{"as_of":"2026-08-11T13:47:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:f40909a08a2f18cc373bbf04192d260347089844d3fd1352a3047c4ad2e91c7f","coverage":[{"denominator":22,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":22,"source":"paper_references, paper_reference_links","source_observed_at":"2026-05-13T22:27:58.747232Z","state":"measured"},{"denominator":22,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":22,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-11T06:34:44.6726+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/2604.00562/citation-record","integrity":"/paper/2604.00562/integrity","json":"/paper/2604.00562/citation-record.json","paper":"/paper/2604.00562"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"61e2cf98-5116-42c9-9a70-fcba7482c4df","year":2010},"citing_paper":{"arxiv_id":"2604.00562","last_updated":"2026-04-20T05:36:47Z","snapshot_observed_at":"2026-08-10T09:58:42.582359Z","submitted_at":"2026-04-01T07:12:50Z","title":"Rigidity of the Borell-Brascamp-Lieb Inequality on Weighted Riemannian Manifolds","version":2},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-05-13T22:27:58.747232Z"},"links":{"citing_paper":"/paper/2604.00562"},"observation_digest":"sha256:d1ada959b8eaec6c07ea714dcd394560b5878c54015bfef67a5a1feb92975e74","observation_id":"6ca10562-6f04-4032-8602-fea0838c590f","resolution":{"observed_at":"2026-05-13T22:28:21.440071Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"490e5b95-6222-46db-9df0-c01f11bb31fd","year":2018},"citing_paper":{"arxiv_id":"2604.00562","last_updated":"2026-04-20T05:36:47Z","snapshot_observed_at":"2026-08-10T09:58:42.582359Z","submitted_at":"2026-04-01T07:12:50Z","title":"Rigidity of the Borell-Brascamp-Lieb Inequality on Weighted Riemannian Manifolds","version":2},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-05-13T22:27:58.747232Z"},"links":{"citing_paper":"/paper/2604.00562"},"observation_digest":"sha256:e84c25ec9acba5bf5e9479c05c819d69912d2c3a202ad21fee8ee52b055abc99","observation_id":"264aba2b-0948-4bb2-9a5d-c87c96ddfa5f","resolution":{"observed_at":"2026-05-13T22:28:21.441654Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"b81cf476-68c7-453b-a233-a934e4947e20","year":1975},"citing_paper":{"arxiv_id":"2604.00562","last_updated":"2026-04-20T05:36:47Z","snapshot_observed_at":"2026-08-10T09:58:42.582359Z","submitted_at":"2026-04-01T07:12:50Z","title":"Rigidity of the Borell-Brascamp-Lieb Inequality on Weighted Riemannian Manifolds","version":2},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-05-13T22:27:58.747232Z"},"links":{"citing_paper":"/paper/2604.00562"},"observation_digest":"sha256:6eef276bcbf707ca3345027064db9024c7fabd4a8bd0bc4c5d06c82a48befe8c","observation_id":"9fc0f221-4e58-48c3-a9ad-64a553b202ff","resolution":{"observed_at":"2026-05-13T22:28:21.436538Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"80134c21-bb58-4f37-8992-91d3eff59b76","year":1976},"citing_paper":{"arxiv_id":"2604.00562","last_updated":"2026-04-20T05:36:47Z","snapshot_observed_at":"2026-08-10T09:58:42.582359Z","submitted_at":"2026-04-01T07:12:50Z","title":"Rigidity of the Borell-Brascamp-Lieb Inequality on Weighted Riemannian Manifolds","version":2},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-05-13T22:27:58.747232Z"},"links":{"citing_paper":"/paper/2604.00562"},"observation_digest":"sha256:b4c5b0fb00875496b9b1024e7c5477651e47d7c5e0b9188d9ed4fe3bdf9566ee","observation_id":"26e35d19-9f24-47e9-9d79-4973df6eeb4c","resolution":{"observed_at":"2026-05-13T22:28:21.434996Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2401.03949","last_updated":"2025-02-03T17:09:29Z","snapshot_observed_at":"2026-08-04T14:46:31.568257Z","submitted_at":"2024-01-08T15:13:34Z","title":"A sharp