{"as_of":"2026-08-09T05:44:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:4d9e969df824c633e294935338d8ff019a15f50638e0260794bf6e46d65a20dc","coverage":[{"denominator":47,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":47,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-01T08:55:19.212287Z","state":"measured"},{"denominator":47,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":47,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-08T06:32:00.761636+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/2607.21024/citation-record","integrity":"/paper/2607.21024/integrity","json":"/paper/2607.21024/citation-record.json","paper":"/paper/2607.21024"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1002/cpa.20360","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Fundamental solutions of homogeneous fully nonlinear elliptic equations","venue":"Communications on Pure and Applied Mathematics","work_id":"a2b483c1-0338-49cf-9d44-bc52e959cacc","year":2011},"citing_paper":{"arxiv_id":"2607.21024","last_updated":"2026-07-23T08:07:44Z","snapshot_observed_at":"2026-08-07T19:01:29.829642Z","submitted_at":"2026-07-23T08:07:44Z","title":"Liouville Rigidity for Real and Complex Degenerate Hessian Equations","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-01T08:55:15.030683Z"},"links":{"citing_paper":"/paper/2607.21024"},"observation_digest":"sha256:9cea4441ca0deac0499410bedbb02ea5d7797b3f751891a7d300bf7b4bfae272","observation_id":"4b46332c-6a4a-47b6-80c7-08c9d3c87029","resolution":{"observed_at":"2026-08-01T08:58:20.547993Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T08:55:15.137258Z","title":"Liouville property and regularity of a Hessian quotient equation","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2607.21024","last_updated":"2026-07-23T08:07:44Z","snapshot_observed_at":"2026-08-07T19:01:29.829642Z","submitted_at":"2026-07-23T08:07:44Z","title":"Liouville Rigidity for Real and Complex Degenerate Hessian Equations","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-01T08:55:15.137258Z"},"links":{"citing_paper":"/paper/2607.21024"},"observation_digest":"sha256:38759ede64c134a47cd1026d30b9e07fd5aa76642f95499de02e90a85b3a7113","observation_id":"64018951-67bf-49d9-b35f-89f5c111311f","resolution":{"observed_at":"2026-08-01T08:55:15.137258Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T08:55:15.220254Z","title":"The Dirichlet problem for nonlin- ear second-order elliptic equations. I. Monge-Ampère equation","venue":null,"work_id":null,"year":1984},"citing_paper":{"arxiv_id":"2607.21024","last_updated":"2026-07-23T08:07:44Z","snapshot_observed_at":"2026-08-07T19:01:29.829642Z","submitted_at":"2026-07-23T08:07:44Z","title":"Liouville Rigidity for Real and Complex Degenerate Hessian Equations","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-01T08:55:15.220254Z"},"links":{"citing_paper":"/paper/2607.21024"},"observation_digest":"sha256:c79351404e1f048a6e6c845c3fb73d13a8c840b8d0a82069a829a8ba7fcf2dc9","observation_id":"5258e98d-3f3e-4088-b42c-d696403bfb1f","resolution":{"observed_at":"2026-08-01T08:55:15.220254Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T08:55:15.309740Z","title":"The Dirichlet problem for non- linear second-order elliptic equations. III. Functions of the eigenvalues of the Hessian","venue":null,"work_id":null,"year":1985},"citing_paper":{"arxiv_id":"2607.21024","last_updated":"2026-07-23T08:07:44Z","snapshot_observed_at":"2026-08-07T19:01:29.829642Z","submitted_at":"2026-07-23T08:07:44Z","title":"Liouville Rigidity for Real and Complex Degenerate Hessian Equations","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-01T08:55:15.309740Z"},"links":{"citing_paper":"/paper/2607.21024"},"observation_digest":"sha256:8c303ac8dcc9373d88bda322b9a3b8b39f16396eac39055f2ddbba5eeeb5ebc3","observation_id":"9571dc2e-dc42-4525-a532-dd1e94713a23","resolution":{"observed_at":"2026-08-01T08:55:15.309740Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T08:55:15.451453Z","title":"The Dirichlet problem for nonlinear second-order elliptic equations. II. Complex Monge-Ampère, and uniformly