16:44:50.230036Z"},"links":{"citing_paper":"/paper/2507.13060"},"observation_digest":"sha256:2cae4ba9e7cfdbb0650f270e320facb5a9e0e50e2a4754652ed2182aae1a7509","observation_id":"77138908-9bc3-48f3-bba5-3c52452695ba","resolution":{"observed_at":"2026-08-06T16:44:55.283747Z","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":"2026-08-06T16:44:54.947986Z","title":"Fathi, D","venue":null,"work_id":"807dae88-c8e1-43ea-bf9f-4a7181f76b45","year":2024},"citing_paper":{"arxiv_id":"2507.13060","last_updated":"2025-07-17T12:29:04Z","snapshot_observed_at":"2026-08-21T07:56:50.311067Z","submitted_at":"2025-07-17T12:29:04Z","title":"Exponential convergence for ultrafast diffusion equations with log-concave weights","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-06T16:44:50.314442Z"},"links":{"citing_paper":"/paper/2507.13060"},"observation_digest":"sha256:6e48a1fe2d55721cf07c7d9bbcf74eca9a441c416f181e5d9dca5e821b79319e","observation_id":"d410e294-2022-40cc-bbdc-3bdbd9c92441","resolution":{"observed_at":"2026-08-06T16:44:55.026133Z","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":"2026-08-06T16:44:54.741000Z","title":"Graf and H","venue":null,"work_id":"a374a181-a9ee-45b5-83d8-74c377a0108e","year":2000},"citing_paper":{"arxiv_id":"2507.13060","last_updated":"2025-07-17T12:29:04Z","snapshot_observed_at":"2026-08-21T07:56:50.311067Z","submitted_at":"2025-07-17T12:29:04Z","title":"Exponential convergence for ultrafast diffusion equations with log-concave weights","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-06T16:44:50.396484Z"},"links":{"citing_paper":"/paper/2507.13060"},"observation_digest":"sha256:48df6a9d13baab1acd89f3f7dff7ee621a988fcf1db1ec78cbe881439a500cbb","observation_id":"4fddfa61-6177-4a97-a4d3-21eff22337d1","resolution":{"observed_at":"2026-08-06T16:44:54.861277Z","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":"2026-08-06T16:44:54.569045Z","title":"Golse,Quantization of probability densities: a gradient flow approach, inFrom par- ticle systems to partial differential equations, Springer Proc","venue":null,"work_id":"1e278eb5-3fdb-4c3c-bfa8-61cdfac0c605","year":2018},"citing_paper":{"arxiv_id":"2507.13060","last_updated":"2025-07-17T12:29:04Z","snapshot_observed_at":"2026-08-21T07:56:50.311067Z","submitted_at":"2025-07-17T12:29:04Z","title":"Exponential convergence for ultrafast diffusion equations with log-concave weights","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-06T16:44:50.491822Z"},"links":{"citing_paper":"/paper/2507.13060"},"observation_digest":"sha256:9a85448a6a73b6f2cd0ca04f4841913309c9a9dd4773cd58b81c733e48131c93","observation_id":"3fa1f6a7-c080-4ea7-b521-4c0dc9c1b914","resolution":{"observed_at":"2026-08-06T16:44:54.669398Z","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":"2026-08-06T16:44:54.382285Z","title":"Iacobelli, Asymptotic analysis for a very fast diffusion equation arising from the 1D quantization problem, Discrete Contin","venue":null,"work_id":"64b68df3-b73f-43f7-b7cc-ac962d0fc6af","year":2019},"citing_paper":{"arxiv_id":"2507.13060","last_updated":"2025-07-17T12:29:04Z","snapshot_observed_at":"2026-08-21T07:56:50.311067Z","submitted_at":"2025-07-17T12:29:04Z","title":"Exponential convergence for ultrafast diffusion equations with log-concave weights","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-06T16:44:50.622344Z"},"links":{"citing_paper":"/paper/2507.13060"},"observation_digest":"sha256:f1f0246bcfc84402891446dc723153cd20a3d399c1e3b2c2df648fc1e78c95b0","observation_id":"bbb9ce4c-2f4b-4225-98a4-65844d5fabb0","resolution":{"observed_at":"2026-08-06T16:44:54.498255Z","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":"2026-08-06T16:44:54.218712Z","title":"Iacobelli,A Gradient Flow Perspective on the Quantization Problem, PDE Models for Multi-Agent Phenomena, Springer INdAM Ser.,vol","venue":null,"work_id":"c85c2949-95e1-43f2-b22e-fbf160ff1986","year":2018},"citing_paper":{"arxiv_id":"2507.13060","last_updated":"2025-07-17T12:29:04Z","snapshot_observed_at":"2026-08-21T07:56:50.311067Z","submitted_at":"2025-07-17T12:29:04Z","title":"Exponential