{"as_of":"2026-08-20T21:28:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:4c94b8bed5b3f99ff6f09e9ccf85afe864940cbc07615d7db74b7c4aa849ae91","coverage":[{"denominator":34,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":34,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-04T05:48:25.209394Z","state":"measured"},{"denominator":34,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":34,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-20T06:33:59.587034+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/2603.29989/citation-record","integrity":"/paper/2603.29989/integrity","json":"/paper/2603.29989/citation-record.json","paper":"/paper/2603.29989"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T05:48:21.795722Z","title":"Andrews and J","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2603.29989","last_updated":"2026-08-03T16:46:38Z","snapshot_observed_at":"2026-08-14T16:03:09.542975Z","submitted_at":"2026-03-31T16:54:27Z","title":"A Brunn-Minkowski inequality for Schr\\\"odinger operators with Kato class potentials","version":6},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-04T05:48:21.795722Z"},"links":{"citing_paper":"/paper/2603.29989"},"observation_digest":"sha256:7c595ac632056ab64ddc2cbdd2635b58555bc22e4409ff90b745d3492b989df3","observation_id":"b8bb88b8-53b8-4bac-8d01-30c48e2f7662","resolution":{"observed_at":"2026-08-04T05:48:21.795722Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T05:48:21.864744Z","title":null,"venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2603.29989","last_updated":"2026-08-03T16:46:38Z","snapshot_observed_at":"2026-08-14T16:03:09.542975Z","submitted_at":"2026-03-31T16:54:27Z","title":"A Brunn-Minkowski inequality for Schr\\\"odinger operators with Kato class potentials","version":6},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-04T05:48:21.864744Z"},"links":{"citing_paper":"/paper/2603.29989"},"observation_digest":"sha256:987da6818199475bb404df3c5a59d7a0ece33e8d43d96e6c32d526dfcd48e8bc","observation_id":"730013e3-aa06-4890-9458-af93d8820743","resolution":{"observed_at":"2026-08-04T05:48:21.864744Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T05:48:21.935199Z","title":null,"venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2603.29989","last_updated":"2026-08-03T16:46:38Z","snapshot_observed_at":"2026-08-14T16:03:09.542975Z","submitted_at":"2026-03-31T16:54:27Z","title":"A Brunn-Minkowski inequality for Schr\\\"odinger operators with Kato class potentials","version":6},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-04T05:48:21.935199Z"},"links":{"citing_paper":"/paper/2603.29989"},"observation_digest":"sha256:21b5f465f8f2d01a481d6cf4e66663811ae09c1e483917b5e348615c437c0a30","observation_id":"fb99765b-2356-455e-b80d-2721f51b5361","resolution":{"observed_at":"2026-08-04T05:48:21.935199Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T05:48:21.992341Z","title":"Borell,The Brunn-Minkowski inequality in Gauss space, Invent","venue":null,"work_id":null,"year":1975},"citing_paper":{"arxiv_id":"2603.29989","last_updated":"2026-08-03T16:46:38Z","snapshot_observed_at":"2026-08-14T16:03:09.542975Z","submitted_at":"2026-03-31T16:54:27Z","title":"A Brunn-Minkowski inequality for Schr\\\"odinger operators with Kato class potentials","version":6},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-04T05:48:21.992341Z"},"links":{"citing_paper":"/paper/2603.29989"},"observation_digest":"sha256:f1acc0d226d34f0d4ed91a3be90b25d5b38162622065c5796d9acaa54a048118","observation_id":"38aab127-107e-49cd-bcd7-73cd2062a305","resolution":{"observed_at":"2026-08-04T05:48:21.992341Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T05:48:22.032385Z","title":null,"venue":null,"work_id":null,"year":1975},"citing_paper":{"arxiv_id":"2603.29989","last_updated":"2026-08-03T16:46:38Z","snapshot_observed_at":"2026-08-14T16:03:09.542975Z","submitted_at":"2026-03-31T16:54:27Z","title":"A