{"as_of":"2026-08-14T07:41:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:656da1fb70f347f33b3f2b53baf34cba88afa3a75705afa1390a51c358ee501f","coverage":[{"denominator":50,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":50,"source":"paper_references, paper_reference_links","source_observed_at":"2026-05-08T07:36:13.730113Z","state":"measured"},{"denominator":50,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":50,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-14T06:32:32.682623+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/2604.23349/citation-record","integrity":"/paper/2604.23349/integrity","json":"/paper/2604.23349/citation-record.json","paper":"/paper/2604.23349"},"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":"Liouville property and regularity of a Hessian quotient equation","venue":null,"work_id":"04a9f7f1-9445-415f-af9d-563fc3b33ff6","year":2003},"citing_paper":{"arxiv_id":"2604.23349","last_updated":"2026-04-25T15:17:50Z","snapshot_observed_at":"2026-07-06T23:09:34.300163Z","submitted_at":"2026-04-25T15:17:50Z","title":"Interior $C^{2}$ estimate for semi-convex solutions to a class of Hessian quotient equations in arbitrary dimensions","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-05-08T07:36:13.730113Z"},"links":{"citing_paper":"/paper/2604.23349"},"observation_digest":"sha256:5949a77eeb6db7b02313d76b7072fa537138417222b2e17950b7d19107bad3b7","observation_id":"4d8b5618-1330-42cf-af0f-9c791457024a","resolution":{"observed_at":"2026-05-26T17:47:46.913130Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"Asymptotic behavior of flows by powers of the Gaussian curvature","venue":null,"work_id":"fd2ad133-5841-4348-9de8-2f6adc3edeab","year":2017},"citing_paper":{"arxiv_id":"2604.23349","last_updated":"2026-04-25T15:17:50Z","snapshot_observed_at":"2026-07-06T23:09:34.300163Z","submitted_at":"2026-04-25T15:17:50Z","title":"Interior $C^{2}$ estimate for semi-convex solutions to a class of Hessian quotient equations in arbitrary dimensions","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-05-08T07:36:13.730113Z"},"links":{"citing_paper":"/paper/2604.23349"},"observation_digest":"sha256:d6ffbdfea42ee466c6e2c66f1b99113c457fadfebfc94ce11b3b9cd62cc91766","observation_id":"6f71f62a-43eb-43c2-bbf0-085c5bafede0","resolution":{"observed_at":"2026-05-26T17:47:46.930537Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"AnextensiontoatheoremofJörgens,Calabi,andPogorelov","venue":null,"work_id":"93aad2ed-8115-4c5a-b1d0-6b99dfcaf03a","year":2003},"citing_paper":{"arxiv_id":"2604.23349","last_updated":"2026-04-25T15:17:50Z","snapshot_observed_at":"2026-07-06T23:09:34.300163Z","submitted_at":"2026-04-25T15:17:50Z","title":"Interior $C^{2}$ estimate for semi-convex solutions to a class of Hessian quotient equations in arbitrary dimensions","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-05-08T07:36:13.730113Z"},"links":{"citing_paper":"/paper/2604.23349"},"observation_digest":"sha256:4c640459c3c2c35cd3f256f748ee5054bdc264b3ae284ce37adaef3068748bcd","observation_id":"2202b4aa-35eb-454b-8967-d13145df873b","resolution":{"observed_at":"2026-05-26T17:47:46.934896Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"A localization property of viscosity solutions to the Monge-Ampere equationandtheirstrictconvexity","venue":null,"work_id":"65e5329b-27b0-4ff4-9392-382488e0b455","year":1990},"citing_paper":{"arxiv_id":"2604.23349","last_updated":"2026-04-25T15:17:50Z","snapshot_observed_at":"2026-07-06T23:09:34.300163Z","submitted_at":"2026-04-25T15:17:50Z","title":"Interior $C^{2}$ estimate for semi-convex solutions to a class of Hessian quotient equations in arbitrary dimensions","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-05-08T07:36:13.730113Z"},"links":{"citing_paper":"/paper/2604.23349"},"observation_digest":"sha256:1345ffdb64bd582a4bfb3bd583c2630274561eac638059b0d3b336eadbf89c1c","observation_id":"08d54058-b42a-42d4-9c6c-3a1c5684bbf8","resolution":{"observed_at":"2026-05-26T17:47:46.904744Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"68d68914-c6da-45f0-ae82-c09019e9b61a","year":1995},"citing_paper":{"arxiv_id":"2604.23349","last_updated":"2026-04-25T15:17:50Z","snapshot_observed_at":"2026-07-06T23:09:34.300163Z","submitted_at":"2026-04-25T15:17:50Z","title":"Interior $C^{2}$ estimate for semi-convex solutions to a class of Hessian quotient equations in arbitrary dimensions","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-05-08T07:36:13.730113Z"},"links":{"citing_paper":"/paper/2604.23349"},"observation_digest":"sha256:2d5b80681d15cad52f1da6055a559ba71189cdbe603a2d9c40bbb395fbad2142","observation_id":"4c439f74-5d33-4156-9135-f10e95a264ab","resolution":{"observed_at":"2026-05-26T17:47:46.946615Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"Improper affine hyperspheres of convex type and a generalization of a theorem by K. Jörgens","venue":null,"work_id":"a5771ea7-e7cc-46aa-9a67-486d4c1d0e78","year":1958},"citing_paper":{"arxiv_id":"2604.23349","last_updated":"2026-04-25T15:17:50Z","snapshot_observed_at":"2026-07-06T23:09:34.300163Z","submitted_at":"2026-04-25T15:17:50Z","title":"Interior $C^{2}$ estimate for semi-convex solutions to a class of Hessian quotient equations in arbitrary dimensions","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-05-08T07:36:13.730113Z"},"links":{"citing_paper":"/paper/2604.23349"},"observation_digest":"sha256:60b1ea2ab61cd1416e4a9d5e979a426ae4e29eda8bd4f5811d39bfbcd09df36d","observation_id":"e88c55cb-ecf0-4784-b764-0b25c06a404c","resolution":{"observed_at":"2026-05-26T17:47:46.909734Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"A