isoperimetric-type inequality for Lorentzian spaces satisfying timelike Ricci lower bounds","version":2},"cited_work":{"arxiv_id":"2401.03949","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2401.03949","snapshot_observed_at":"2026-07-03T13:08:08.101177Z","title":"Cavalletti and A","venue":null,"work_id":"90d5c074-aa8b-4bc6-86ff-02050540e5b9","year":2024},"citing_paper":{"arxiv_id":"2604.00562","last_updated":"2026-04-20T05:36:47Z","snapshot_observed_at":"2026-08-10T09:58:42.582359Z","submitted_at":"2026-04-01T07:12:50Z","title":"Rigidity of the Borell-Brascamp-Lieb Inequality on Weighted Riemannian Manifolds","version":2},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-05-13T22:27:58.747232Z"},"links":{"cited_paper":"/paper/2401.03949","citing_paper":"/paper/2604.00562"},"observation_digest":"sha256:b2619891792ca3932a40f47fcb5fd3967d82f3c331d70823165ea5e6b11293da","observation_id":"6a5d7f26-f4ed-49f7-bd1e-53fe0d78e07f","resolution":{"observed_at":"2026-05-13T22:28:21.196682Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-06-05T21:23:00.469572Z","title":"Cordero-Erausquin, R","venue":null,"work_id":"e01fa6a7-f092-4853-952a-84cf20b99108","year":2001},"citing_paper":{"arxiv_id":"2604.00562","last_updated":"2026-04-20T05:36:47Z","snapshot_observed_at":"2026-08-10T09:58:42.582359Z","submitted_at":"2026-04-01T07:12:50Z","title":"Rigidity of the Borell-Brascamp-Lieb Inequality on Weighted Riemannian Manifolds","version":2},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-05-13T22:27:58.747232Z"},"links":{"citing_paper":"/paper/2604.00562"},"observation_digest":"sha256:80db52e09d2d2b51e04a46f8752d3b32b41c48342cb00c4c6455b4d79bfb7c97","observation_id":"206b4ad8-093f-4fab-bae8-26dde5ba961e","resolution":{"observed_at":"2026-05-13T22:28:21.433283Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-06-05T21:23:00.469572Z","title":"De Philippis and N","venue":null,"work_id":"831fbfbf-417e-4fd5-bcc1-344e20a12cdc","year":2016},"citing_paper":{"arxiv_id":"2604.00562","last_updated":"2026-04-20T05:36:47Z","snapshot_observed_at":"2026-08-10T09:58:42.582359Z","submitted_at":"2026-04-01T07:12:50Z","title":"Rigidity of the Borell-Brascamp-Lieb Inequality on Weighted Riemannian Manifolds","version":2},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-05-13T22:27:58.747232Z"},"links":{"citing_paper":"/paper/2604.00562"},"observation_digest":"sha256:204dcf3429acff591d70ac26520a0f58f08f033c7e8cb0b881ea9f70e426eb54","observation_id":"7d027f21-2c7c-4c71-aa2d-d7bde2a7b706","resolution":{"observed_at":"2026-05-13T22:28:21.421540Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"791eacc4-de92-4bb6-af90-625ef414040e","year":1977},"citing_paper":{"arxiv_id":"2604.00562","last_updated":"2026-04-20T05:36:47Z","snapshot_observed_at":"2026-08-10T09:58:42.582359Z","submitted_at":"2026-04-01T07:12:50Z","title":"Rigidity of the Borell-Brascamp-Lieb Inequality on Weighted Riemannian Manifolds","version":2},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-05-13T22:27:58.747232Z"},"links":{"citing_paper":"/paper/2604.00562"},"observation_digest":"sha256:332974aa112067075cbe127c1d18ccff379f30e97f598bf875a6094244495c23","observation_id":"4e45ec90-528d-486d-9ea6-820a117b6935","resolution":{"observed_at":"2026-05-13T22:28:21.419892Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2504.06186","last_updated":"2025-04-08T16:28:07Z","snapshot_observed_at":"2026-08-07T16:07:27.584743Z","submitted_at":"2025-04-08T16:28:07Z","title":"Equivalence between the timelike Brunn-Minkowski inequality and timelike Bakry-\\'Emery-Ricci lower bound on weighted globally hyperbolic