Brunn-Minkowski inequality for Schr\\\"odinger operators with Kato class potentials","version":6},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-04T05:48:22.032385Z"},"links":{"citing_paper":"/paper/2603.29989"},"observation_digest":"sha256:be870f9a133c8e40684becb3a4abf21175f64a7ce79e5a7e468254ab81a0c65c","observation_id":"cd2c6d07-be20-4390-8293-b75cf5ca68cf","resolution":{"observed_at":"2026-08-04T05:48:22.032385Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T05:48:22.109494Z","title":"Brascamp and E.H","venue":null,"work_id":null,"year":1975},"citing_paper":{"arxiv_id":"2603.29989","last_updated":"2026-08-03T16:46:38Z","snapshot_observed_at":"2026-08-14T16:03:09.542975Z","submitted_at":"2026-03-31T16:54:27Z","title":"A Brunn-Minkowski inequality for Schr\\\"odinger operators with Kato class potentials","version":6},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-04T05:48:22.109494Z"},"links":{"citing_paper":"/paper/2603.29989"},"observation_digest":"sha256:666cb840110b0ce8d6555d496e8a1575d7fa0213b188708dca05cbd80c019736","observation_id":"2bb3eb7d-c7f8-4223-81aa-1d071e572a61","resolution":{"observed_at":"2026-08-04T05:48:22.109494Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T05:48:22.249319Z","title":null,"venue":null,"work_id":null,"year":1976},"citing_paper":{"arxiv_id":"2603.29989","last_updated":"2026-08-03T16:46:38Z","snapshot_observed_at":"2026-08-14T16:03:09.542975Z","submitted_at":"2026-03-31T16:54:27Z","title":"A Brunn-Minkowski inequality for Schr\\\"odinger operators with Kato class potentials","version":6},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-04T05:48:22.249319Z"},"links":{"citing_paper":"/paper/2603.29989"},"observation_digest":"sha256:13d5ba19c0df80fcd6fb5cb41d3cd8db9ccdf7f676b92c913b0c934fe628a6a9","observation_id":"4339ae27-5470-472e-99ac-1ee6b0fd9db7","resolution":{"observed_at":"2026-08-04T05:48:22.249319Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T05:48:22.378483Z","title":"Brasco, G","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2603.29989","last_updated":"2026-08-03T16:46:38Z","snapshot_observed_at":"2026-08-14T16:03:09.542975Z","submitted_at":"2026-03-31T16:54:27Z","title":"A Brunn-Minkowski inequality for Schr\\\"odinger operators with Kato class potentials","version":6},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-04T05:48:22.378483Z"},"links":{"citing_paper":"/paper/2603.29989"},"observation_digest":"sha256:5a9f55c727b1de4799e2eae2ed1ca1309fc5b548e9defa3f1e61396a54f92379","observation_id":"3820dcb6-e0d7-495f-b408-62e89aadb50b","resolution":{"observed_at":"2026-08-04T05:48:22.378483Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T05:48:22.481966Z","title":"Buccheri, L","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2603.29989","last_updated":"2026-08-03T16:46:38Z","snapshot_observed_at":"2026-08-14T16:03:09.542975Z","submitted_at":"2026-03-31T16:54:27Z","title":"A Brunn-Minkowski inequality for Schr\\\"odinger operators with Kato class potentials","version":6},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-04T05:48:22.481966Z"},"links":{"citing_paper":"/paper/2603.29989"},"observation_digest":"sha256:05f4c982751016b83e4e34b83b95c2cc525626749b89c79b74aa92a1f6f9fced","observation_id":"e34a6d67-f4f1-42a4-8fbc-b293341dd54d","resolution":{"observed_at":"2026-08-04T05:48:22.481966Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T05:48:22.639914Z","title":null,"venue":null,"work_id":null,"year":1982},"citing_paper":{"arxiv_id":"2603.29989","last_updated":"2026-08-03T16:46:38Z","snapshot_observed_at":"2026-08-14T16:03:09.542975Z","submitted_at":"2026-03-31T16:54:27Z","title":"A Brunn-Minkowski inequality for Schr\\\"odinger operators with Kato class