Liouville problem for the sigma-2 equation","venue":null,"work_id":"dc474067-2896-4a2a-938a-cc3a525bdde1","year":2010},"citing_paper":{"arxiv_id":"2604.23349","last_updated":"2026-04-25T15:17:50Z","snapshot_observed_at":"2026-07-06T23:09:34.300163Z","submitted_at":"2026-04-25T15:17:50Z","title":"Interior $C^{2}$ estimate for semi-convex solutions to a class of Hessian quotient equations in arbitrary dimensions","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-05-08T07:36:13.730113Z"},"links":{"citing_paper":"/paper/2604.23349"},"observation_digest":"sha256:adb3ca4e2edaabf65a8fbccf5f31909d8cd34e19ad55ed21a0b12d59e14b6d2a","observation_id":"7b4992ad-e5bc-4772-969a-3f124f54cfed","resolution":{"observed_at":"2026-05-26T17:47:46.924417Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"The interiorC2 estimate for the Monge-Ampère equation in dimensionn= 2","venue":null,"work_id":"990434a1-8f50-40f5-9c26-040723ece54d","year":2016},"citing_paper":{"arxiv_id":"2604.23349","last_updated":"2026-04-25T15:17:50Z","snapshot_observed_at":"2026-07-06T23:09:34.300163Z","submitted_at":"2026-04-25T15:17:50Z","title":"Interior $C^{2}$ estimate for semi-convex solutions to a class of Hessian quotient equations in arbitrary dimensions","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-05-08T07:36:13.730113Z"},"links":{"citing_paper":"/paper/2604.23349"},"observation_digest":"sha256:a7669a0b78a6ad620a7ed928890f12220bb4fd51339518aed390a6e9397283a6","observation_id":"9f46280e-a2bd-420d-a8ca-224a81c0cff2","resolution":{"observed_at":"2026-05-26T17:47:46.916461Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"A priori estimate for convex solutions to special Lagrangian equations and its application","venue":null,"work_id":"723301c4-7d6c-4281-8c6b-6c804eba0494","year":2009},"citing_paper":{"arxiv_id":"2604.23349","last_updated":"2026-04-25T15:17:50Z","snapshot_observed_at":"2026-07-06T23:09:34.300163Z","submitted_at":"2026-04-25T15:17:50Z","title":"Interior $C^{2}$ estimate for semi-convex solutions to a class of Hessian quotient equations in arbitrary dimensions","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-05-08T07:36:13.730113Z"},"links":{"citing_paper":"/paper/2604.23349"},"observation_digest":"sha256:7944ffa29bba244c3a1d9ee47db5811d1dc36fd173cbababb78788525cb989ea","observation_id":"12f95e42-b4fd-4057-a7e4-79da1b896af9","resolution":{"observed_at":"2026-05-26T17:47:46.938755Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"Anintegralapproachtoprescribingscalarcurvature equations","venue":null,"work_id":"276fe7f5-254f-4d26-85e2-bb3150935538","year":2026},"citing_paper":{"arxiv_id":"2604.23349","last_updated":"2026-04-25T15:17:50Z","snapshot_observed_at":"2026-07-06T23:09:34.300163Z","submitted_at":"2026-04-25T15:17:50Z","title":"Interior $C^{2}$ estimate for semi-convex solutions to a class of Hessian quotient equations in arbitrary dimensions","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-05-08T07:36:13.730113Z"},"links":{"citing_paper":"/paper/2604.23349"},"observation_digest":"sha256:a736002c4bf824dd61bf14270022a76b446abb6e7f7d80ef432ff2057f90e16e","observation_id":"9bfad9ec-e105-4d65-a19a-664153d98191","resolution":{"observed_at":"2026-05-26T17:47:46.920524Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"Complete affine hypersurfaces. I. The completeness of affine metrics","venue":null,"work_id":"d5f5d792-eb0d-4e7a-849c-d053b9e30a97","year":1986},"citing_paper":{"arxiv_id":"2604.23349","last_updated":"2026-04-25T15:17:50Z","snapshot_observed_at":"2026-07-06T23:09:34.300163Z","submitted_at":"2026-04-25T15:17:50Z","title":"Interior $C^{2}$ estimate for semi-convex solutions to a class of Hessian quotient equations in arbitrary dimensions","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-05-08T07:36:13.730113Z"},"links":{"citing_paper":"/paper/2604.23349"},"observation_digest":"sha256:f8c4f0619cdcd1c0770d69768e283a99c50ecbab39fcd0ed75234c1079c689a9","observation_id":"17f7fdfa-ee2d-44fc-ad65-f28dad39bdc8","resolution":{"observed_at":"2026-05-26T17:47:46.943374Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2603.15345","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"82bd5bd7-9bc2-4d21-ae66-4ee14774d189","year":2026},"citing_paper":{"arxiv_id":"2604.23349","last_updated":"2026-04-25T15:17:50Z","snapshot_observed_at":"2026-07-06T23:09:34.300163Z","submitted_at":"2026-04-25T15:17:50Z","title":"Interior $C^{2}$ estimate for semi-convex solutions to a class of Hessian quotient equations in arbitrary dimensions","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-05-08T07:36:13.730113Z"},"links":{"citing_paper":"/paper/2604.23349"},"observation_digest":"sha256:63d2dbd2b91a36b7117913e1f7321c9be28197a7616677918dc025c64915c2d8","observation_id":"62d9ae40-cd1a-48a3-aa36-bf2978e189e3","resolution":{"observed_at":"2026-05-11T21:01:10.183347Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"Hessian estimates for the sigma-2 equation with variable right-hand side terms in dimension 4","venue":null,"work_id":"dafe1530-5f26-44b2-99a2-04b95e66b378","year":2026},"citing_paper":{"arxiv_id":"2604.23349","last_updated":"2026-04-25T15:17:50Z","snapshot_observed_at":"2026-07-06T23:09:34.300163Z","submitted_at":"2026-04-25T15:17:50Z","title":"Interior $C^{2}$ estimate for semi-convex