elliptic, equations","venue":null,"work_id":null,"year":1985},"citing_paper":{"arxiv_id":"2607.21024","last_updated":"2026-07-23T08:07:44Z","snapshot_observed_at":"2026-08-07T19:01:29.829642Z","submitted_at":"2026-07-23T08:07:44Z","title":"Liouville Rigidity for Real and Complex Degenerate Hessian Equations","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-01T08:55:15.451453Z"},"links":{"citing_paper":"/paper/2607.21024"},"observation_digest":"sha256:5ba537327bdea993cddafcf3b34b2ee9a930429b97a3883bde04c7f093ca16fc","observation_id":"bcccb7a0-4849-451d-a4d1-513b5d45bb66","resolution":{"observed_at":"2026-08-01T08:55:15.451453Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T08:55:15.517332Z","title":"Caffarelli and Xavier Cabré.Fully nonlinear elliptic equations","venue":null,"work_id":null,"year":1995},"citing_paper":{"arxiv_id":"2607.21024","last_updated":"2026-07-23T08:07:44Z","snapshot_observed_at":"2026-08-07T19:01:29.829642Z","submitted_at":"2026-07-23T08:07:44Z","title":"Liouville Rigidity for Real and Complex Degenerate Hessian Equations","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-01T08:55:15.517332Z"},"links":{"citing_paper":"/paper/2607.21024"},"observation_digest":"sha256:132de54a099bfaad4eb063aaf92d34f08679cbd13b8515fed7a1dd1d761692a0","observation_id":"6d075a52-8872-4a3c-aeaa-666d925085ac","resolution":{"observed_at":"2026-08-01T08:55:15.517332Z","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":"10.3934/dcds.2010.28.659","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"A Liouville problem for the sigma- 2 equation","venue":"Discrete and Continuous Dynamical Systems","work_id":"f653a3c4-ca24-448f-9f9d-3c2271ee07b5","year":2010},"citing_paper":{"arxiv_id":"2607.21024","last_updated":"2026-07-23T08:07:44Z","snapshot_observed_at":"2026-08-07T19:01:29.829642Z","submitted_at":"2026-07-23T08:07:44Z","title":"Liouville Rigidity for Real and Complex Degenerate Hessian Equations","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-01T08:55:15.599129Z"},"links":{"citing_paper":"/paper/2607.21024"},"observation_digest":"sha256:ab0999e62233bac72686a9d8750e8d2f650d67b7f8a8f7d546bb48ba7e7ae064","observation_id":"e631f97e-a537-47f5-8628-e012f9058e1b","resolution":{"observed_at":"2026-08-01T08:58:20.523305Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2311.07542","last_updated":"2024-09-19T18:33:30Z","snapshot_observed_at":"2026-07-06T16:46:57.403995Z","submitted_at":"2023-11-13T18:32:55Z","title":"Liouville theorems for conformally invariant fully nonlinear equations. I","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2311.07542","snapshot_observed_at":"2026-08-01T08:55:15.741657Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.21024","last_updated":"2026-07-23T08:07:44Z","snapshot_observed_at":"2026-08-07T19:01:29.829642Z","submitted_at":"2026-07-23T08:07:44Z","title":"Liouville Rigidity for Real and Complex Degenerate Hessian Equations","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-01T08:55:15.741657Z"},"links":{"cited_paper":"/paper/2311.07542","citing_paper":"/paper/2607.21024"},"observation_digest":"sha256:87f1153a993f6ac78cc7889d68ff7fc73a6492d1f5db48eeb3513dce311e805d","observation_id":"f214ed4e-4484-41db-90ed-35ad4cf32cec","resolution":{"observed_at":"2026-08-01T08:55:15.741657Z","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":"10.1090/s0273-0979-","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T08:58:20.511656Z","title":"User’s guide to viscosity solutions of second order partial differential equations","venue":null,"work_id":"370e2f9b-bd95-462b-8dc0-aaa5a171504f","year":1992},"citing_paper":{"arxiv_id":"2607.21024","last_updated":"2026-07-23T08:07:44Z","snapshot_observed_at":"2026-08-07T19:01:29.829642Z","submitted_at":"2026-07-23T08:07:44Z","title":"Liouville Rigidity for Real and Complex Degenerate Hessian Equations","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-01T08:55:15.796224Z"},"links":{"citing_paper":"/paper/2607.21024"},"observation_digest":"sha256:e74c5219fbfcd185bdfc5566f08ca62e69a1432ac73e601c0e40d6789f24e53b","observation_id":"13aa3ac8-bb2d-4ca3-a3d0-1293c6dc07fb","resolution":{"observed_at":"2026-08-01T08:58:20.514783Z","resolver_source":"doi_truncated","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/bf01898787","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"All