{"as_of":"2026-08-13T16:13:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:7f6543015ccf69052793aa7ee36052a992685cdad06b37b3c39b1c4a49304632","coverage":[{"denominator":27,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":27,"source":"paper_references, paper_reference_links","source_observed_at":"2026-06-26T08:04:53.898891Z","state":"measured"},{"denominator":30,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":30,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-13T06:32:02.005865+00:00","state":"measured"},{"denominator":3,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":3,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-12T00:30:59.214145Z","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":"2026-07-10T00:06:37.987030Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2606.22847","last_updated":"2026-06-22T04:47:02Z","snapshot_observed_at":"2026-08-01T16:48:43.883187Z","submitted_at":"2026-06-22T04:47:02Z","title":"A Brunn--Minkowski inequality for the Hessian eigenvalue in convex domain","version":1},"cited_work":{"arxiv_id":"2606.22847","doi":null,"metadata_source":"pith","pith_arxiv_id":"2606.22847","snapshot_observed_at":"2026-07-10T00:06:37.987030Z","title":"A Brunn--Minkowski inequality for the Hessian eigenvalue in convex domain","venue":"math.AP","work_id":"e0fd430b-97fc-42a9-8d1b-ba315764f043","year":2026},"citing_paper":{"arxiv_id":"2606.25678","last_updated":"2026-06-24T10:43:44Z","snapshot_observed_at":"2026-07-07T00:00:07.201776Z","submitted_at":"2026-06-24T10:43:44Z","title":"Brunn--Minkowski Inequality for the First Complex $\\sigma_{2}$-Hessian Eigenvalue","version":1},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-06-25T20:33:18.653661Z"},"links":{"cited_paper":"/paper/2606.22847","citing_paper":"/paper/2606.25678"},"observation_digest":"sha256:03f7fcf3b9d92ee13230aac0833bb6a298f56e50215cf57900096da225b5649d","observation_id":"2eed924a-153d-408b-bb93-acb823bc739e","resolution":{"observed_at":"2026-07-04T20:10:08.778787Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2606.22847","last_updated":"2026-06-22T04:47:02Z","snapshot_observed_at":"2026-08-01T16:48:43.883187Z","submitted_at":"2026-06-22T04:47:02Z","title":"A Brunn--Minkowski inequality for the Hessian eigenvalue in convex domain","version":1},"cited_work":{"arxiv_id":"2606.22847","doi":null,"metadata_source":"pith","pith_arxiv_id":"2606.22847","snapshot_observed_at":"2026-07-10T00:06:37.987030Z","title":"A Brunn--Minkowski inequality for the Hessian eigenvalue in convex domain","venue":"math.AP","work_id":"e0fd430b-97fc-42a9-8d1b-ba315764f043","year":2026},"citing_paper":{"arxiv_id":"2607.06895","last_updated":"2026-07-08T01:38:44Z","snapshot_observed_at":"2026-08-04T02:50:43.148533Z","submitted_at":"2026-07-08T01:38:44Z","title":"Power Convexity of Solutions to the Complex Monge-Amp\\`{e}re Equation $\\det(u_{i\\overline{j}})=1$ in Complex Dimension Two","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-07-10T00:00:13.638081Z"},"links":{"cited_paper":"/paper/2606.22847","citing_paper":"/paper/2607.06895"},"observation_digest":"sha256:6f66147f8e5eaa1298b0f79762cc35cf887658f37bf7b0decb0469788871f4ef","observation_id":"26e2d75c-c999-43d3-85e7-0b25735531fc","resolution":{"observed_at":"2026-07-10T00:06:37.988374Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2606.22847","last_updated":"2026-06-22T04:47:02Z","snapshot_observed_at":"2026-08-01T16:48:43.883187Z","submitted_at":"2026-06-22T04:47:02Z","title":"A Brunn--Minkowski inequality for the Hessian eigenvalue in convex domain","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2606.22847","snapshot_observed_at":"2026-08-12T00:30:59.214145Z","title":"A Brunn–Minkowski inequality for the Hessian eigenvalue in convex domain","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2608.08186","last_updated":"2026-08-08T15:27:38Z","snapshot_observed_at":"2026-08-13T15:14:31.873682Z","submitted_at":"2026-08-08T15:27:38Z","title":"Nonconvex Sublevel Sets for the Three-Dimensional Special Lagrangian