solutions to a class of Hessian quotient equations in arbitrary dimensions","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-05-08T07:36:13.730113Z"},"links":{"citing_paper":"/paper/2604.23349"},"observation_digest":"sha256:a78f241c687d4c31dc2047cfe7076bf3dabafcb9a953b0d9bb95a4d5d84d01b2","observation_id":"b8adfc84-5772-4222-9cae-18180c4ef74b","resolution":{"observed_at":"2026-05-26T17:47:47.001338Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"InteriorC2 regularity of convex solutions to prescribing scalar curvature equations","venue":null,"work_id":"6b239d3d-0044-448e-be8c-19babfaa6da2","year":2019},"citing_paper":{"arxiv_id":"2604.23349","last_updated":"2026-04-25T15:17:50Z","snapshot_observed_at":"2026-07-06T23:09:34.300163Z","submitted_at":"2026-04-25T15:17:50Z","title":"Interior $C^{2}$ estimate for semi-convex solutions to a class of Hessian quotient equations in arbitrary dimensions","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-05-08T07:36:13.730113Z"},"links":{"citing_paper":"/paper/2604.23349"},"observation_digest":"sha256:8fa07a2a2c324fd664aae8cdc01730851c252814c46b75efe8a1b113f2767b02","observation_id":"48b28e9a-cc29-4a9a-9b72-8d4633f64715","resolution":{"observed_at":"2026-05-26T17:47:47.020651Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2509.16406","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Guan and M","venue":null,"work_id":"8d6d4097-f6d3-45cb-a6ca-fea5d36fc4de","year":2025},"citing_paper":{"arxiv_id":"2604.23349","last_updated":"2026-04-25T15:17:50Z","snapshot_observed_at":"2026-07-06T23:09:34.300163Z","submitted_at":"2026-04-25T15:17:50Z","title":"Interior $C^{2}$ estimate for semi-convex solutions to a class of Hessian quotient equations in arbitrary dimensions","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-05-08T07:36:13.730113Z"},"links":{"citing_paper":"/paper/2604.23349"},"observation_digest":"sha256:e2a1c297f35324e34fe0ea9f4e985f12120f9078446040ea53904193b67c2971","observation_id":"9be2a218-02dc-44ba-b9a0-073a23c42af1","resolution":{"observed_at":"2026-05-11T21:01:10.138596Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"A class of curvature type equations","venue":null,"work_id":"e6b1f694-79cc-4e3e-8cfb-7b6fbe3f6be4","year":2021},"citing_paper":{"arxiv_id":"2604.23349","last_updated":"2026-04-25T15:17:50Z","snapshot_observed_at":"2026-07-06T23:09:34.300163Z","submitted_at":"2026-04-25T15:17:50Z","title":"Interior $C^{2}$ estimate for semi-convex solutions to a class of Hessian quotient equations in arbitrary dimensions","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-05-08T07:36:13.730113Z"},"links":{"citing_paper":"/paper/2604.23349"},"observation_digest":"sha256:7bbeb9533484879ee44e18acda5a5dcaa534ba48d80a2dd2b4a78d3e10f6eacb","observation_id":"cc97b2c6-39e7-4718-a30e-3483809f5aa6","resolution":{"observed_at":"2026-05-26T17:47:46.986961Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"On elliptic Monge-Ampère equations and Weyl’s embedding problem","venue":null,"work_id":"7856d1a4-7deb-49da-86e6-b74d0ed57a51","year":1959},"citing_paper":{"arxiv_id":"2604.23349","last_updated":"2026-04-25T15:17:50Z","snapshot_observed_at":"2026-07-06T23:09:34.300163Z","submitted_at":"2026-04-25T15:17:50Z","title":"Interior $C^{2}$ estimate for semi-convex solutions to a class of Hessian quotient equations in arbitrary dimensions","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-05-08T07:36:13.730113Z"},"links":{"citing_paper":"/paper/2604.23349"},"observation_digest":"sha256:686bbc978ea0204961e64000c90d940e9d2b5af49e9af4fe540fe08c1fdadb31","observation_id":"fd5ec2f9-0b0c-4ddf-8ad1-00d02fc20073","resolution":{"observed_at":"2026-05-26T17:47:47.056156Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"Convexity estimates for mean curvature flow and singularities of mean convex surfaces","venue":null,"work_id":"c9eb9687-2162-4391-bbb8-75fe05932164","year":1999},"citing_paper":{"arxiv_id":"2604.23349","last_updated":"2026-04-25T15:17:50Z","snapshot_observed_at":"2026-07-06T23:09:34.300163Z","submitted_at":"2026-04-25T15:17:50Z","title":"Interior $C^{2}$ estimate for semi-convex solutions to a class of Hessian quotient equations in arbitrary dimensions","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-05-08T07:36:13.730113Z"},"links":{"citing_paper":"/paper/2604.23349"},"observation_digest":"sha256:0018a932047188641f7ea71e2817cc2d90f36362f7404a2db5c66d02883bb1d8","observation_id":"4d27e487-27b4-4181-a9b7-8013ac1af957","resolution":{"observed_at":"2026-05-26T17:47:47.011221Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"On the equivalence of two notions of weak solutions, viscosity solutions and distribution solutions","venue":null,"work_id":"3afdccad-4c0c-4239-85d3-2444c3049817","year":1995},"citing_paper":{"arxiv_id":"2604.23349","last_updated":"2026-04-25T15:17:50Z","snapshot_observed_at":"2026-07-06T23:09:34.300163Z","submitted_at":"2026-04-25T15:17:50Z","title":"Interior $C^{2}$ estimate for semi-convex solutions to a class of Hessian quotient equations in arbitrary dimensions","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-05-08T07:36:13.730113Z"},"links":{"citing_paper":"/paper/2604.23349"},"observation_digest":"sha256:f13800e5717d9ce8e568e0210c1ba455be5b407829ca09d45574c1941d7725cb","observation_id":"bf844304-e905-4d1b-98c3-7f1e9114a1f8","resolution":{"observed_at":"2026-05-26T17:47:47.047520Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2602.14064","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Interior