potentials","version":6},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-04T05:48:22.639914Z"},"links":{"citing_paper":"/paper/2603.29989"},"observation_digest":"sha256:fe809072756d04c7c540e81f6bf6e23161c3f093db1721aa6c8ef882eb73a1c0","observation_id":"2b23cdf0-d825-4dfd-98be-952bdb946200","resolution":{"observed_at":"2026-08-04T05:48:22.639914Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T05:48:22.809889Z","title":"Carbotti, S","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2603.29989","last_updated":"2026-08-03T16:46:38Z","snapshot_observed_at":"2026-08-14T16:03:09.542975Z","submitted_at":"2026-03-31T16:54:27Z","title":"A Brunn-Minkowski inequality for Schr\\\"odinger operators with Kato class potentials","version":6},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-04T05:48:22.809889Z"},"links":{"citing_paper":"/paper/2603.29989"},"observation_digest":"sha256:12d827dd2883701075e961a57cda71e46c8385f3a57dbca8b3d02e2ce7e1e8ab","observation_id":"d333cc74-edf6-45f6-90d5-1e42fa35bebe","resolution":{"observed_at":"2026-08-04T05:48:22.809889Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T05:48:22.987814Z","title":"Colesanti,Brunn–Minkowski inequalities for variational functionals and related problems, Adv","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2603.29989","last_updated":"2026-08-03T16:46:38Z","snapshot_observed_at":"2026-08-14T16:03:09.542975Z","submitted_at":"2026-03-31T16:54:27Z","title":"A Brunn-Minkowski inequality for Schr\\\"odinger operators with Kato class potentials","version":6},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-04T05:48:22.987814Z"},"links":{"citing_paper":"/paper/2603.29989"},"observation_digest":"sha256:8637d11d64c75ecdd092726ddb1e11982e6559880977608c7d7fa8f86a810f44","observation_id":"a93498c3-dbff-455c-a63e-186c0e7f5af1","resolution":{"observed_at":"2026-08-04T05:48:22.987814Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T05:48:23.049663Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2603.29989","last_updated":"2026-08-03T16:46:38Z","snapshot_observed_at":"2026-08-14T16:03:09.542975Z","submitted_at":"2026-03-31T16:54:27Z","title":"A Brunn-Minkowski inequality for Schr\\\"odinger operators with Kato class potentials","version":6},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-04T05:48:23.049663Z"},"links":{"citing_paper":"/paper/2603.29989"},"observation_digest":"sha256:a71b26e233d56dc27651e77020cf52ded0b329798a08621790eaa5ad58d53211","observation_id":"8364310a-a556-48c5-9884-9c7e4e9e8f37","resolution":{"observed_at":"2026-08-04T05:48:23.049663Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2407.21354","last_updated":"2024-08-06T07:27:13Z","snapshot_observed_at":"2026-08-19T12:10:13.089715Z","submitted_at":"2024-07-31T05:52:08Z","title":"The Brunn-Minkowski inequality for the first eigenvalue of the Ornstein-Uhlenbeck operator and log-concavity of the relevant eigenfunction","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2407.21354","snapshot_observed_at":"2026-08-04T05:48:23.110972Z","title":"Colesanti, E","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2603.29989","last_updated":"2026-08-03T16:46:38Z","snapshot_observed_at":"2026-08-14T16:03:09.542975Z","submitted_at":"2026-03-31T16:54:27Z","title":"A Brunn-Minkowski inequality for Schr\\\"odinger operators with Kato class potentials","version":6},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-04T05:48:23.110972Z"},"links":{"cited_paper":"/paper/2407.21354","citing_paper":"/paper/2603.29989"},"observation_digest":"sha256:6bf9ccf7fac205b03a0450cddc5d6aba03f456230f88f2c278df972e24569495","observation_id":"49921105-48ce-43f4-8c50-c52a887af1c8","resolution":{"observed_at":"2026-08-04T05:48:23.110972Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T05:48:23.187211Z","title":"Colesanti, L","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2603.29989","last_updated":"2026-08-03T16:46:38Z","snapshot_observed_at":"2026-08-14T16:03:09.542975Z","submitted_at":"2026-03-31T16:54:27Z","title":"A