Equation","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-12T00:30:59.214145Z"},"links":{"cited_paper":"/paper/2606.22847","citing_paper":"/paper/2608.08186"},"observation_digest":"sha256:cebe6c5c343e862a8cbd8b9ce49d6daa913fc2a99bca7977d3e33a734a08bb8e","observation_id":"d693ae68-daff-457e-b302-40faadca08cc","resolution":{"observed_at":"2026-08-12T00:30:59.214145Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2606.22847/citation-record","integrity":"/paper/2606.22847/integrity","json":"/paper/2606.22847/citation-record.json","paper":"/paper/2606.22847"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-26T08:04:53.898891Z","title":"and Lasry, J","venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"2606.22847","last_updated":"2026-06-22T04:47:02Z","snapshot_observed_at":"2026-08-01T16:48:43.883187Z","submitted_at":"2026-06-22T04:47:02Z","title":"A Brunn--Minkowski inequality for the Hessian eigenvalue in convex domain","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-06-26T08:04:53.898891Z"},"links":{"citing_paper":"/paper/2606.22847"},"observation_digest":"sha256:b5cddc00ce624fe165a07253d2c6a601d19c2d2a74428df68393d010542a955e","observation_id":"57d0f1f8-9e12-415d-99d8-4751b21ed430","resolution":{"observed_at":"2026-06-26T08:04:53.898891Z","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":"2026-06-26T08:04:53.898891Z","title":null,"venue":null,"work_id":null,"year":1976},"citing_paper":{"arxiv_id":"2606.22847","last_updated":"2026-06-22T04:47:02Z","snapshot_observed_at":"2026-08-01T16:48:43.883187Z","submitted_at":"2026-06-22T04:47:02Z","title":"A Brunn--Minkowski inequality for the Hessian eigenvalue in convex domain","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-06-26T08:04:53.898891Z"},"links":{"citing_paper":"/paper/2606.22847"},"observation_digest":"sha256:3c63ec694f49ca821638d9126ddea70106078d8c9ce0c765cdab02a468dc83c9","observation_id":"92603035-2d8f-4d85-bf5e-f0ad543d040a","resolution":{"observed_at":"2026-06-26T08:04:53.898891Z","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":"2026-06-26T08:04:53.898891Z","title":"and Friedman, A","venue":null,"work_id":null,"year":1985},"citing_paper":{"arxiv_id":"2606.22847","last_updated":"2026-06-22T04:47:02Z","snapshot_observed_at":"2026-08-01T16:48:43.883187Z","submitted_at":"2026-06-22T04:47:02Z","title":"A Brunn--Minkowski inequality for the Hessian eigenvalue in convex domain","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-06-26T08:04:53.898891Z"},"links":{"citing_paper":"/paper/2606.22847"},"observation_digest":"sha256:892495eae2db33a7f5d570d4678c33061e3f0a9627ed47c980c7f77448053713","observation_id":"26d45471-345b-4229-8b1f-c23732df3366","resolution":{"observed_at":"2026-06-26T08:04:53.898891Z","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":"2026-06-26T08:04:53.898891Z","title":"and Nirenberg, L","venue":null,"work_id":null,"year":1985},"citing_paper":{"arxiv_id":"2606.22847","last_updated":"2026-06-22T04:47:02Z","snapshot_observed_at":"2026-08-01T16:48:43.883187Z","submitted_at":"2026-06-22T04:47:02Z","title":"A Brunn--Minkowski inequality for the Hessian eigenvalue in convex domain","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-06-26T08:04:53.898891Z"},"links":{"citing_paper":"/paper/2606.22847"},"observation_digest":"sha256:60058c4c75093676161fca8b396c8e60e1adf086c8d3240774d06d6b12595a3b","observation_id":"7845ce03-3a93-401b-b111-d8831287d430","resolution":{"observed_at":"2026-06-26T08:04:53.898891Z","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":"2026-06-26T08:04:53.898891Z","title":", title =","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2606.22847","last_updated":"2026-06-22T04:47:02Z","snapshot_observed_at":"2026-08-01T16:48:43.883187Z","submitted_at":"2026-06-22T04:47:02Z","title":"A Brunn--Minkowski inequality for the Hessian eigenvalue in convex domain","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-06-26T08:04:53.898891Z"},"links":{"citing_paper":"/paper/2606.22847"},"observation_digest":"sha256:2858c2ad262fcf9b58a7205a12c098d399b2539d4c02bccbfb4596ad8314e1ef","observation_id":"ccd6a95c-df22-44ee-89f8-91100ce5b4a0","resolution":{"observed_at":"2026-06-26T08:04:53.898891Z","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":"2026-06-26T08:04:53.898891Z","title":"and