spacetimes","version":1},"cited_work":{"arxiv_id":"2504.06186","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2504.06186","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Farooqui","venue":null,"work_id":"0ff85a82-24bb-43d8-8b08-aa9244c059c6","year":2025},"citing_paper":{"arxiv_id":"2604.00562","last_updated":"2026-04-20T05:36:47Z","snapshot_observed_at":"2026-08-10T09:58:42.582359Z","submitted_at":"2026-04-01T07:12:50Z","title":"Rigidity of the Borell-Brascamp-Lieb Inequality on Weighted Riemannian Manifolds","version":2},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-05-13T22:27:58.747232Z"},"links":{"cited_paper":"/paper/2504.06186","citing_paper":"/paper/2604.00562"},"observation_digest":"sha256:ea1529961944b3bc7274326262ee49b2e6cf919b77b670619484857e8da503ec","observation_id":"0b93ae45-7a19-4b73-9d91-f78a7453d0a9","resolution":{"observed_at":"2026-05-13T22:28:21.194155Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-06-05T21:23:00.469572Z","title":"Local Semiconvexity of Kantorovich Potentials on Non-compact Manifolds","venue":null,"work_id":"5fdaae79-fe91-4bfd-8b79-03644d79f971","year":2011},"citing_paper":{"arxiv_id":"2604.00562","last_updated":"2026-04-20T05:36:47Z","snapshot_observed_at":"2026-08-10T09:58:42.582359Z","submitted_at":"2026-04-01T07:12:50Z","title":"Rigidity of the Borell-Brascamp-Lieb Inequality on Weighted Riemannian Manifolds","version":2},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-05-13T22:27:58.747232Z"},"links":{"citing_paper":"/paper/2604.00562"},"observation_digest":"sha256:e7878956d8ed18fece02667da76d42ac71e2f7c5345cd301c5003ecdc3545651","observation_id":"c349de90-386e-4d89-a861-f7c045030006","resolution":{"observed_at":"2026-05-13T22:28:21.414915Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"00d8fe26-846c-4717-82a4-bf2e86feff6c","year":2002},"citing_paper":{"arxiv_id":"2604.00562","last_updated":"2026-04-20T05:36:47Z","snapshot_observed_at":"2026-08-10T09:58:42.582359Z","submitted_at":"2026-04-01T07:12:50Z","title":"Rigidity of the Borell-Brascamp-Lieb Inequality on Weighted Riemannian Manifolds","version":2},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-05-13T22:27:58.747232Z"},"links":{"citing_paper":"/paper/2604.00562"},"observation_digest":"sha256:425c006af94bb2a85d96833dc2564c8ac440db60546cb3a2d06a41f7273f6239","observation_id":"30350814-2114-4a1d-b8ec-c4bd45f5c2b5","resolution":{"observed_at":"2026-05-13T22:28:21.413209Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-06-05T21:23:00.469572Z","title":"Henstock and A","venue":null,"work_id":"6c759301-7f06-41ca-b2cd-cd1cb1469f0f","year":1953},"citing_paper":{"arxiv_id":"2604.00562","last_updated":"2026-04-20T05:36:47Z","snapshot_observed_at":"2026-08-10T09:58:42.582359Z","submitted_at":"2026-04-01T07:12:50Z","title":"Rigidity of the Borell-Brascamp-Lieb Inequality on Weighted Riemannian Manifolds","version":2},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-05-13T22:27:58.747232Z"},"links":{"citing_paper":"/paper/2604.00562"},"observation_digest":"sha256:6c65f916c122d3f71cb253899f33defed2bf1cabd1dab7d5274d859238229726","observation_id":"b1b617a6-e728-4a7f-b630-4b0bf537d008","resolution":{"observed_at":"2026-05-13T22:28:21.443194Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-06-05T21:23:00.469572Z","title":"Lott and C","venue":null,"work_id":"2f4535a1-65f4-4569-a43c-ee577fd106e6","year":2009},"citing_paper":{"arxiv_id":"2604.00562","last_updated":"2026-04-20T05:36:47Z","snapshot_observed_at":"2026-08-10T09:58:42.582359Z","submitted_at":"2026-04-01T07:12:50Z","title":"Rigidity of the Borell-Brascamp-Lieb Inequality on Weighted Riemannian