Brunn-Minkowski inequality for Schr\\\"odinger operators with Kato class potentials","version":6},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-04T05:48:23.187211Z"},"links":{"citing_paper":"/paper/2603.29989"},"observation_digest":"sha256:cc3359219d0245d472d24b08d32d9f61cca8c07b1ef27cf99b1b5a8476c1946f","observation_id":"f9d809e4-2d45-4d66-b9d3-50764ed26f8f","resolution":{"observed_at":"2026-08-04T05:48:23.187211Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T05:48:23.255434Z","title":null,"venue":null,"work_id":null,"year":1984},"citing_paper":{"arxiv_id":"2603.29989","last_updated":"2026-08-03T16:46:38Z","snapshot_observed_at":"2026-08-14T16:03:09.542975Z","submitted_at":"2026-03-31T16:54:27Z","title":"A Brunn-Minkowski inequality for Schr\\\"odinger operators with Kato class potentials","version":6},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-04T05:48:23.255434Z"},"links":{"citing_paper":"/paper/2603.29989"},"observation_digest":"sha256:dfa6b83e2a2ed063b46b64d8adedd0e31dd6ee8587699a9755fcc33b89750c70","observation_id":"301e0795-cff0-411d-8d69-d5cb2c7388fc","resolution":{"observed_at":"2026-08-04T05:48:23.255434Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T05:48:23.387759Z","title":"Engel and R","venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2603.29989","last_updated":"2026-08-03T16:46:38Z","snapshot_observed_at":"2026-08-14T16:03:09.542975Z","submitted_at":"2026-03-31T16:54:27Z","title":"A Brunn-Minkowski inequality for Schr\\\"odinger operators with Kato class potentials","version":6},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-04T05:48:23.387759Z"},"links":{"citing_paper":"/paper/2603.29989"},"observation_digest":"sha256:0c2e2df6401191d94c74fd8127061366a337705333ccb558d410a08e6e080366","observation_id":"70a09419-4977-4934-b549-00189008385b","resolution":{"observed_at":"2026-08-04T05:48:23.387759Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T05:48:23.453925Z","title":null,"venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2603.29989","last_updated":"2026-08-03T16:46:38Z","snapshot_observed_at":"2026-08-14T16:03:09.542975Z","submitted_at":"2026-03-31T16:54:27Z","title":"A Brunn-Minkowski inequality for Schr\\\"odinger operators with Kato class potentials","version":6},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-04T05:48:23.453925Z"},"links":{"citing_paper":"/paper/2603.29989"},"observation_digest":"sha256:051b012285ea6bbea9dc5a2a2713a48810098cb4dca6568e384d8056d7d1e5a6","observation_id":"0bcc0c33-db1e-423a-bd48-f542da1be738","resolution":{"observed_at":"2026-08-04T05:48:23.453925Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T05:48:23.575598Z","title":"Eskenazis and G","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2603.29989","last_updated":"2026-08-03T16:46:38Z","snapshot_observed_at":"2026-08-14T16:03:09.542975Z","submitted_at":"2026-03-31T16:54:27Z","title":"A Brunn-Minkowski inequality for Schr\\\"odinger operators with Kato class potentials","version":6},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-04T05:48:23.575598Z"},"links":{"citing_paper":"/paper/2603.29989"},"observation_digest":"sha256:a07ff1f8b0161251480f9abefaceeae1cfae0f1cad98a4b1193f38797fdf9581","observation_id":"d3ffe759-21e3-4a43-8117-ba5f2e5e627b","resolution":{"observed_at":"2026-08-04T05:48:23.575598Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T05:48:23.703952Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2603.29989","last_updated":"2026-08-03T16:46:38Z","snapshot_observed_at":"2026-08-14T16:03:09.542975Z","submitted_at":"2026-03-31T16:54:27Z","title":"A Brunn-Minkowski inequality for Schr\\\"odinger operators with Kato class