Ma, X","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2606.22847","last_updated":"2026-06-22T04:47:02Z","snapshot_observed_at":"2026-08-01T16:48:43.883187Z","submitted_at":"2026-06-22T04:47:02Z","title":"A Brunn--Minkowski inequality for the Hessian eigenvalue in convex domain","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-06-26T08:04:53.898891Z"},"links":{"citing_paper":"/paper/2606.22847"},"observation_digest":"sha256:29b041fbb54267e6b936637906d28fbb4963e9dabf9222419c3a0fb15b3d1ed1","observation_id":"60a65529-6f7a-4384-86ce-f6ab7850450d","resolution":{"observed_at":"2026-06-26T08:04:53.898891Z","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":"2026-06-26T08:04:53.898891Z","title":", title =","venue":null,"work_id":null,"year":1996},"citing_paper":{"arxiv_id":"2606.22847","last_updated":"2026-06-22T04:47:02Z","snapshot_observed_at":"2026-08-01T16:48:43.883187Z","submitted_at":"2026-06-22T04:47:02Z","title":"A Brunn--Minkowski inequality for the Hessian eigenvalue in convex domain","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-06-26T08:04:53.898891Z"},"links":{"citing_paper":"/paper/2606.22847"},"observation_digest":"sha256:e75935eb4cad60ffd1813add184e8d09e73febb7ba20f8da260e14460db8be70","observation_id":"1e36963c-2895-4031-9e9d-528cf1aeb77d","resolution":{"observed_at":"2026-06-26T08:04:53.898891Z","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":"2026-06-26T08:04:53.898891Z","title":", title =","venue":null,"work_id":null,"year":1983},"citing_paper":{"arxiv_id":"2606.22847","last_updated":"2026-06-22T04:47:02Z","snapshot_observed_at":"2026-08-01T16:48:43.883187Z","submitted_at":"2026-06-22T04:47:02Z","title":"A Brunn--Minkowski inequality for the Hessian eigenvalue in convex domain","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-06-26T08:04:53.898891Z"},"links":{"citing_paper":"/paper/2606.22847"},"observation_digest":"sha256:60ad1612c934f22a47dc59ca64727570c5e236924ba7c8d20b2fe5080a93b8b6","observation_id":"20aa672d-c231-4c7c-ab0a-f376d9fcec43","resolution":{"observed_at":"2026-06-26T08:04:53.898891Z","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":"2026-06-26T08:04:53.898891Z","title":"and Lewis, J","venue":null,"work_id":null,"year":1987},"citing_paper":{"arxiv_id":"2606.22847","last_updated":"2026-06-22T04:47:02Z","snapshot_observed_at":"2026-08-01T16:48:43.883187Z","submitted_at":"2026-06-22T04:47:02Z","title":"A Brunn--Minkowski inequality for the Hessian eigenvalue in convex domain","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-06-26T08:04:53.898891Z"},"links":{"citing_paper":"/paper/2606.22847"},"observation_digest":"sha256:ac28c94696361fc94014649069c22948a4c5ca3c05d11fdeef87edb995faba9d","observation_id":"9d461c1e-048f-47ce-989e-6dcbbc46d4a0","resolution":{"observed_at":"2026-06-26T08:04:53.898891Z","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":"2026-06-26T08:04:53.898891Z","title":", title =","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.22847","last_updated":"2026-06-22T04:47:02Z","snapshot_observed_at":"2026-08-01T16:48:43.883187Z","submitted_at":"2026-06-22T04:47:02Z","title":"A Brunn--Minkowski inequality for the Hessian eigenvalue in convex domain","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-06-26T08:04:53.898891Z"},"links":{"citing_paper":"/paper/2606.22847"},"observation_digest":"sha256:fad7a88cfde1233089c06c5eebadacaf9fbe516fb4100d6f2b3915c00b21986e","observation_id":"ae65acdc-8031-4660-a032-9481b85e3629","resolution":{"observed_at":"2026-06-26T08:04:53.898891Z","resolver_source":null,"status":"parse_uncertain"},"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":"2026-06-26T08:04:53.898891Z","title":null,"venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2606.22847","last_updated":"2026-06-22T04:47:02Z","snapshot_observed_at":"2026-08-01T16:48:43.883187Z","submitted_at":"2026-06-22T04:47:02Z","title":"A Brunn--Minkowski inequality for the Hessian eigenvalue in convex domain","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-06-26T08:04:53.898891Z"},"links":{"citing_paper":"/paper/2606.22847"},"observation_digest":"sha256:3e758d60588a386f06a7eb82beb50737de57eb79da42b075de0de4b5258eb670","observation_id":"b9148a19-b8b2-48a4-87dd-6fc74f73be26","resolution":{"observed_at":"2026-06-26T08:04:53.898891Z","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":"2026-06-26T08:04:53.898891Z","title":", title =","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2606.22847","last_updated":"2026-06-22T04:47:02Z","snapshot_observed_at":"2026-08-01T16:48:43.883187Z","submitted_at":"2026-06-22T04:47:02Z","title":"A Brunn--Minkowski inequality for the Hessian eigenvalue in convex domain","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-06-26T08:04:53.898891Z"},"links":{"citing_paper":"/paper/2606.22847"},"observation_digest":"sha256:54af7ada381eb4654d35a5aaaf9c1e90a4213c7ad5321e0e2f388f25b173fa0b","observation_id":"da38d29b-fa81-4385-8fee-2ca88ca5c23c","resolution":{"observed_at":"2026-06-26T08:04:53.898891Z","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":"2026-06-26T08:04:53.898891Z","title":", title =","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.22847","last_updated":"2026-06-22T04:47:02Z","snapshot_observed_at":"2026-08-01T16:48:43.883187Z","submitted_at":"2026-06-22T04:47:02Z","title":"A Brunn--Minkowski inequality for the Hessian eigenvalue in convex domain","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-06-26T08:04:53.898891Z"},"links":{"citing_paper":"/paper/2606.22847"},"observation_digest":"sha256:8f5c2fc049a599f2c589295359b87d002fa3a89d5eb1ec30f5722d1470c449be","observation_id":"ac204ca4-22f8-4ecf-90fc-4f1d13dce5d1","resolution":{"observed_at":"2026-06-26T08:04:53.898891Z","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":"2026-06-26T08:04:53.898891Z","title":", title =","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2606.22847","last_updated":"2026-06-22T04:47:02Z","snapshot_observed_at":"2026-08-01T16:48:43.883187Z","submitted_at":"2026-06-22T04:47:02Z","title":"A Brunn--Minkowski inequality for the Hessian eigenvalue in convex domain","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-06-26T08:04:53.898891Z"},"links":{"citing_paper":"/paper/2606.22847"},"observation_digest":"sha256:fe463c857a98cd9a1a54159cb8d1836486f889823448121cde1c6519736a0065","observation_id":"51b053ba-b2f3-45e9-acec-12b1529d609e","resolution":{"observed_at":"2026-06-26T08:04:53.898891Z","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":"2026-06-26T08:04:53.898891Z","title":"An inequality for hyperbolic polynomials , journal =","venue":null,"work_id":null,"year":1959},"citing_paper":{"arxiv_id":"2606.22847","last_updated":"2026-06-22T04:47:02Z","snapshot_observed_at":"2026-08-01T16:48:43.883187Z","submitted_at":"2026-06-22T04:47:02Z","title":"A Brunn--Minkowski inequality for the Hessian eigenvalue in convex domain","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-06-26T08:04:53.898891Z"},"links":{"citing_paper":"/paper/2606.22847"},"observation_digest":"sha256:4aa7168ebc7636a3b4d2b50fec5b7465069ad4311db5f96f804eaae69218e53a","observation_id":"3d2169cd-2b38-44e8-b676-a3bb77d1eea7","resolution":{"observed_at":"2026-06-26T08:04:53.898891Z","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":"2026-06-26T08:04:53.898891Z","title":null,"venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2606.22847","last_updated":"2026-06-22T04:47:02Z","snapshot_observed_at":"2026-08-01T16:48:43.883187Z","submitted_at":"2026-06-22T04:47:02Z","title":"A Brunn--Minkowski inequality for the Hessian eigenvalue in convex domain","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-06-26T08:04:53.898891Z"},"links":{"citing_paper":"/paper/2606.22847"},"observation_digest":"sha256:d2d73f5f3265923f655deb4bfddd01d19ae76c14db2db596196a49a209917cdf","observation_id":"eb3d1aaf-b94f-4f4e-84c8-70844be0ebd8","resolution":{"observed_at":"2026-06-26T08:04:53.898891Z","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":"2026-06-26T08:04:53.898891Z","title":"Foundations of Computational Mathematics , volume =","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2606.22847","last_updated":"2026-06-22T04:47:02Z","snapshot_observed_at":"2026-08-01T16:48:43.883187Z","submitted_at":"2026-06-22T04:47:02Z","title":"A Brunn--Minkowski inequality for the Hessian eigenvalue in convex