Hessian estimates for Hessian quotient equations in dimension three","venue":null,"work_id":"943d7631-31a9-4aad-824e-f016f3ce13b8","year":2026},"citing_paper":{"arxiv_id":"2604.23349","last_updated":"2026-04-25T15:17:50Z","snapshot_observed_at":"2026-07-06T23:09:34.300163Z","submitted_at":"2026-04-25T15:17:50Z","title":"Interior $C^{2}$ estimate for semi-convex solutions to a class of Hessian quotient equations in arbitrary dimensions","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-05-08T07:36:13.730113Z"},"links":{"citing_paper":"/paper/2604.23349"},"observation_digest":"sha256:491a399c97a632464e0abcf4abd45b67e331d08e934bec0869ab4b4e61684764","observation_id":"9d6bfcce-b05d-4e42-9cc3-d4c2d7f5342c","resolution":{"observed_at":"2026-05-11T21:01:10.174355Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"Über die Lösungen der Differentialgleichungrt−s 2 = 1","venue":null,"work_id":"a6c938ea-6dee-43ba-ac19-342c2885a959","year":1954},"citing_paper":{"arxiv_id":"2604.23349","last_updated":"2026-04-25T15:17:50Z","snapshot_observed_at":"2026-07-06T23:09:34.300163Z","submitted_at":"2026-04-25T15:17:50Z","title":"Interior $C^{2}$ estimate for semi-convex solutions to a class of Hessian quotient equations in arbitrary dimensions","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-05-08T07:36:13.730113Z"},"links":{"citing_paper":"/paper/2604.23349"},"observation_digest":"sha256:0fd5bae83cb4a0f2d174eb2c3b7f49ca3177fcabad9cbc5a8c10d6991ce1d313","observation_id":"fbccf2dc-41f6-43ad-abc4-335b37c7a314","resolution":{"observed_at":"2026-05-26T17:47:47.025177Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"Curvature estimates for convex solutions of some fully nonlinear Hessian-type equations","venue":null,"work_id":"6f38cab5-c402-49f9-b219-35466223e495","year":2019},"citing_paper":{"arxiv_id":"2604.23349","last_updated":"2026-04-25T15:17:50Z","snapshot_observed_at":"2026-07-06T23:09:34.300163Z","submitted_at":"2026-04-25T15:17:50Z","title":"Interior $C^{2}$ estimate for semi-convex solutions to a class of Hessian quotient equations in arbitrary dimensions","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-05-08T07:36:13.730113Z"},"links":{"citing_paper":"/paper/2604.23349"},"observation_digest":"sha256:781bbfa2670e421f7ea95d678914306b74998bd21f60a92e479b0ba0a985361f","observation_id":"a2900f64-f577-4622-a55f-0ddb54bb6618","resolution":{"observed_at":"2026-05-26T17:47:47.033156Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"An interior estimate for convex solutions and a rigidity theorem","venue":null,"work_id":"98f9923e-1e7e-4197-b6b9-b437ca4dd503","year":2016},"citing_paper":{"arxiv_id":"2604.23349","last_updated":"2026-04-25T15:17:50Z","snapshot_observed_at":"2026-07-06T23:09:34.300163Z","submitted_at":"2026-04-25T15:17:50Z","title":"Interior $C^{2}$ estimate for semi-convex solutions to a class of Hessian quotient equations in arbitrary dimensions","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-05-08T07:36:13.730113Z"},"links":{"citing_paper":"/paper/2604.23349"},"observation_digest":"sha256:cf2db38b46f3c5c3340f728e7be005739c6033d4a14d1dac4b73357b0b7981bc","observation_id":"b766dada-67c5-4e14-8ade-0149fbd62bb6","resolution":{"observed_at":"2026-05-26T17:47:47.051740Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2412.11822","last_updated":"2025-01-13T10:48:51Z","snapshot_observed_at":"2026-08-11T20:50:49.102293Z","submitted_at":"2024-12-16T14:42:08Z","title":"The Pogorelov estimates for the sum Hessian equation with rigidity theorem and parabolic versions","version":2},"cited_work":{"arxiv_id":"2412.11822","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2412.11822","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"127fdffe-1290-4a2f-8f69-c81aefdcc48a","year":2025},"citing_paper":{"arxiv_id":"2604.23349","last_updated":"2026-04-25T15:17:50Z","snapshot_observed_at":"2026-07-06T23:09:34.300163Z","submitted_at":"2026-04-25T15:17:50Z","title":"Interior $C^{2}$ estimate for semi-convex solutions to a class of Hessian quotient equations in arbitrary dimensions","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-05-08T07:36:13.730113Z"},"links":{"cited_paper":"/paper/2412.11822","citing_paper":"/paper/2604.23349"},"observation_digest":"sha256:aedd79216636d43449d69820acb283537cb8977debcb16ad314a88b5e13186b2","observation_id":"2e6cd714-6613-45fc-abe8-e4693d9a8a48","resolution":{"observed_at":"2026-05-11T21:01:10.165024Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"InteriorC 2 estimate for Monge-Ampère equation in dimension two","venue":null,"work_id":"80205d97-cdf2-430a-8f49-f9e129e8ed74","year":2021},"citing_paper":{"arxiv_id":"2604.23349","last_updated":"2026-04-25T15:17:50Z","snapshot_observed_at":"2026-07-06T23:09:34.300163Z","submitted_at":"2026-04-25T15:17:50Z","title":"Interior $C^{2}$ estimate for semi-convex solutions to a class of Hessian quotient equations in arbitrary dimensions","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-05-08T07:36:13.730113Z"},"links":{"citing_paper":"/paper/2604.23349"},"observation_digest":"sha256:9d54ef8b9ad37199a86dc8624e76ace26b036b5858b572a6570ee0db8f087e6d","observation_id":"34e5d771-92e1-42a7-8671-a017bbb5f5cb","resolution":{"observed_at":"2026-05-26T17:47:46.956394Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"Pogorelov typeC2 estimates for sum Hessian equations and a rigidity