convex invariant functions of hermitian matrices","venue":"Archiv der Mathematik","work_id":"28498cfc-6410-4c42-8622-03fd923ddfc4","year":1957},"citing_paper":{"arxiv_id":"2607.21024","last_updated":"2026-07-23T08:07:44Z","snapshot_observed_at":"2026-08-07T19:01:29.829642Z","submitted_at":"2026-07-23T08:07:44Z","title":"Liouville Rigidity for Real and Complex Degenerate Hessian Equations","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-01T08:55:15.887644Z"},"links":{"citing_paper":"/paper/2607.21024"},"observation_digest":"sha256:970089248ab37b94ca833fd5aaa8f5f28dde161829103dbf6ae39c6377a319a7","observation_id":"d42da51e-a190-4e4e-8f96-fe37c8d50a5a","resolution":{"observed_at":"2026-08-01T08:58:20.505994Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T08:55:15.972927Z","title":"Liouville and Calabi-Yau type theorems for complex Hessian equations","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2607.21024","last_updated":"2026-07-23T08:07:44Z","snapshot_observed_at":"2026-08-07T19:01:29.829642Z","submitted_at":"2026-07-23T08:07:44Z","title":"Liouville Rigidity for Real and Complex Degenerate Hessian Equations","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-01T08:55:15.972927Z"},"links":{"citing_paper":"/paper/2607.21024"},"observation_digest":"sha256:cc3c64d9f8f2346c1a4bc3369aba99c42ec1033d72ffa5035d7234aaa2ec3d0d","observation_id":"30909c5d-fa88-497b-af62-86bbb67a039f","resolution":{"observed_at":"2026-08-01T08:55:15.972927Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T08:55:16.057659Z","title":"Onafullynonlinearellipticequationwithdifferential forms","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.21024","last_updated":"2026-07-23T08:07:44Z","snapshot_observed_at":"2026-08-07T19:01:29.829642Z","submitted_at":"2026-07-23T08:07:44Z","title":"Liouville Rigidity for Real and Complex Degenerate Hessian Equations","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-01T08:55:16.057659Z"},"links":{"citing_paper":"/paper/2607.21024"},"observation_digest":"sha256:6fc8072de258f4e09422846bd7e5701fbe00199cbd84432b64c715587243d881","observation_id":"44d1c921-901d-4576-a84a-ac920eafc491","resolution":{"observed_at":"2026-08-01T08:55:16.057659Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T08:55:16.123203Z","title":"Gårding Polynomials","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.21024","last_updated":"2026-07-23T08:07:44Z","snapshot_observed_at":"2026-08-07T19:01:29.829642Z","submitted_at":"2026-07-23T08:07:44Z","title":"Liouville Rigidity for Real and Complex Degenerate Hessian Equations","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-01T08:55:16.123203Z"},"links":{"citing_paper":"/paper/2607.21024"},"observation_digest":"sha256:6ae5fcf1e1579572c37021dd025f4c6fece02351e94bd5997b8a2bfad59e5686","observation_id":"08e936df-69a9-44dd-bd3c-796a73100e0c","resolution":{"observed_at":"2026-08-01T08:55:16.123203Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2607.16832","last_updated":"2026-07-18T14:07:17Z","snapshot_observed_at":"2026-08-02T06:19:11.456290Z","submitted_at":"2026-07-18T14:07:17Z","title":"Ideal G{\\aa}rding polynomials","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2607.16832","snapshot_observed_at":"2026-08-01T08:55:16.180441Z","title":null,"venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.21024","last_updated":"2026-07-23T08:07:44Z","snapshot_observed_at":"2026-08-07T19:01:29.829642Z","submitted_at":"2026-07-23T08:07:44Z","title":"Liouville Rigidity for Real and Complex Degenerate Hessian Equations","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-01T08:55:16.180441Z"},"links":{"cited_paper":"/paper/2607.16832","citing_paper":"/paper/2607.21024"},"observation_digest":"sha256:e625d7cc8c611f60972bebd2f4ef443612ca3c1f79e4dc31dd338490a8922195","observation_id":"c279577d-2ee6-411e-bef0-ff55857bc445","resolution":{"observed_at":"2026-08-01T08:55:16.180441Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2511.21492","last_updated":"2026-06-10T19:31:41Z","snapshot_observed_at":"2026-08-03T20:10:20.829652Z","submitted_at":"2025-11-26T15:25:13Z","title":"The Critical LYZ Equation in K\\\"ahler