Manifolds","version":2},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-05-13T22:27:58.747232Z"},"links":{"citing_paper":"/paper/2604.00562"},"observation_digest":"sha256:a6776cdbb677ddb6b434776ce03b3e53afd5452a73c0dcb75b630b1254beb22f","observation_id":"c70c8760-6e33-4110-b52d-92b5598891ce","resolution":{"observed_at":"2026-05-13T22:28:21.427764Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-06-05T21:23:00.469572Z","title":"Magnabosco, L","venue":null,"work_id":"dcda35d8-1a08-4f3c-b5c5-4dfd17f2988b","year":2024},"citing_paper":{"arxiv_id":"2604.00562","last_updated":"2026-04-20T05:36:47Z","snapshot_observed_at":"2026-08-10T09:58:42.582359Z","submitted_at":"2026-04-01T07:12:50Z","title":"Rigidity of the Borell-Brascamp-Lieb Inequality on Weighted Riemannian Manifolds","version":2},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-05-13T22:27:58.747232Z"},"links":{"citing_paper":"/paper/2604.00562"},"observation_digest":"sha256:b2280d9fad3ea6bbd482950f788e1955b7855f8ee933ec7526ad5e9267facbe5","observation_id":"9b036265-f7a4-4835-a0c4-052adc7b0f90","resolution":{"observed_at":"2026-05-13T22:28:21.424671Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"3063af5f-ff8b-4db4-b184-a561404d5f85","year":2001},"citing_paper":{"arxiv_id":"2604.00562","last_updated":"2026-04-20T05:36:47Z","snapshot_observed_at":"2026-08-10T09:58:42.582359Z","submitted_at":"2026-04-01T07:12:50Z","title":"Rigidity of the Borell-Brascamp-Lieb Inequality on Weighted Riemannian Manifolds","version":2},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-05-13T22:27:58.747232Z"},"links":{"citing_paper":"/paper/2604.00562"},"observation_digest":"sha256:e1565be1226bddf2f1a74085dde68ac070fe03dcb2023ccf3a318b352b63d3ee","observation_id":"c01e60bc-57e0-47ac-a03f-d18832ef8980","resolution":{"observed_at":"2026-05-13T22:28:21.418338Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"cf35b69f-ffe3-4b94-8247-f641ed954492","year":2020},"citing_paper":{"arxiv_id":"2604.00562","last_updated":"2026-04-20T05:36:47Z","snapshot_observed_at":"2026-08-10T09:58:42.582359Z","submitted_at":"2026-04-01T07:12:50Z","title":"Rigidity of the Borell-Brascamp-Lieb Inequality on Weighted Riemannian Manifolds","version":2},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-05-13T22:27:58.747232Z"},"links":{"citing_paper":"/paper/2604.00562"},"observation_digest":"sha256:11a9f1a0388f1610525cbd95d5309b5924ff43616c737e9a457b16d9a7fea15f","observation_id":"1f2113af-11a5-4e59-8b06-5aaecf293492","resolution":{"observed_at":"2026-05-13T22:28:21.423136Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-06-05T21:23:00.469572Z","title":"Mondino and S","venue":null,"work_id":"08da6631-f482-476f-84ec-d8e682121f90","year":2023},"citing_paper":{"arxiv_id":"2604.00562","last_updated":"2026-04-20T05:36:47Z","snapshot_observed_at":"2026-08-10T09:58:42.582359Z","submitted_at":"2026-04-01T07:12:50Z","title":"Rigidity of the Borell-Brascamp-Lieb Inequality on Weighted Riemannian Manifolds","version":2},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-05-13T22:27:58.747232Z"},"links":{"citing_paper":"/paper/2604.00562"},"observation_digest":"sha256:6ea679d659cbb01eaa76083940646229ccb78341ca66b4c4fae492383042d9ca","observation_id":"fbd294d3-287b-4825-88c7-860c76e9f83c","resolution":{"observed_at":"2026-05-13T22:28:21.431494Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"6ba65433-3a94-49a3-84da-5cebe84fd693","year":2009},"citing_paper":{"arxiv_id":"2604.00562","last_updated":"2026-04-20T05:36:47Z","snapshot_observed_at":"2026-08-10T09:58:42.582359Z","submitted_at":"2026-04-01T07:12:50Z","title":"Rigidity of the Borell-Brascamp-Lieb Inequality on Weighted Riemannian Manifolds","version":2},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-05-13T22:27:58.747232Z"},"links":{"citing_paper":"/paper/2604.00562"},"observation_digest":"sha256:06079362c27f0cc8ef1a49a58580c700e8610a9fb68c12816090cc30a2ef7c05","observation_id":"2db73550-c22f-4d33-a40d-2ce223b74a01","resolution":{"observed_at":"2026-05-13T22:28:21.438508Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-06-05T21:23:00.469572Z","title":"Otto