theorem","venue":null,"work_id":"99a903af-5976-48a2-83c5-e7ea69758100","year":2023},"citing_paper":{"arxiv_id":"2604.23349","last_updated":"2026-04-25T15:17:50Z","snapshot_observed_at":"2026-07-06T23:09:34.300163Z","submitted_at":"2026-04-25T15:17:50Z","title":"Interior $C^{2}$ estimate for semi-convex solutions to a class of Hessian quotient equations in arbitrary dimensions","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-05-08T07:36:13.730113Z"},"links":{"citing_paper":"/paper/2604.23349"},"observation_digest":"sha256:983806097c0174f61d35999665e75455f64b583c3acfded97a9aecf46f22b55f","observation_id":"ac8aa360-70b6-443e-a6d9-cf28913f601c","resolution":{"observed_at":"2026-05-26T17:47:46.962878Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2311.05835","last_updated":"2023-11-10T02:47:01Z","snapshot_observed_at":"2026-08-13T05:28:43.085982Z","submitted_at":"2023-11-10T02:47:01Z","title":"Interior $C^2$ estimate for Hessian quotient equation in dimension three","version":1},"cited_work":{"arxiv_id":"2311.05835","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2311.05835","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Lu.InteriorC 2 estimate for Hessian quotient equation in dimension three","venue":null,"work_id":"93da4209-9636-42cd-92d5-fb04631dcf39","year":2023},"citing_paper":{"arxiv_id":"2604.23349","last_updated":"2026-04-25T15:17:50Z","snapshot_observed_at":"2026-07-06T23:09:34.300163Z","submitted_at":"2026-04-25T15:17:50Z","title":"Interior $C^{2}$ estimate for semi-convex solutions to a class of Hessian quotient equations in arbitrary dimensions","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-05-08T07:36:13.730113Z"},"links":{"cited_paper":"/paper/2311.05835","citing_paper":"/paper/2604.23349"},"observation_digest":"sha256:a0953ffbba4509302413afb4323a1be6cf0be64c4a5898b0e6f67656e313bf4a","observation_id":"1786af9e-06ad-4434-a02d-da4bbc5963af","resolution":{"observed_at":"2026-05-11T21:01:10.147699Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"InteriorC2 estimate for Hessian quotient equation in general dimension","venue":null,"work_id":"a05e6ca1-ac7e-4a06-91f2-7b26f564fa6a","year":2025},"citing_paper":{"arxiv_id":"2604.23349","last_updated":"2026-04-25T15:17:50Z","snapshot_observed_at":"2026-07-06T23:09:34.300163Z","submitted_at":"2026-04-25T15:17:50Z","title":"Interior $C^{2}$ estimate for semi-convex solutions to a class of Hessian quotient equations in arbitrary dimensions","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-05-08T07:36:13.730113Z"},"links":{"citing_paper":"/paper/2604.23349"},"observation_digest":"sha256:d18fe024eb71ae53a71e1b3010944a3893e30d8a9f28bc049f276491e6836de5","observation_id":"617b1115-ff68-416d-9145-748b63955e65","resolution":{"observed_at":"2026-05-26T17:47:47.036694Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"Lu and M","venue":null,"work_id":"7fec2e72-62e8-41ae-b9eb-400ef10caf1b","year":null},"citing_paper":{"arxiv_id":"2604.23349","last_updated":"2026-04-25T15:17:50Z","snapshot_observed_at":"2026-07-06T23:09:34.300163Z","submitted_at":"2026-04-25T15:17:50Z","title":"Interior $C^{2}$ estimate for semi-convex solutions to a class of Hessian quotient equations in arbitrary dimensions","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-05-08T07:36:13.730113Z"},"links":{"citing_paper":"/paper/2604.23349"},"observation_digest":"sha256:c1e036f29658b6dc906749c197cee4339a2b8bca906d7d06d8d64b5ecceec539","observation_id":"61f4f950-40cb-4244-8166-4ca05b9609db","resolution":{"observed_at":"2026-05-26T17:47:47.068180Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2602.14946","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"68bc7106-7bea-4458-8661-f0ddfafc5ea2","year":null},"citing_paper":{"arxiv_id":"2604.23349","last_updated":"2026-04-25T15:17:50Z","snapshot_observed_at":"2026-07-06T23:09:34.300163Z","submitted_at":"2026-04-25T15:17:50Z","title":"Interior $C^{2}$ estimate for semi-convex solutions to a class of Hessian quotient equations in arbitrary dimensions","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-05-08T07:36:13.730113Z"},"links":{"citing_paper":"/paper/2604.23349"},"observation_digest":"sha256:5851f5ff3b3563566754adef6c14a4d93a1778311263973b7ea487aa7b9682e1","observation_id":"73f7875c-5b52-4a5c-ad0f-c6fd61753de4","resolution":{"observed_at":"2026-05-11T21:01:10.157499Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"Hessian estimates for convex solutions to quadratic Hessian equation","venue":null,"work_id":"5aa3520a-5a1a-49db-8711-d1a73a94fd5a","year":2019},"citing_paper":{"arxiv_id":"2604.23349","last_updated":"2026-04-25T15:17:50Z","snapshot_observed_at":"2026-07-06T23:09:34.300163Z","submitted_at":"2026-04-25T15:17:50Z","title":"Interior $C^{2}$ estimate for semi-convex solutions to a class of Hessian quotient equations in arbitrary dimensions","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-05-08T07:36:13.730113Z"},"links":{"citing_paper":"/paper/2604.23349"},"observation_digest":"sha256:457adcfc0d5c8ea52b140410a808b236a1ce8dfbde535b3e87f87daaa05daa3f","observation_id":"263e1823-12be-4895-a479-127ff02b341a","resolution":{"observed_at":"2026-05-26T17:47:46.977618Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"Strict 2-convexity of convex solutions to the quadratic Hessian equa- tion","venue":null,"work_id":"5810ae2e-b2b0-402d-9ffb-5635f59325de","year":2021},"citing_paper":{"arxiv_id":"2604.23349","last_updated":"2026-04-25T15:17:50Z","snapshot_observed_at":"2026-07-06T23:09:34.300163Z","submitted_at":"2026-04-25T15:17:50Z","title":"Interior $C^{2}$ estimate for semi-convex solutions to a class of Hessian quotient equations in arbitrary dimensions","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-05-08T07:36:13.730113Z"},"links":{"citing_paper":"/paper/2604.23349"},"observation_digest":"sha256:e1f309c55d6fc60ea207502e0d837f638039f488917f5fbccac4ac335f20a667","observation_id":"4e6f7469-d772-49cb-b16e-f3537b3e66b8","resolution":{"observed_at":"2026-05-26T17:47:46.997556Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"On the improper convex affine hyperspheres","venue":null,"work_id":"32c88faa-c003-4cff-aaf3-8b9d9fd960d8","year":1972},"citing_paper":{"arxiv_id":"2604.23349","last_updated":"2026-04-25T15:17:50Z","snapshot_observed_at":"2026-07-06T23:09:34.300163Z","submitted_at":"2026-04-25T15:17:50Z","title":"Interior $C^{2}$ estimate for semi-convex solutions to a class of Hessian quotient equations in arbitrary dimensions","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-05-08T07:36:13.730113Z"},"links":{"citing_paper":"/paper/2604.23349"},"observation_digest":"sha256:55ef430a3bbb82f71b191142f553c8659451c9914fb0019da0f4c2c953291ae1","observation_id":"92d17510-fd0b-42ed-8bb6-4f52a944a08d","resolution":{"observed_at":"2026-05-26T17:47:46.990255Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"38fb4041-72aa-42d8-a608-b3fc260f09d6","year":1978},"citing_paper":{"arxiv_id":"2604.23349","last_updated":"2026-04-25T15:17:50Z","snapshot_observed_at":"2026-07-06T23:09:34.300163Z","submitted_at":"2026-04-25T15:17:50Z","title":"Interior $C^{2}$ estimate for semi-convex solutions to a class of Hessian quotient equations in arbitrary dimensions","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-05-08T07:36:13.730113Z"},"links":{"citing_paper":"/paper/2604.23349"},"observation_digest":"sha256:41b380254c232cd6d00ab1ecaf2137a7e31ebea414999f66f0a2baef5aa5b846","observation_id":"1b30367d-1caf-4049-9a2d-7dbba33d10b2","resolution":{"observed_at":"2026-05-26T17:47:46.980809Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"Interior curvature estimates for hypersurfaces of prescribing scalar curva- ture in dimension three","venue":null,"work_id":"ec0440fd-51b7-4ffc-a35d-60ad5fe57152","year":2024},"citing_paper":{"arxiv_id":"2604.23349","last_updated":"2026-04-25T15:17:50Z","snapshot_observed_at":"2026-07-06T23:09:34.300163Z","submitted_at":"2026-04-25T15:17:50Z","title":"Interior $C^{2}$ estimate for semi-convex solutions to a class of Hessian quotient equations in arbitrary dimensions","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-05-08T07:36:13.730113Z"},"links":{"citing_paper":"/paper/2604.23349"},"observation_digest":"sha256:fa6814cfe62395dba717191bb309513b91daab7bb69f443f6c8b5919eef9b76e","observation_id":"dd131184-c612-4301-93ff-c8a0b55ed890","resolution":{"observed_at":"2026-05-26T17:47:47.005904Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"Interior Hessian estimates forσ2 equations in dimension three","venue":null,"work_id":"81095592-3954-4a9a-929b-15326b69738b","year":2024},"citing_paper":{"arxiv_id":"2604.23349","last_updated":"2026-04-25T15:17:50Z","snapshot_observed_at":"2026-07-06T23:09:34.300163Z","submitted_at":"2026-04-25T15:17:50Z","title":"Interior $C^{2}$ estimate for semi-convex solutions to a class of Hessian quotient equations in arbitrary dimensions","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-05-08T07:36:13.730113Z"},"links":{"citing_paper":"/paper/2604.23349"},"observation_digest":"sha256:3bb4b66b67dd2b05cbcd8f4e0e7ba9ddd0cb5f6fd559c9747a6362f7aec7caf7","observation_id":"fd2e8f9e-2bda-4fc8-8740-beca4d431105","resolution":{"observed_at":"2026-05-26T17:47:47.029265Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2407.15159","last_updated":"2024-07-21T13:29:20Z","snapshot_observed_at":"2026-08-14T07:34:22.043617Z","submitted_at":"2024-07-21T13:29:20Z","title":"A priori interior estimates for special Lagrangian curvature equations","version":1},"cited_work":{"arxiv_id":"2407.15159","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2407.15159","snapshot_observed_at":"2026-07-01T19:56:10.568277Z","title":"Qiu and X","venue":null,"work_id":"e7454e13-e4b9-4116-84b6-1a2574c05674","year":2024},"citing_paper":{"arxiv_id":"2604.23349","last_updated":"2026-04-25T15:17:50Z","snapshot_observed_at":"2026-07-06T23:09:34.300163Z","submitted_at":"2026-04-25T15:17:50Z","title":"Interior $C^{2}$ estimate for semi-convex solutions to a class of Hessian quotient equations in arbitrary dimensions","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-05-08T07:36:13.730113Z"},"links":{"cited_paper":"/paper/2407.15159","citing_paper":"/paper/2604.23349"},"observation_digest":"sha256:6ad3260dc08c9dba3ee5afa0641df0fd2c048ce1f268c0f5ec78413e8a0b5b5c","observation_id":"f0d868bb-44c8-41c5-ba6b-ed7fa83f7724","resolution":{"observed_at":"2026-05-11T21:01:10.125352Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"A generalization of Newton-Maclaurin’s inequalities","venue":null,"work_id":"c407a3d1-25fb-4205-a934-f2e8a8747e2d","year":2024},"citing_paper":{"arxiv_id":"2604.23349","last_updated":"2026-04-25T15:17:50Z","snapshot_observed_at":"2026-07-06T23:09:34.300163Z","submitted_at":"2026-04-25T15:17:50Z","title":"Interior $C^{2}$ estimate for semi-convex solutions to a class of Hessian quotient equations in arbitrary