Geometry","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2511.21492","snapshot_observed_at":"2026-08-01T08:55:16.255138Z","title":"The Critical LYZ Equation in Kähler Geometry","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.21024","last_updated":"2026-07-23T08:07:44Z","snapshot_observed_at":"2026-08-07T19:01:29.829642Z","submitted_at":"2026-07-23T08:07:44Z","title":"Liouville Rigidity for Real and Complex Degenerate Hessian Equations","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-01T08:55:16.255138Z"},"links":{"cited_paper":"/paper/2511.21492","citing_paper":"/paper/2607.21024"},"observation_digest":"sha256:7d5b73ecd7a0a4834a6c4b7a9ddd1d023250c02c3b29e5ffce7f39880ae1043c","observation_id":"86a4ef96-8da4-46cc-a4a7-f6bedfe1bdd4","resolution":{"observed_at":"2026-08-01T08:55:16.255138Z","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":"10.1515/ans-2022-0039","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"TheexteriorDirichletproblem for the homogeneous complexk-Hessian equation","venue":"Advanced Nonlinear Studies","work_id":"c4c34489-f853-4551-be9d-eb441e07ff0f","year":2023},"citing_paper":{"arxiv_id":"2607.21024","last_updated":"2026-07-23T08:07:44Z","snapshot_observed_at":"2026-08-07T19:01:29.829642Z","submitted_at":"2026-07-23T08:07:44Z","title":"Liouville Rigidity for Real and Complex Degenerate Hessian Equations","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-01T08:55:16.341273Z"},"links":{"citing_paper":"/paper/2607.21024"},"observation_digest":"sha256:2425af22f3e91d765ee96dbd18e235ee70414fa517e8dfcc27c5800a94f3e583","observation_id":"d469acfa-4dd2-4b1a-8191-fbd170828b27","resolution":{"observed_at":"2026-08-01T08:58:20.497280Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T08:55:16.449527Z","title":"Second-order estimates and regularity for fully nonlinear ellip- tic equations on Riemannian manifolds","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2607.21024","last_updated":"2026-07-23T08:07:44Z","snapshot_observed_at":"2026-08-07T19:01:29.829642Z","submitted_at":"2026-07-23T08:07:44Z","title":"Liouville Rigidity for Real and Complex Degenerate Hessian Equations","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-01T08:55:16.449527Z"},"links":{"citing_paper":"/paper/2607.21024"},"observation_digest":"sha256:ebc45461493dff0c2b30cd3f93a81b49b057a8f4987559bab557744b96aabe05","observation_id":"307c8e65-f989-42ce-921a-98c66f2c8b9e","resolution":{"observed_at":"2026-08-01T08:55:16.449527Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T08:55:16.541332Z","title":"The Dirichlet problem for fully nonlinear elliptic equations on Riemannian manifolds","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.21024","last_updated":"2026-07-23T08:07:44Z","snapshot_observed_at":"2026-08-07T19:01:29.829642Z","submitted_at":"2026-07-23T08:07:44Z","title":"Liouville Rigidity for Real and Complex Degenerate Hessian Equations","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-01T08:55:16.541332Z"},"links":{"citing_paper":"/paper/2607.21024"},"observation_digest":"sha256:4a8056fd86915eb1b588e998be4c4dc25891629342eb4e3a6a6923cd60fbe736","observation_id":"4c0c658c-b8c5-43b1-b40b-aa4a22ff8df8","resolution":{"observed_at":"2026-08-01T08:55:16.541332Z","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":"10.1016/j.aim.2013.07.006","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"The Dirichlet problem for a complex Monge-Ampère type equation on Hermitian manifolds","venue":"Advances in Mathematics","work_id":"c88a602b-539f-4af3-85ce-14e2603b73b3","year":2013},"citing_paper":{"arxiv_id":"2607.21024","last_updated":"2026-07-23T08:07:44Z","snapshot_observed_at":"2026-08-07T19:01:29.829642Z","submitted_at":"2026-07-23T08:07:44Z","title":"Liouville Rigidity for Real and Complex Degenerate Hessian Equations","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-01T08:55:16.629677Z"},"links":{"citing_paper":"/paper/2607.21024"},"observation_digest":"sha256:873a84a87d7a9c65ae9ecccdfa5e1524de383c478aa68e8d246f0cb4c8d5fbeb","observation_id":"aef05329-b251-4db0-a06e-52fdffd38879","resolution":{"observed_at":"2026-08-01T08:58:20.482784Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s00526-014-0810-1","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"On