convergence for ultrafast diffusion equations with log-concave weights","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-06T16:44:50.713922Z"},"links":{"citing_paper":"/paper/2507.13060"},"observation_digest":"sha256:70a6a68d649b966e70fbddc8d3907e1e257caafcf44f01c20d395b39ec8d6ef2","observation_id":"e00bc900-931d-4e18-8b36-d442425241b0","resolution":{"observed_at":"2026-08-06T16:44:54.257244Z","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":"2026-08-06T16:44:54.058456Z","title":"Iacobelli, F","venue":null,"work_id":"1f7cfdfb-2237-40c9-b253-af8df6c2583a","year":2019},"citing_paper":{"arxiv_id":"2507.13060","last_updated":"2025-07-17T12:29:04Z","snapshot_observed_at":"2026-08-21T07:56:50.311067Z","submitted_at":"2025-07-17T12:29:04Z","title":"Exponential convergence for ultrafast diffusion equations with log-concave weights","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-06T16:44:50.788079Z"},"links":{"citing_paper":"/paper/2507.13060"},"observation_digest":"sha256:c264f2944d015a6038bb6eaa241ac87f8ff93bde48ac08d946d281a541f864ef","observation_id":"db37bef7-f2d1-4525-ac89-5b00ef895cbc","resolution":{"observed_at":"2026-08-06T16:44:54.139390Z","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":"2026-08-06T16:44:53.912300Z","title":"Jüngel, Entropy methods for diffusive partial differential equations","venue":null,"work_id":"87b19e9b-9a5f-4215-bde6-ea16f9358b61","year":null},"citing_paper":{"arxiv_id":"2507.13060","last_updated":"2025-07-17T12:29:04Z","snapshot_observed_at":"2026-08-21T07:56:50.311067Z","submitted_at":"2025-07-17T12:29:04Z","title":"Exponential convergence for ultrafast diffusion equations with log-concave weights","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-06T16:44:50.863186Z"},"links":{"citing_paper":"/paper/2507.13060"},"observation_digest":"sha256:5c3df9163b68f9cdc8ed17714c4ce4dafe1efadb82c4c031471e2203706c9bf5","observation_id":"00455825-f878-4f09-b0d7-805911ad8bdb","resolution":{"observed_at":"2026-08-06T16:44:53.993455Z","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":"2026-08-06T16:44:53.691263Z","title":null,"venue":null,"work_id":"433f1699-1c26-4a02-9ada-cb181f1aa258","year":2013},"citing_paper":{"arxiv_id":"2507.13060","last_updated":"2025-07-17T12:29:04Z","snapshot_observed_at":"2026-08-21T07:56:50.311067Z","submitted_at":"2025-07-17T12:29:04Z","title":"Exponential convergence for ultrafast diffusion equations with log-concave weights","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-06T16:44:50.958845Z"},"links":{"citing_paper":"/paper/2507.13060"},"observation_digest":"sha256:3e3be3cec804eeca963f1be5bca734324035fb46eeb9d6bc4c32e8e30c733e95","observation_id":"181a85dd-cc79-46eb-86c7-3eaad7bd8ab3","resolution":{"observed_at":"2026-08-06T16:44:53.760207Z","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":"2026-08-06T16:44:53.537259Z","title":"Milman, Spectral estimates, contractions, and hypercontractivity, J","venue":null,"work_id":"98a6cca7-5d2e-4067-b7d9-885e02c5de32","year":2007},"citing_paper":{"arxiv_id":"2507.13060","last_updated":"2025-07-17T12:29:04Z","snapshot_observed_at":"2026-08-21T07:56:50.311067Z","submitted_at":"2025-07-17T12:29:04Z","title":"Exponential convergence for ultrafast diffusion equations with log-concave weights","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-06T16:44:51.107087Z"},"links":{"citing_paper":"/paper/2507.13060"},"observation_digest":"sha256:69d59c1d319ab6474da7481c70870384f2a74338a1aeb0c8f1aba42b432c15b2","observation_id":"14dbf084-bd5d-45a8-887f-9c81dc6e87e2","resolution":{"observed_at":"2026-08-06T16:44:53.591755Z","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":"2026-08-06T16:44:53.349348Z","title":null,"venue":null,"work_id":"ac9a1604-a52f-4e46-98f1-b40bcdc6bf36","year":2001},"citing_paper":{"arxiv_id":"2507.13060","last_updated":"2025-07-17T12:29:04Z","snapshot_observed_at":"2026-08-21T07:56:50.311067Z","submitted_at":"2025-07-17T12:29:04Z","title":"Exponential