dimensions","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-05-08T07:36:13.730113Z"},"links":{"citing_paper":"/paper/2604.23349"},"observation_digest":"sha256:7fb16a7e66abaea9cf2eb37eae5e5e9ffb3d4aac87801cf90c8686af6137b9bf","observation_id":"b5935bc5-b88f-45eb-a08f-319d9f8b2472","resolution":{"observed_at":"2026-05-26T17:47:46.973278Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"Hessian estimate for semiconvex solutions to the sigma-2 equation","venue":null,"work_id":"280e375a-c802-4ccf-9c99-9d554c2623ff","year":2020},"citing_paper":{"arxiv_id":"2604.23349","last_updated":"2026-04-25T15:17:50Z","snapshot_observed_at":"2026-07-06T23:09:34.300163Z","submitted_at":"2026-04-25T15:17:50Z","title":"Interior $C^{2}$ estimate for semi-convex solutions to a class of Hessian quotient equations in arbitrary dimensions","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-05-08T07:36:13.730113Z"},"links":{"citing_paper":"/paper/2604.23349"},"observation_digest":"sha256:f88e2197ef8fefe335aa3927995402bb495fbb1dc65f7f863224c0a778ec93d0","observation_id":"561c21b5-0967-47b6-a9f4-d95b7020e5b4","resolution":{"observed_at":"2026-05-26T17:47:47.076481Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"Hessian estimates for the sigma-2 equation in dimension four","venue":null,"work_id":"f111f460-cbd9-40bc-955d-19ffa66a7dce","year":2025},"citing_paper":{"arxiv_id":"2604.23349","last_updated":"2026-04-25T15:17:50Z","snapshot_observed_at":"2026-07-06T23:09:34.300163Z","submitted_at":"2026-04-25T15:17:50Z","title":"Interior $C^{2}$ estimate for semi-convex solutions to a class of Hessian quotient equations in arbitrary dimensions","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-05-08T07:36:13.730113Z"},"links":{"citing_paper":"/paper/2604.23349"},"observation_digest":"sha256:2074cf89b6e2f6dcd861618461b48ad5c972d5b9cd94da58049b96b3eb25891a","observation_id":"b4631a0b-ece8-4ab8-86fa-50b1eb33e36a","resolution":{"observed_at":"2026-05-26T17:47:46.950527Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"Rigidity for general semiconvex entire solutions to the sigma-2 equation","venue":null,"work_id":"7af04c78-ede6-47d5-a0f9-f3f89b349d92","year":2022},"citing_paper":{"arxiv_id":"2604.23349","last_updated":"2026-04-25T15:17:50Z","snapshot_observed_at":"2026-07-06T23:09:34.300163Z","submitted_at":"2026-04-25T15:17:50Z","title":"Interior $C^{2}$ estimate for semi-convex solutions to a class of Hessian quotient equations in arbitrary dimensions","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-05-08T07:36:13.730113Z"},"links":{"citing_paper":"/paper/2604.23349"},"observation_digest":"sha256:018607b1ffbee9091a61fbc48409ed875c49ddac0a4543a5aae5b51e245eb97f","observation_id":"391c43b8-b6ed-4c54-b4bd-5496f6222efd","resolution":{"observed_at":"2026-05-26T17:47:47.016151Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"Interior curvature bounds for a class of curvature equations","venue":null,"work_id":"4e58f5f0-61ff-48e7-947f-a951358c7c4a","year":2004},"citing_paper":{"arxiv_id":"2604.23349","last_updated":"2026-04-25T15:17:50Z","snapshot_observed_at":"2026-07-06T23:09:34.300163Z","submitted_at":"2026-04-25T15:17:50Z","title":"Interior $C^{2}$ estimate for semi-convex solutions to a class of Hessian quotient equations in arbitrary dimensions","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-05-08T07:36:13.730113Z"},"links":{"citing_paper":"/paper/2604.23349"},"observation_digest":"sha256:3a71091fb4016b6f815190246a1430332957399de14961be44374ab07357cc62","observation_id":"d3841172-131f-48af-9cfd-900cb571bc1b","resolution":{"observed_at":"2026-05-26T17:47:46.959560Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"Geometric aspects of the theory of fully nonlinear elliptic equations","venue":null,"work_id":"12d2e651-ef0c-4b53-96c8-0106636dfe95","year":2005},"citing_paper":{"arxiv_id":"2604.23349","last_updated":"2026-04-25T15:17:50Z","snapshot_observed_at":"2026-07-06T23:09:34.300163Z","submitted_at":"2026-04-25T15:17:50Z","title":"Interior $C^{2}$ estimate for semi-convex solutions to a class of Hessian quotient equations in arbitrary dimensions","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-05-08T07:36:13.730113Z"},"links":{"citing_paper":"/paper/2604.23349"},"observation_digest":"sha256:1d23f7b75d3d03715ee752eda881768b23a12672d424af2ff5502b5c94ca0a27","observation_id":"5cb2d48e-e454-44fb-88dc-8bb09089df45","resolution":{"observed_at":"2026-05-26T17:47:47.065250Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"On the existence of nonclassical solutions for two classes of fully nonlinear elliptic equations","venue":null,"work_id":"c6681f74-2b54-4a8b-b688-5dd0e12d787f","year":1990},"citing_paper":{"arxiv_id":"2604.23349","last_updated":"2026-04-25T15:17:50Z","snapshot_observed_at":"2026-07-06T23:09:34.300163Z","submitted_at":"2026-04-25T15:17:50Z","title":"Interior $C^{2}$ estimate for semi-convex solutions to a class of Hessian quotient equations in arbitrary dimensions","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-05-08T07:36:13.730113Z"},"links":{"citing_paper":"/paper/2604.23349"},"observation_digest":"sha256:31f6c156acf05c5af85dacf761af3dd67fdffa64fe362061da58ccfdbff9c0e6","observation_id":"5ed5323f-d2f5-42ae-8e13-33369394e37e","resolution":{"observed_at":"2026-05-26T17:47:46.994255Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"Hessian estimates for special Lagrangian equations with critical and supercritical phases in general