a class of fully nonlinear elliptic equations on Her- mitian manifolds","venue":"Calculus of Variations and Partial Differential Equations","work_id":"8c213562-8eed-41c4-9df8-409c31c04e36","year":2015},"citing_paper":{"arxiv_id":"2607.21024","last_updated":"2026-07-23T08:07:44Z","snapshot_observed_at":"2026-08-07T19:01:29.829642Z","submitted_at":"2026-07-23T08:07:44Z","title":"Liouville Rigidity for Real and Complex Degenerate Hessian Equations","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-01T08:55:16.772412Z"},"links":{"citing_paper":"/paper/2607.21024"},"observation_digest":"sha256:66420a982f14041ab688370948f124c54847012616ee86fed77072896864c67c","observation_id":"c227b60b-3d20-4948-8b38-b502e9a77b3a","resolution":{"observed_at":"2026-08-01T08:58:20.473898Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.4310/pamq.2021","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T08:58:20.461433Z","title":"A class of curvature type equations","venue":null,"work_id":"0e8c50d3-42df-404a-a4df-42984e1c2dce","year":2021},"citing_paper":{"arxiv_id":"2607.21024","last_updated":"2026-07-23T08:07:44Z","snapshot_observed_at":"2026-08-07T19:01:29.829642Z","submitted_at":"2026-07-23T08:07:44Z","title":"Liouville Rigidity for Real and Complex Degenerate Hessian Equations","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-01T08:55:16.834695Z"},"links":{"citing_paper":"/paper/2607.21024"},"observation_digest":"sha256:f38efb6da2280597d01c03ff37bac5abc75fa28b898724a0b3cd59b5b4c51267","observation_id":"bf945acb-74ca-424f-b29c-666f18f6dc96","resolution":{"observed_at":"2026-08-01T08:58:20.465009Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.5802/afst.1583","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Tangents to subsolutions: existence and uniqueness, Part I","venue":"Annales de la faculté des sciences de Toulouse Mathématiques","work_id":"3e789f34-aab7-4703-8d3a-58878b9f6ac7","year":2018},"citing_paper":{"arxiv_id":"2607.21024","last_updated":"2026-07-23T08:07:44Z","snapshot_observed_at":"2026-08-07T19:01:29.829642Z","submitted_at":"2026-07-23T08:07:44Z","title":"Liouville Rigidity for Real and Complex Degenerate Hessian Equations","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-01T08:55:16.897267Z"},"links":{"citing_paper":"/paper/2607.21024"},"observation_digest":"sha256:2a5f5acbf1325a683db73ab5c400b51bf8582a449d86ca336c4bdcc2c0efb655","observation_id":"db48fd37-18ab-4d1c-a0dd-41cbb83cb285","resolution":{"observed_at":"2026-08-01T08:58:20.455493Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1002/cpa.20265","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Dirichletdualityandthenonlinear Dirichlet problem","venue":"Communications on Pure and Applied Mathematics","work_id":"2dd49bc8-2fa3-4920-9a1a-86726735f23d","year":2009},"citing_paper":{"arxiv_id":"2607.21024","last_updated":"2026-07-23T08:07:44Z","snapshot_observed_at":"2026-08-07T19:01:29.829642Z","submitted_at":"2026-07-23T08:07:44Z","title":"Liouville Rigidity for Real and Complex Degenerate Hessian Equations","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-01T08:55:16.983649Z"},"links":{"citing_paper":"/paper/2607.21024"},"observation_digest":"sha256:509406097901a077bb1a4277ef97a0b90fe85493c17a88045a6d3bff0891cb8f","observation_id":"97200791-879a-49c8-ac7f-2dfeb8ff8f7e","resolution":{"observed_at":"2026-08-01T08:58:20.442778Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T08:55:17.133088Z","title":"Dirichletdualityandthenonlinear Dirichlet problem on Riemannian manifolds","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2607.21024","last_updated":"2026-07-23T08:07:44Z","snapshot_observed_at":"2026-08-07T19:01:29.829642Z","submitted_at":"2026-07-23T08:07:44Z","title":"Liouville Rigidity for Real and Complex Degenerate Hessian Equations","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-01T08:55:17.133088Z"},"links":{"citing_paper":"/paper/2607.21024"},"observation_digest":"sha256:f82ebb39adfd367a120be08503543f7a2ab9e263d3f3bcbb79b8537b2b50d7eb","observation_id":"761f5935-1d88-4c86-b9bd-bfb6ad51f895","resolution":{"observed_at":"2026-08-01T08:55:17.133088Z","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":"10.5802/aif.2846","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"The