convergence for ultrafast diffusion equations with log-concave weights","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-06T16:44:51.162017Z"},"links":{"citing_paper":"/paper/2507.13060"},"observation_digest":"sha256:8b15b3270f2e19e01d9d160078471316673a99df7c58386a0eec5ff3675fdbb1","observation_id":"c357afb0-c6a2-4c8c-9012-37bed7167930","resolution":{"observed_at":"2026-08-06T16:44:53.429950Z","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":"2026-08-06T16:44:53.181454Z","title":"Otto and C","venue":null,"work_id":"cbe8b4bb-cbeb-47e4-b2c8-731032444a45","year":2000},"citing_paper":{"arxiv_id":"2507.13060","last_updated":"2025-07-17T12:29:04Z","snapshot_observed_at":"2026-08-21T07:56:50.311067Z","submitted_at":"2025-07-17T12:29:04Z","title":"Exponential convergence for ultrafast diffusion equations with log-concave weights","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-06T16:44:51.236066Z"},"links":{"citing_paper":"/paper/2507.13060"},"observation_digest":"sha256:1d0bbde99254eddd4f45a786a5c6bdc29c48fbc82b96660873a4673a9b82f617","observation_id":"2140bf7c-ef6d-4f90-a39d-76b7a020949f","resolution":{"observed_at":"2026-08-06T16:44:53.257414Z","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":"2026-08-06T16:44:53.045970Z","title":null,"venue":null,"work_id":"34d68073-c333-455f-9ff5-160d86149cca","year":2018},"citing_paper":{"arxiv_id":"2507.13060","last_updated":"2025-07-17T12:29:04Z","snapshot_observed_at":"2026-08-21T07:56:50.311067Z","submitted_at":"2025-07-17T12:29:04Z","title":"Exponential convergence for ultrafast diffusion equations with log-concave weights","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-06T16:44:51.317274Z"},"links":{"citing_paper":"/paper/2507.13060"},"observation_digest":"sha256:7ecfc04c9d4b06a67a56aed57879a3b5fb7ebc3877e45a86c1b9571d3c9c7da3","observation_id":"ac2ed11c-9c93-4244-b7b9-17510820264b","resolution":{"observed_at":"2026-08-06T16:44:53.102754Z","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":"2026-08-06T16:44:52.853633Z","title":"Rodríguez and J","venue":null,"work_id":"d70dc404-4c46-48da-9f25-9ec0e8e5024c","year":1990},"citing_paper":{"arxiv_id":"2507.13060","last_updated":"2025-07-17T12:29:04Z","snapshot_observed_at":"2026-08-21T07:56:50.311067Z","submitted_at":"2025-07-17T12:29:04Z","title":"Exponential convergence for ultrafast diffusion equations with log-concave weights","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-06T16:44:51.384718Z"},"links":{"citing_paper":"/paper/2507.13060"},"observation_digest":"sha256:9a8f5db113a182ac61ecdaf7dff38445efcb4893d1c2fa925b297e44ccf9da78","observation_id":"301082be-11fd-4e46-b688-f9d7f6306e29","resolution":{"observed_at":"2026-08-06T16:44:52.922850Z","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":"2026-08-06T16:44:52.682613Z","title":"Salvarani and G","venue":null,"work_id":"c54c957a-2362-4500-96f7-dde994d41f05","year":2009},"citing_paper":{"arxiv_id":"2507.13060","last_updated":"2025-07-17T12:29:04Z","snapshot_observed_at":"2026-08-21T07:56:50.311067Z","submitted_at":"2025-07-17T12:29:04Z","title":"Exponential convergence for ultrafast diffusion equations with log-concave weights","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-06T16:44:51.456436Z"},"links":{"citing_paper":"/paper/2507.13060"},"observation_digest":"sha256:84845dcc07d88b36096feb3f5719105073b46f866f45b6445ba4473984883a2e","observation_id":"6fac6e82-33b2-4cc7-bdf7-7d8f0e1537d4","resolution":{"observed_at":"2026-08-06T16:44:52.748821Z","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":"2026-08-06T16:44:51.528995Z","title":"Villani,Topics in Optimal Transportation, Graduate Studies in Mathematics, vol","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2507.13060","last_updated":"2025-07-17T12:29:04Z","snapshot_observed_at":"2026-08-21T07:56:50.311067Z","submitted_at":"2025-07-17T12:29:04Z","title":"Exponential convergence for ultrafast diffusion equations with log-concave