domain","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-06-26T08:04:53.898891Z"},"links":{"citing_paper":"/paper/2606.22847"},"observation_digest":"sha256:52c5d3dde45404f47c7318165b6d55155f3505f6f06ed8844c204c17f321216f","observation_id":"a84c1aaa-b991-43d9-9457-793215d5561f","resolution":{"observed_at":"2026-06-26T08:04:53.898891Z","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":"2026-06-26T08:04:53.898891Z","title":null,"venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2606.22847","last_updated":"2026-06-22T04:47:02Z","snapshot_observed_at":"2026-08-01T16:48:43.883187Z","submitted_at":"2026-06-22T04:47:02Z","title":"A Brunn--Minkowski inequality for the Hessian eigenvalue in convex domain","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-06-26T08:04:53.898891Z"},"links":{"citing_paper":"/paper/2606.22847"},"observation_digest":"sha256:217864c3714f4ee7263be4289ca0130a2be62cd9517e894855230049a93f505b","observation_id":"45502723-103c-4252-bddc-f96e9b271cc5","resolution":{"observed_at":"2026-06-26T08:04:53.898891Z","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":"2026-06-26T08:04:53.898891Z","title":"Discrete Contin","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2606.22847","last_updated":"2026-06-22T04:47:02Z","snapshot_observed_at":"2026-08-01T16:48:43.883187Z","submitted_at":"2026-06-22T04:47:02Z","title":"A Brunn--Minkowski inequality for the Hessian eigenvalue in convex domain","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-06-26T08:04:53.898891Z"},"links":{"citing_paper":"/paper/2606.22847"},"observation_digest":"sha256:dd900f277dbaa7870fe5bfff1a1e5e05385beb9965512c82fbfbdf6df11b5873","observation_id":"6b2a2bab-39b3-4847-9218-c5ddd0fb83b1","resolution":{"observed_at":"2026-06-26T08:04:53.898891Z","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":"2026-06-26T08:04:53.898891Z","title":"On a constant rank theorem for nonlinear elliptic","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2606.22847","last_updated":"2026-06-22T04:47:02Z","snapshot_observed_at":"2026-08-01T16:48:43.883187Z","submitted_at":"2026-06-22T04:47:02Z","title":"A Brunn--Minkowski inequality for the Hessian eigenvalue in convex domain","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-06-26T08:04:53.898891Z"},"links":{"citing_paper":"/paper/2606.22847"},"observation_digest":"sha256:ecfa609fac269d7ac0a93b7101482c7ea092c2500824f917a670798d1ef6ad2f","observation_id":"17a72246-fd70-4f7e-91fe-5ed97ff2e61c","resolution":{"observed_at":"2026-06-26T08:04:53.898891Z","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":"2026-06-26T08:04:53.898891Z","title":"and Guan, Pengfei and Ma, Xi-Nan , title =","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2606.22847","last_updated":"2026-06-22T04:47:02Z","snapshot_observed_at":"2026-08-01T16:48:43.883187Z","submitted_at":"2026-06-22T04:47:02Z","title":"A Brunn--Minkowski inequality for the Hessian eigenvalue in convex domain","version":1},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-06-26T08:04:53.898891Z"},"links":{"citing_paper":"/paper/2606.22847"},"observation_digest":"sha256:e302eae1fa3c284631ccdf4cd4f8de77645f16a8776d3058f28d5049bad40c52","observation_id":"3befdd1b-36ad-4e16-93d2-34ac7c8a880d","resolution":{"observed_at":"2026-06-26T08:04:53.898891Z","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":"2026-06-26T08:04:53.898891Z","title":"Adv.Math , volume =","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2606.22847","last_updated":"2026-06-22T04:47:02Z","snapshot_observed_at":"2026-08-01T16:48:43.883187Z","submitted_at":"2026-06-22T04:47:02Z","title":"A Brunn--Minkowski inequality for the Hessian eigenvalue in convex domain","version":1},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-06-26T08:04:53.898891Z"},"links":{"citing_paper":"/paper/2606.22847"},"observation_digest":"sha256:ec62642b138cc0b0025ce44f3061ac2cb31ee7730334bdd474a9a9e7219ebccb","observation_id":"db567998-cacd-4d39-a6dc-b5022c167565","resolution":{"observed_at":"2026-06-26T08:04:53.898891Z","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":"2026-06-26T08:04:53.898891Z","title":", title =","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2606.22847","last_updated":"2026-06-22T04:47:02Z","snapshot_observed_at":"2026-08-01T16:48:43.883187Z","submitted_at":"2026-06-22T04:47:02Z","title":"A