dimensions","venue":null,"work_id":"d10e39d3-ece7-4976-b499-9fdaeb46a029","year":2014},"citing_paper":{"arxiv_id":"2604.23349","last_updated":"2026-04-25T15:17:50Z","snapshot_observed_at":"2026-07-06T23:09:34.300163Z","submitted_at":"2026-04-25T15:17:50Z","title":"Interior $C^{2}$ estimate for semi-convex solutions to a class of Hessian quotient equations in arbitrary dimensions","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-05-08T07:36:13.730113Z"},"links":{"citing_paper":"/paper/2604.23349"},"observation_digest":"sha256:282bf1450324cd0351b1afdc02abaeaea2dd2f186dbbaf6355e7d6997983143d","observation_id":"f18f6987-edf2-44f4-bf7a-1c035f1765f3","resolution":{"observed_at":"2026-05-26T17:47:47.071620Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"Nonpolynomial entire solutions toσk equations","venue":null,"work_id":"962c9851-4aa5-49a5-be41-36d4a438043e","year":2016},"citing_paper":{"arxiv_id":"2604.23349","last_updated":"2026-04-25T15:17:50Z","snapshot_observed_at":"2026-07-06T23:09:34.300163Z","submitted_at":"2026-04-25T15:17:50Z","title":"Interior $C^{2}$ estimate for semi-convex solutions to a class of Hessian quotient equations in arbitrary dimensions","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-05-08T07:36:13.730113Z"},"links":{"citing_paper":"/paper/2604.23349"},"observation_digest":"sha256:1b9dc3896e8bf363a9421979493b20a0897eeb33e723dcb4686888faf9e4c579","observation_id":"a50d9ac4-ec38-4094-91cd-a0f9b05dd1ac","resolution":{"observed_at":"2026-05-26T17:47:46.968465Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"Hessian estimates for the sigma-2 equation in dimension 3","venue":null,"work_id":"b660dc31-78e3-4769-95b0-7950fd30fa2e","year":2009},"citing_paper":{"arxiv_id":"2604.23349","last_updated":"2026-04-25T15:17:50Z","snapshot_observed_at":"2026-07-06T23:09:34.300163Z","submitted_at":"2026-04-25T15:17:50Z","title":"Interior $C^{2}$ estimate for semi-convex solutions to a class of Hessian quotient equations in arbitrary dimensions","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-05-08T07:36:13.730113Z"},"links":{"citing_paper":"/paper/2604.23349"},"observation_digest":"sha256:e63273f1600c29ce48712c277adf322bc762158612e030b1337de57b8868297a","observation_id":"5e5ae788-bec9-412c-bd91-b78756fdd806","resolution":{"observed_at":"2026-05-26T17:47:47.061060Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"C2 estimates fork-Hessian equations and a rigidity theorem","venue":null,"work_id":"dd650310-94a9-4978-87e1-fd4dd0aabd83","year":2025},"citing_paper":{"arxiv_id":"2604.23349","last_updated":"2026-04-25T15:17:50Z","snapshot_observed_at":"2026-07-06T23:09:34.300163Z","submitted_at":"2026-04-25T15:17:50Z","title":"Interior $C^{2}$ estimate for semi-convex solutions to a class of Hessian quotient equations in arbitrary dimensions","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-05-08T07:36:13.730113Z"},"links":{"citing_paper":"/paper/2604.23349"},"observation_digest":"sha256:1eb5db1662607773de46593be7de4aed2becaa4fbfe1202b0b9219a76b01b60e","observation_id":"4c5b0d4d-d201-4c58-80ef-9bb0d916cb16","resolution":{"observed_at":"2026-05-26T17:47:46.983808Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"Notes on generalized special Lagrangian equation","venue":null,"work_id":"3bbbea77-cdf2-4290-a1a7-d0748ed57a35","year":2024},"citing_paper":{"arxiv_id":"2604.23349","last_updated":"2026-04-25T15:17:50Z","snapshot_observed_at":"2026-07-06T23:09:34.300163Z","submitted_at":"2026-04-25T15:17:50Z","title":"Interior $C^{2}$ estimate for semi-convex solutions to a class of Hessian quotient equations in arbitrary dimensions","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-05-08T07:36:13.730113Z"},"links":{"citing_paper":"/paper/2604.23349"},"observation_digest":"sha256:a11ea3b6bc20e3aeab30b36d5fd83a64e9104f49d53ca302daeb05ec562df683","observation_id":"da7b0b6a-8775-4704-bf2d-9bcb50eb18e0","resolution":{"observed_at":"2026-05-26T17:47:47.044263Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"Hessian estimates for Lagrangian mean curvature equation with sharp Lipschitz phase: X. Zhou","venue":null,"work_id":"e4b57ffd-696e-4a42-b33f-3ad81a020fcf","year":2025},"citing_paper":{"arxiv_id":"2604.23349","last_updated":"2026-04-25T15:17:50Z","snapshot_observed_at":"2026-07-06T23:09:34.300163Z","submitted_at":"2026-04-25T15:17:50Z","title":"Interior $C^{2}$ estimate for semi-convex solutions to a class of Hessian quotient equations in arbitrary dimensions","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-05-08T07:36:13.730113Z"},"links":{"citing_paper":"/paper/2604.23349"},"observation_digest":"sha256:502ef68dd4e747581fc3e07ed438805123a6c127fb413b098b7a8a4aca6d8428","observation_id":"66d8b987-56ad-426b-9afb-983206c1cfd1","resolution":{"observed_at":"2026-05-26T17:47:47.040152Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2604.23349","last_updated":"2026-04-25T15:17:50Z","latest_version":1,"primary_category":"math.AP","snapshot_observed_at":"2026-07-06T23:09:34.300163Z","submitted_at":"2026-04-25T15:17:50Z","title":"Interior $C^{2}$ estimate for semi-convex solutions to a class of Hessian quotient equations in arbitrary dimensions"},"reference_resolution":{"displayed":50,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":2,"verified_exact":7,"verified_fuzzy":41},"total_outbound_references":50},"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":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"thesis":"As of 14 August 2026, this Paper Citation Record lists 50 of 50 outbound references and 0 inbound Pith citation observations for arXiv:2604.23349."}