Restriction Theorem for Fully Nonlinear Subequations","venue":"Annales de l’institut Fourier","work_id":"0da8e363-b3f9-416a-9fb3-f0f7485ba513","year":2014},"citing_paper":{"arxiv_id":"2607.21024","last_updated":"2026-07-23T08:07:44Z","snapshot_observed_at":"2026-08-07T19:01:29.829642Z","submitted_at":"2026-07-23T08:07:44Z","title":"Liouville Rigidity for Real and Complex Degenerate Hessian Equations","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-01T08:55:17.285248Z"},"links":{"citing_paper":"/paper/2607.21024"},"observation_digest":"sha256:0aa016734a2f32d5e5e80036e435200e33561482c4a924686844323320ef767a","observation_id":"37f5843f-e0dd-4023-9e80-2878ce4a6cf1","resolution":{"observed_at":"2026-08-01T08:58:20.339449Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T08:55:17.366276Z","title":null,"venue":null,"work_id":null,"year":1976},"citing_paper":{"arxiv_id":"2607.21024","last_updated":"2026-07-23T08:07:44Z","snapshot_observed_at":"2026-08-07T19:01:29.829642Z","submitted_at":"2026-07-23T08:07:44Z","title":"Liouville Rigidity for Real and Complex Degenerate Hessian Equations","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-01T08:55:17.366276Z"},"links":{"citing_paper":"/paper/2607.21024"},"observation_digest":"sha256:00fe506be9835e43c010182885415a125f09ddedfbc6be037dc73fc6f3c97ec3","observation_id":"274334ca-bb86-4a57-ad98-d044ff97a871","resolution":{"observed_at":"2026-08-01T08:55:17.366276Z","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":"10.4310/mrl.2010.v17.n3.a12","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"A second order estimate for complex Hessian equations on a compact Kähler manifold","venue":"Mathematical Research Letters","work_id":"b44068cc-1a61-4af9-8c4b-737059390adf","year":2010},"citing_paper":{"arxiv_id":"2607.21024","last_updated":"2026-07-23T08:07:44Z","snapshot_observed_at":"2026-08-07T19:01:29.829642Z","submitted_at":"2026-07-23T08:07:44Z","title":"Liouville Rigidity for Real and Complex Degenerate Hessian Equations","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-01T08:55:17.486684Z"},"links":{"citing_paper":"/paper/2607.21024"},"observation_digest":"sha256:0d2768a8164bffe3afeef26b12da5767c234903facf43d78447b2bef626362ae","observation_id":"35b3deaa-0263-40e0-b54e-439a7e3e0ccb","resolution":{"observed_at":"2026-08-01T08:58:20.179655Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T08:55:17.582211Z","title":"Existence of entire solutions to the Monge- Ampère equation","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2607.21024","last_updated":"2026-07-23T08:07:44Z","snapshot_observed_at":"2026-08-07T19:01:29.829642Z","submitted_at":"2026-07-23T08:07:44Z","title":"Liouville Rigidity for Real and Complex Degenerate Hessian Equations","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-01T08:55:17.582211Z"},"links":{"citing_paper":"/paper/2607.21024"},"observation_digest":"sha256:2b7d91c4329e666226e862921f81ae793164c49bbba6d9a12c90860b5260bf61","observation_id":"d3e0d330-a8ac-4c85-89b6-164526767bfc","resolution":{"observed_at":"2026-08-01T08:55:17.582211Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T08:55:17.649453Z","title":"A Liouville theorem for solutions of degen- erate Monge-Ampère equations","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2607.21024","last_updated":"2026-07-23T08:07:44Z","snapshot_observed_at":"2026-08-07T19:01:29.829642Z","submitted_at":"2026-07-23T08:07:44Z","title":"Liouville Rigidity for Real and Complex Degenerate Hessian Equations","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-01T08:55:17.649453Z"},"links":{"citing_paper":"/paper/2607.21024"},"observation_digest":"sha256:d8c318c96540234156f9441b46f4a43ff8ca4db41ddf33b005964d22a0a07fd3","observation_id":"20138d30-c2fb-4628-9212-98cd5a588116","resolution":{"observed_at":"2026-08-01T08:55:17.649453Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T08:55:17.726104Z","title":"Isolated singularities for fully nonlinear elliptic equations","venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2607.21024","last_updated":"2026-07-23T08:07:44Z","snapshot_observed_at":"2026-08-07T19:01:29.829642Z","submitted_at":"2026-07-23T08:07:44Z","title":"Liouville