Brunn--Minkowski inequality for the Hessian eigenvalue in convex domain","version":1},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-06-26T08:04:53.898891Z"},"links":{"citing_paper":"/paper/2606.22847"},"observation_digest":"sha256:15e4d786fed191a27df1a5665017f5523f835e00aabbc189db0bda8c0d703b6b","observation_id":"b333c3b3-3480-42bf-9ea6-d8e31e971f36","resolution":{"observed_at":"2026-06-26T08:04:53.898891Z","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":"2026-06-26T08:04:53.898891Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2606.22847","last_updated":"2026-06-22T04:47:02Z","snapshot_observed_at":"2026-08-01T16:48:43.883187Z","submitted_at":"2026-06-22T04:47:02Z","title":"A Brunn--Minkowski inequality for the Hessian eigenvalue in convex domain","version":1},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-06-26T08:04:53.898891Z"},"links":{"citing_paper":"/paper/2606.22847"},"observation_digest":"sha256:b595b906c4fc0d9471f440ee2e92871d2e572eafef7c8e3bdd7f2b9b0b5bafcf","observation_id":"0bd9001e-feff-403d-8cb4-9d82de7d17c2","resolution":{"observed_at":"2026-06-26T08:04:53.898891Z","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":"2026-06-26T08:04:53.898891Z","title":null,"venue":null,"work_id":null,"year":1994},"citing_paper":{"arxiv_id":"2606.22847","last_updated":"2026-06-22T04:47:02Z","snapshot_observed_at":"2026-08-01T16:48:43.883187Z","submitted_at":"2026-06-22T04:47:02Z","title":"A Brunn--Minkowski inequality for the Hessian eigenvalue in convex domain","version":1},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-06-26T08:04:53.898891Z"},"links":{"citing_paper":"/paper/2606.22847"},"observation_digest":"sha256:21b9161b182be5b941b39a57d7b1af78568cc49695ff6c8a81e79bf65345fc7f","observation_id":"2d3fff21-cd94-4be3-bea0-eb851b05cae2","resolution":{"observed_at":"2026-06-26T08:04:53.898891Z","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":"2026-06-26T08:04:53.898891Z","title":", title =","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.22847","last_updated":"2026-06-22T04:47:02Z","snapshot_observed_at":"2026-08-01T16:48:43.883187Z","submitted_at":"2026-06-22T04:47:02Z","title":"A Brunn--Minkowski inequality for the Hessian eigenvalue in convex domain","version":1},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-06-26T08:04:53.898891Z"},"links":{"citing_paper":"/paper/2606.22847"},"observation_digest":"sha256:106018ea9e0182b1acaf9b50a2a2903819123ec142ec7cf9e5a96596baa1896c","observation_id":"f56da7d5-bcbf-43a9-85af-9eea5d2bcf62","resolution":{"observed_at":"2026-06-26T08:04:53.898891Z","resolver_source":null,"status":"parse_uncertain"},"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":"2026-06-26T08:04:53.898891Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.22847","last_updated":"2026-06-22T04:47:02Z","snapshot_observed_at":"2026-08-01T16:48:43.883187Z","submitted_at":"2026-06-22T04:47:02Z","title":"A Brunn--Minkowski inequality for the Hessian eigenvalue in convex domain","version":1},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-06-26T08:04:53.898891Z"},"links":{"citing_paper":"/paper/2606.22847"},"observation_digest":"sha256:5ebb6ba3521da866dd95b314cee760ef0d85611e887661a479e0492f24929a1c","observation_id":"4a842c26-36f9-4ad6-8043-0ff10c12981a","resolution":{"observed_at":"2026-06-26T08:04:53.898891Z","resolver_source":null,"status":"parse_uncertain"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2606.22847","last_updated":"2026-06-22T04:47:02Z","latest_version":1,"primary_category":"math.AP","snapshot_observed_at":"2026-08-01T16:48:43.883187Z","submitted_at":"2026-06-22T04:47:02Z","title":"A Brunn--Minkowski inequality for the Hessian eigenvalue in convex domain"},"reference_resolution":{"displayed":27,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":3,"unresolved":24,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":27},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"thesis":"As of 13 August 2026, this Paper Citation Record lists 27 of 27 outbound references and 3 inbound Pith citation observations for arXiv:2606.22847."}