potentials","version":6},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-04T05:48:23.703952Z"},"links":{"citing_paper":"/paper/2603.29989"},"observation_digest":"sha256:70065b79a307482f103223b6ac5a953204c272e6f9aaad54ba0047bc5f80dd1a","observation_id":"051bc00a-1c2a-4f7d-8c90-0ddfabc40698","resolution":{"observed_at":"2026-08-04T05:48:23.703952Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T05:48:23.882882Z","title":null,"venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2603.29989","last_updated":"2026-08-03T16:46:38Z","snapshot_observed_at":"2026-08-14T16:03:09.542975Z","submitted_at":"2026-03-31T16:54:27Z","title":"A Brunn-Minkowski inequality for Schr\\\"odinger operators with Kato class potentials","version":6},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-04T05:48:23.882882Z"},"links":{"citing_paper":"/paper/2603.29989"},"observation_digest":"sha256:f281ee2409811fa88604bd3ad2aa4ae11bda3fcffc117df0ca522cdd8c6f51ea","observation_id":"9357d93e-c4c5-4d82-9110-6f9f19830c0c","resolution":{"observed_at":"2026-08-04T05:48:23.882882Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T05:48:23.951136Z","title":null,"venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2603.29989","last_updated":"2026-08-03T16:46:38Z","snapshot_observed_at":"2026-08-14T16:03:09.542975Z","submitted_at":"2026-03-31T16:54:27Z","title":"A Brunn-Minkowski inequality for Schr\\\"odinger operators with Kato class potentials","version":6},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-04T05:48:23.951136Z"},"links":{"citing_paper":"/paper/2603.29989"},"observation_digest":"sha256:bcbb22e79f2c3aa7dc28c0adc927db32e4ed12f695fe91b2bbc99a50b7c3a65f","observation_id":"9d208be6-7931-4d35-bcab-b1ca84976048","resolution":{"observed_at":"2026-08-04T05:48:23.951136Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T05:48:24.094407Z","title":null,"venue":null,"work_id":null,"year":1983},"citing_paper":{"arxiv_id":"2603.29989","last_updated":"2026-08-03T16:46:38Z","snapshot_observed_at":"2026-08-14T16:03:09.542975Z","submitted_at":"2026-03-31T16:54:27Z","title":"A Brunn-Minkowski inequality for Schr\\\"odinger operators with Kato class potentials","version":6},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-04T05:48:24.094407Z"},"links":{"citing_paper":"/paper/2603.29989"},"observation_digest":"sha256:0d98a87c2c1fe20cc5109e76ce9721b18aea2d501cccb13231dad31553eff73e","observation_id":"f39d0141-d835-4e5d-aa62-0a5832c032f8","resolution":{"observed_at":"2026-08-04T05:48:24.094407Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T05:48:24.140602Z","title":null,"venue":null,"work_id":null,"year":1987},"citing_paper":{"arxiv_id":"2603.29989","last_updated":"2026-08-03T16:46:38Z","snapshot_observed_at":"2026-08-14T16:03:09.542975Z","submitted_at":"2026-03-31T16:54:27Z","title":"A Brunn-Minkowski inequality for Schr\\\"odinger operators with Kato class potentials","version":6},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-04T05:48:24.140602Z"},"links":{"citing_paper":"/paper/2603.29989"},"observation_digest":"sha256:3d1c171951a19e6a0bdf826e1807b11ab35fa394adbb42340667d314f313a2d9","observation_id":"3801bbce-2cca-4145-8602-fb0af1a7420d","resolution":{"observed_at":"2026-08-04T05:48:24.140602Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T05:48:24.200085Z","title":"Leindler,On a certain converse of Hölder’s inequality, Acta Sci","venue":null,"work_id":null,"year":1972},"citing_paper":{"arxiv_id":"2603.29989","last_updated":"2026-08-03T16:46:38Z","snapshot_observed_at":"2026-08-14T16:03:09.542975Z","submitted_at":"2026-03-31T16:54:27Z","title":"A Brunn-Minkowski inequality for Schr\\\"odinger operators with Kato class potentials","version":6},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-04T05:48:24.200085Z"},"links":{"citing_paper":"/paper/2603.29989"},"observation_digest":"sha256:657929294d536a4673c09f73a06b06dc5d792e266347afd9b2c412d77669afd3","observation_id":"ca925ade-64d8-48cb-a0c5-16c9291c3007","resolution":{"observed_at":"2026-08-04T05:48:24.200085Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T05:48:24.237415Z","title":"Maz′ya