and C","venue":null,"work_id":"c593eb5f-e924-4b0c-b0ed-f04896ba5045","year":2000},"citing_paper":{"arxiv_id":"2604.00562","last_updated":"2026-04-20T05:36:47Z","snapshot_observed_at":"2026-08-10T09:58:42.582359Z","submitted_at":"2026-04-01T07:12:50Z","title":"Rigidity of the Borell-Brascamp-Lieb Inequality on Weighted Riemannian Manifolds","version":2},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-05-13T22:27:58.747232Z"},"links":{"citing_paper":"/paper/2604.00562"},"observation_digest":"sha256:8400ca109b00ae80b7513fd3db57c94e4cf92e3da04a9efea4b47fefbed79dd5","observation_id":"29ad427d-1e6a-4f94-9e17-b506084a32a9","resolution":{"observed_at":"2026-05-13T22:28:21.444797Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"3ef3c5ef-8b67-492c-9907-e74558444534","year":2006},"citing_paper":{"arxiv_id":"2604.00562","last_updated":"2026-04-20T05:36:47Z","snapshot_observed_at":"2026-08-10T09:58:42.582359Z","submitted_at":"2026-04-01T07:12:50Z","title":"Rigidity of the Borell-Brascamp-Lieb Inequality on Weighted Riemannian Manifolds","version":2},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-05-13T22:27:58.747232Z"},"links":{"citing_paper":"/paper/2604.00562"},"observation_digest":"sha256:132b97d8e088f88be5b2935d50df06b506595054e68af7da3c8571ed36b6eeca","observation_id":"84cb4539-30f4-45e1-ade6-47afb0f2ad69","resolution":{"observed_at":"2026-05-13T22:28:21.416676Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"b934eff8-2aec-4565-94e9-3e389111ce6f","year":2003},"citing_paper":{"arxiv_id":"2604.00562","last_updated":"2026-04-20T05:36:47Z","snapshot_observed_at":"2026-08-10T09:58:42.582359Z","submitted_at":"2026-04-01T07:12:50Z","title":"Rigidity of the Borell-Brascamp-Lieb Inequality on Weighted Riemannian Manifolds","version":2},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-05-13T22:27:58.747232Z"},"links":{"citing_paper":"/paper/2604.00562"},"observation_digest":"sha256:284a78153a992e5aee25867af62f04137146ed213f1aa94aad4d5244ae454b85","observation_id":"86cf0922-627c-44b3-8883-fa29b500a49b","resolution":{"observed_at":"2026-05-13T22:28:21.429443Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"76a17966-f959-4aa1-a0a7-f4b448254ab9","year":2009},"citing_paper":{"arxiv_id":"2604.00562","last_updated":"2026-04-20T05:36:47Z","snapshot_observed_at":"2026-08-10T09:58:42.582359Z","submitted_at":"2026-04-01T07:12:50Z","title":"Rigidity of the Borell-Brascamp-Lieb Inequality on Weighted Riemannian Manifolds","version":2},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-05-13T22:27:58.747232Z"},"links":{"citing_paper":"/paper/2604.00562"},"observation_digest":"sha256:f16e7e8a247851b206a6ff902f96bbc21dd47aa45bcbabd8bef53c4d897b68d5","observation_id":"a482b540-d2db-4489-bdf8-11756d67dedf","resolution":{"observed_at":"2026-05-13T22:28:21.426181Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2604.00562","last_updated":"2026-04-20T05:36:47Z","latest_version":2,"primary_category":"math.DG","snapshot_observed_at":"2026-08-10T09:58:42.582359Z","submitted_at":"2026-04-01T07:12:50Z","title":"Rigidity of the Borell-Brascamp-Lieb Inequality on Weighted Riemannian Manifolds"},"reference_resolution":{"displayed":22,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":12,"verified_exact":2,"verified_fuzzy":8},"total_outbound_references":22},"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":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"thesis":"As of 11 August 2026, this Paper Citation Record lists 22 of 22 outbound references and 0 inbound Pith citation observations for arXiv:2604.00562."}