weights","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-06T16:44:51.528995Z"},"links":{"citing_paper":"/paper/2507.13060"},"observation_digest":"sha256:a5f64afa875cd64136038acf8623d28ae1ed434863dd25592a224970ae82ff33","observation_id":"b1a8b6a1-620f-41ed-880c-b737b24bf0aa","resolution":{"observed_at":"2026-08-06T16:44:51.528995Z","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":"2026-08-06T16:44:52.511916Z","title":null,"venue":null,"work_id":"b20561e2-345f-4710-bf0f-0c51fc3e6c6e","year":2006},"citing_paper":{"arxiv_id":"2507.13060","last_updated":"2025-07-17T12:29:04Z","snapshot_observed_at":"2026-08-21T07:56:50.311067Z","submitted_at":"2025-07-17T12:29:04Z","title":"Exponential convergence for ultrafast diffusion equations with log-concave weights","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-06T16:44:51.635344Z"},"links":{"citing_paper":"/paper/2507.13060"},"observation_digest":"sha256:474e51fdf33b147a6d21eec4576880db537a3a3f1b1dfbbede72a0ddbbb6e089","observation_id":"be422970-ff25-4a3f-8f6b-7a77e5a3e5d9","resolution":{"observed_at":"2026-08-06T16:44:52.595481Z","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":"2026-08-06T16:44:52.341467Z","title":null,"venue":null,"work_id":"f08ac13f-1233-4866-9964-df29967e7355","year":2007},"citing_paper":{"arxiv_id":"2507.13060","last_updated":"2025-07-17T12:29:04Z","snapshot_observed_at":"2026-08-21T07:56:50.311067Z","submitted_at":"2025-07-17T12:29:04Z","title":"Exponential convergence for ultrafast diffusion equations with log-concave weights","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-06T16:44:51.712030Z"},"links":{"citing_paper":"/paper/2507.13060"},"observation_digest":"sha256:bab15356d775f85361670dc4ff74bb0cc90e85428200f904fd31ac7ef0ceefd3","observation_id":"1fd50958-9bac-471d-9009-03e292cfb7cb","resolution":{"observed_at":"2026-08-06T16:44:52.407180Z","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":"2026-08-06T16:44:52.191102Z","title":null,"venue":null,"work_id":"345b29d4-e38a-446a-82ec-1387861f392b","year":2005},"citing_paper":{"arxiv_id":"2507.13060","last_updated":"2025-07-17T12:29:04Z","snapshot_observed_at":"2026-08-21T07:56:50.311067Z","submitted_at":"2025-07-17T12:29:04Z","title":"Exponential convergence for ultrafast diffusion equations with log-concave weights","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-06T16:44:51.781819Z"},"links":{"citing_paper":"/paper/2507.13060"},"observation_digest":"sha256:15bf22495ec307013aa48e7592357c165c6372a47c28bf892ce29791dba71184","observation_id":"2eaba211-24ca-4cb8-aa25-4e5fd9ea2dc9","resolution":{"observed_at":"2026-08-06T16:44:52.269440Z","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":"2026-08-06T16:44:52.017195Z","title":"Villani, Optimal transport","venue":null,"work_id":"5810af15-2c09-4f27-b785-b815b18104a5","year":null},"citing_paper":{"arxiv_id":"2507.13060","last_updated":"2025-07-17T12:29:04Z","snapshot_observed_at":"2026-08-21T07:56:50.311067Z","submitted_at":"2025-07-17T12:29:04Z","title":"Exponential convergence for ultrafast diffusion equations with log-concave weights","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-06T16:44:51.861900Z"},"links":{"citing_paper":"/paper/2507.13060"},"observation_digest":"sha256:d4838e655643e0cac43869244b87816d23acebd414e1573e635c6ce26b3186da","observation_id":"78e8a207-0b67-4111-b400-074f6f8d5ca2","resolution":{"observed_at":"2026-08-06T16:44:52.111004Z","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":"2507.13060","last_updated":"2025-07-17T12:29:04Z","latest_version":1,"primary_category":"math.AP","snapshot_observed_at":"2026-08-21T07:56:50.311067Z","submitted_at":"2025-07-17T12:29:04Z","title":"Exponential convergence for ultrafast diffusion equations with log-concave weights"},"reference_resolution":{"displayed":37,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":13,"verified_exact":0,"verified_fuzzy":24},"total_outbound_references":37},"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 21 August 2026, this Paper Citation Record lists 37 of 37 outbound references and 1 inbound Pith citation observation for arXiv:2507.13060."}