and M","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2603.29989","last_updated":"2026-08-03T16:46:38Z","snapshot_observed_at":"2026-08-14T16:03:09.542975Z","submitted_at":"2026-03-31T16:54:27Z","title":"A Brunn-Minkowski inequality for Schr\\\"odinger operators with Kato class potentials","version":6},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-04T05:48:24.237415Z"},"links":{"citing_paper":"/paper/2603.29989"},"observation_digest":"sha256:32dd856362b57fdaaab3eba43004078dbeef77b30387b6a7bdbc715c38bc9854","observation_id":"d90bd6d6-aeab-466d-8e9c-126199651c4e","resolution":{"observed_at":"2026-08-04T05:48:24.237415Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T05:48:24.324601Z","title":null,"venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2603.29989","last_updated":"2026-08-03T16:46:38Z","snapshot_observed_at":"2026-08-14T16:03:09.542975Z","submitted_at":"2026-03-31T16:54:27Z","title":"A Brunn-Minkowski inequality for Schr\\\"odinger operators with Kato class potentials","version":6},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-04T05:48:24.324601Z"},"links":{"citing_paper":"/paper/2603.29989"},"observation_digest":"sha256:607fb72f52fe4984b8130a9ed22c2e478aa9f2769f99ea835d5eb0ae14afb1cc","observation_id":"6a2d66bb-bae7-4cd6-9808-0f285e289530","resolution":{"observed_at":"2026-08-04T05:48:24.324601Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T05:48:24.423535Z","title":"Prékopa,Logarithmic concave measures with application to stochastic programming, Acta Sci","venue":null,"work_id":null,"year":1971},"citing_paper":{"arxiv_id":"2603.29989","last_updated":"2026-08-03T16:46:38Z","snapshot_observed_at":"2026-08-14T16:03:09.542975Z","submitted_at":"2026-03-31T16:54:27Z","title":"A Brunn-Minkowski inequality for Schr\\\"odinger operators with Kato class potentials","version":6},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-04T05:48:24.423535Z"},"links":{"citing_paper":"/paper/2603.29989"},"observation_digest":"sha256:1700ca91fc8ff64a8421606f817f8032ec36447888148d549d293bce91ae8423","observation_id":"76a54230-ab7a-4cd4-a6ed-bec2ac4bc1e5","resolution":{"observed_at":"2026-08-04T05:48:24.423535Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T05:48:24.527083Z","title":null,"venue":null,"work_id":null,"year":1973},"citing_paper":{"arxiv_id":"2603.29989","last_updated":"2026-08-03T16:46:38Z","snapshot_observed_at":"2026-08-14T16:03:09.542975Z","submitted_at":"2026-03-31T16:54:27Z","title":"A Brunn-Minkowski inequality for Schr\\\"odinger operators with Kato class potentials","version":6},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-04T05:48:24.527083Z"},"links":{"citing_paper":"/paper/2603.29989"},"observation_digest":"sha256:9946902eecdd2fa5576706e3910e62c831f6bae485f794919f98e57306474aa3","observation_id":"50a4d386-29a6-431d-8136-a1fbb8e9270c","resolution":{"observed_at":"2026-08-04T05:48:24.527083Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T05:48:24.649959Z","title":"Qin,The strong log-concavity for first eigenfunction of the Ornstein-Uhlenbeck operator in the class of convex bodies, Proc","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2603.29989","last_updated":"2026-08-03T16:46:38Z","snapshot_observed_at":"2026-08-14T16:03:09.542975Z","submitted_at":"2026-03-31T16:54:27Z","title":"A Brunn-Minkowski inequality for Schr\\\"odinger operators with Kato class potentials","version":6},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-04T05:48:24.649959Z"},"links":{"citing_paper":"/paper/2603.29989"},"observation_digest":"sha256:e34aa89aa7eec5ba1f1daf4d699008641b282512f22030606bbb42e96a943116","observation_id":"7b4939f4-f536-40dd-9a2e-71317408f11e","resolution":{"observed_at":"2026-08-04T05:48:24.649959Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T05:48:24.739928Z","title":"Reed