Rigidity for Real and Complex Degenerate Hessian Equations","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-01T08:55:17.726104Z"},"links":{"citing_paper":"/paper/2607.21024"},"observation_digest":"sha256:87802fb04821007a706a8e0fb7b787c49eceb3e8192423b3daf130c541adeec1","observation_id":"c84b5791-1a64-4ab9-b1cb-ae34227d33c7","resolution":{"observed_at":"2026-08-01T08:55:17.726104Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1002/cpa.10099","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"On some conformally invariant fully nonlinear equations","venue":"Communications on Pure and Applied Mathematics","work_id":"6318d689-3e36-4949-8606-ab75c38910b3","year":2003},"citing_paper":{"arxiv_id":"2607.21024","last_updated":"2026-07-23T08:07:44Z","snapshot_observed_at":"2026-08-07T19:01:29.829642Z","submitted_at":"2026-07-23T08:07:44Z","title":"Liouville Rigidity for Real and Complex Degenerate Hessian Equations","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-01T08:55:17.853383Z"},"links":{"citing_paper":"/paper/2607.21024"},"observation_digest":"sha256:e922f5a86a5f0567d67e3c8fb7d5fbcb0d5836dd491a20a43b18b4a7f54e511a","observation_id":"2b4efafb-f61c-414c-a69e-6e4ac88ac04f","resolution":{"observed_at":"2026-08-01T08:58:20.073212Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.jfa.2016.01.008","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"An interior estimate for convex solutions and a rigidity theorem","venue":"Journal of Functional Analysis","work_id":"fcb643af-117b-4a1e-8baa-96f361c79380","year":2016},"citing_paper":{"arxiv_id":"2607.21024","last_updated":"2026-07-23T08:07:44Z","snapshot_observed_at":"2026-08-07T19:01:29.829642Z","submitted_at":"2026-07-23T08:07:44Z","title":"Liouville Rigidity for Real and Complex Degenerate Hessian Equations","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-01T08:55:17.916104Z"},"links":{"citing_paper":"/paper/2607.21024"},"observation_digest":"sha256:798068a86e10af0a6026197ef337fcb76abbbaed3ae04c0fbbb9710aaff58245","observation_id":"dd6809d6-0ef0-44ea-9368-470aa45c8973","resolution":{"observed_at":"2026-08-01T08:58:19.953374Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T08:55:17.999842Z","title":"Local gradient estimates of solutions to some conformally invari- ant fully nonlinear equations","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2607.21024","last_updated":"2026-07-23T08:07:44Z","snapshot_observed_at":"2026-08-07T19:01:29.829642Z","submitted_at":"2026-07-23T08:07:44Z","title":"Liouville Rigidity for Real and Complex Degenerate Hessian Equations","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-01T08:55:17.999842Z"},"links":{"citing_paper":"/paper/2607.21024"},"observation_digest":"sha256:6513685b8cd2fd6f6995036055b11355c12effd162b49e8198a430df145c27ba","observation_id":"ef7e5f54-f0c2-4394-af74-1db888705e71","resolution":{"observed_at":"2026-08-01T08:55:17.999842Z","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":"10.1007/s00526-017-1192-y","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Symmetry, quantitative Liouville theorems and analysis of large solutions of conformally invariant fully nonlinear elliptic equations","venue":"Calculus of Variations and Partial Differential Equations","work_id":"ab228605-aa08-4055-a208-601a194a106e","year":2017},"citing_paper":{"arxiv_id":"2607.21024","last_updated":"2026-07-23T08:07:44Z","snapshot_observed_at":"2026-08-07T19:01:29.829642Z","submitted_at":"2026-07-23T08:07:44Z","title":"Liouville Rigidity for Real and Complex Degenerate Hessian Equations","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-01T08:55:18.087967Z"},"links":{"citing_paper":"/paper/2607.21024"},"observation_digest":"sha256:fb5f6124c856644d78e9f5bcb5735a45accdd0c9f6533d5b7e1884139e0b22d5","observation_id":"99a7b2f1-1bc5-44d6-9309-dbf3cddf06bf","resolution":{"observed_at":"2026-08-01T08:58:19.859275Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T08:55:18.174505Z","title":"Towards a Liouville theorem for continuousviscositysolutionstofullynonlinearellipticequationsinconformal geometry","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.21024","last_updated":"2026-07-23T08:07:44Z","snapshot_observed_at":"2026-08-07T19:01:29.829642Z","submitted_at":"2026-07-23T08:07:44Z","title":"Liouville