and B","venue":null,"work_id":null,"year":1978},"citing_paper":{"arxiv_id":"2603.29989","last_updated":"2026-08-03T16:46:38Z","snapshot_observed_at":"2026-08-14T16:03:09.542975Z","submitted_at":"2026-03-31T16:54:27Z","title":"A Brunn-Minkowski inequality for Schr\\\"odinger operators with Kato class potentials","version":6},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-04T05:48:24.739928Z"},"links":{"citing_paper":"/paper/2603.29989"},"observation_digest":"sha256:dc8beb3f6346241b6e8fb38f5a9608944449a7347eca2278bcc9df80425287ae","observation_id":"4e3703cf-c4ee-4280-a8dd-7367aa200e10","resolution":{"observed_at":"2026-08-04T05:48:24.739928Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T05:48:24.915464Z","title":null,"venue":null,"work_id":null,"year":1974},"citing_paper":{"arxiv_id":"2603.29989","last_updated":"2026-08-03T16:46:38Z","snapshot_observed_at":"2026-08-14T16:03:09.542975Z","submitted_at":"2026-03-31T16:54:27Z","title":"A Brunn-Minkowski inequality for Schr\\\"odinger operators with Kato class potentials","version":6},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-04T05:48:24.915464Z"},"links":{"citing_paper":"/paper/2603.29989"},"observation_digest":"sha256:1bc1dd70be8272ff746cfc5da3d9f04dcb87ef905253916dd89699feb8a96749","observation_id":"bdd7ddc4-8b8b-41f4-9fba-1536cde3c22b","resolution":{"observed_at":"2026-08-04T05:48:24.915464Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T05:48:25.080013Z","title":"Simon,Functional integration and quantum physics, Pure and Applied Mathematics, vol","venue":null,"work_id":null,"year":1979},"citing_paper":{"arxiv_id":"2603.29989","last_updated":"2026-08-03T16:46:38Z","snapshot_observed_at":"2026-08-14T16:03:09.542975Z","submitted_at":"2026-03-31T16:54:27Z","title":"A Brunn-Minkowski inequality for Schr\\\"odinger operators with Kato class potentials","version":6},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-04T05:48:25.080013Z"},"links":{"citing_paper":"/paper/2603.29989"},"observation_digest":"sha256:6067dc5f1b0c897be2e3d865c1193565a483aad3cd7e346c1ec44524dc660cfd","observation_id":"f9ef9fb7-4a7c-4517-81bc-3c56e562a9f8","resolution":{"observed_at":"2026-08-04T05:48:25.080013Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T05:48:25.209394Z","title":"E. De Giorgi","venue":null,"work_id":null,"year":1982},"citing_paper":{"arxiv_id":"2603.29989","last_updated":"2026-08-03T16:46:38Z","snapshot_observed_at":"2026-08-14T16:03:09.542975Z","submitted_at":"2026-03-31T16:54:27Z","title":"A Brunn-Minkowski inequality for Schr\\\"odinger operators with Kato class potentials","version":6},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-04T05:48:25.209394Z"},"links":{"citing_paper":"/paper/2603.29989"},"observation_digest":"sha256:04c53549bed161883fab982e0a0999d972dcb7a1eca894c040caa1451f7d357c","observation_id":"4d901fb0-2ab5-4a5c-a79d-5d61e14d56ed","resolution":{"observed_at":"2026-08-04T05:48:25.209394Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2603.29989","last_updated":"2026-08-03T16:46:38Z","latest_version":6,"primary_category":"math.AP","snapshot_observed_at":"2026-08-14T16:03:09.542975Z","submitted_at":"2026-03-31T16:54:27Z","title":"A Brunn-Minkowski inequality for Schr\\\"odinger operators with Kato class potentials"},"reference_resolution":{"displayed":34,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":34,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":34},"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":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"thesis":"As of 20 August 2026, this Paper Citation Record lists 34 of 34 outbound references and 0 inbound Pith citation observations for arXiv:2603.29989."}