Rigidity for Real and Complex Degenerate Hessian Equations","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-01T08:55:18.174505Z"},"links":{"citing_paper":"/paper/2607.21024"},"observation_digest":"sha256:b23bf4a5b63e7886491b1054320b2311903f64ed9917728f020070d481d51630","observation_id":"de9d639e-385f-4bc8-b27b-e3070403e056","resolution":{"observed_at":"2026-08-01T08:55:18.174505Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T08:55:18.286277Z","title":"On the convexity of general inverseσ k equations","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.21024","last_updated":"2026-07-23T08:07:44Z","snapshot_observed_at":"2026-08-07T19:01:29.829642Z","submitted_at":"2026-07-23T08:07:44Z","title":"Liouville Rigidity for Real and Complex Degenerate Hessian Equations","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-01T08:55:18.286277Z"},"links":{"citing_paper":"/paper/2607.21024"},"observation_digest":"sha256:393033962710f5acba7ca4174dcce8ddfc2fe9b7c9002698d34ff53b6b31a87d","observation_id":"68ed2ef9-3b9f-44cc-9910-9d0d789dabdf","resolution":{"observed_at":"2026-08-01T08:55:18.286277Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T08:55:18.377068Z","title":"Corrigendum to “On the convexity of general inverse sigma-k equations","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.21024","last_updated":"2026-07-23T08:07:44Z","snapshot_observed_at":"2026-08-07T19:01:29.829642Z","submitted_at":"2026-07-23T08:07:44Z","title":"Liouville Rigidity for Real and Complex Degenerate Hessian Equations","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-01T08:55:18.377068Z"},"links":{"citing_paper":"/paper/2607.21024"},"observation_digest":"sha256:d41b98696b6c66d4d065c7398190564b4933fc9997cd0eff62fb0084e07ca80e","observation_id":"3d834d1d-5eac-4a2e-a119-b902b37d5578","resolution":{"observed_at":"2026-08-01T08:55:18.377068Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T08:55:18.463819Z","title":"The Neumann problem for Hessian equations","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2607.21024","last_updated":"2026-07-23T08:07:44Z","snapshot_observed_at":"2026-08-07T19:01:29.829642Z","submitted_at":"2026-07-23T08:07:44Z","title":"Liouville Rigidity for Real and Complex Degenerate Hessian Equations","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-01T08:55:18.463819Z"},"links":{"citing_paper":"/paper/2607.21024"},"observation_digest":"sha256:8c0da9709e64e9e768b0f1e0f65b40da195bb273e07be5312dd54a4889d2c11e","observation_id":"58bf4f7a-7280-4df3-ba9e-4b3095de294f","resolution":{"observed_at":"2026-08-01T08:55:18.463819Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.3934/cpaa.2017074","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"On uniform estimate of complex elliptic equations on closed Her- mitian manifolds","venue":"Communications on Pure &amp Applied Analysis","work_id":"41c319bf-b61f-40c5-a86b-8b39dcc4bdf7","year":2017},"citing_paper":{"arxiv_id":"2607.21024","last_updated":"2026-07-23T08:07:44Z","snapshot_observed_at":"2026-08-07T19:01:29.829642Z","submitted_at":"2026-07-23T08:07:44Z","title":"Liouville Rigidity for Real and Complex Degenerate Hessian Equations","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-01T08:55:18.541610Z"},"links":{"citing_paper":"/paper/2607.21024"},"observation_digest":"sha256:c4ca965533bd13695243aa79e9ec358f4b4d038a58a2bc536e55449e025b11d4","observation_id":"15df0de7-2ff8-4b2b-9dff-388c19ee534e","resolution":{"observed_at":"2026-08-01T08:58:19.776121Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T08:55:18.628945Z","title":"Fully non-linear elliptic equations on compact Hermitian manifolds","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.21024","last_updated":"2026-07-23T08:07:44Z","snapshot_observed_at":"2026-08-07T19:01:29.829642Z","submitted_at":"2026-07-23T08:07:44Z","title":"Liouville Rigidity for Real and Complex Degenerate Hessian Equations","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-01T08:55:18.628945Z"},"links":{"citing_paper":"/paper/2607.21024"},"observation_digest":"sha256:acda4c8315650f8e74f48b3ba1f2613b2ce1dff1b3eb7935ad883840f521e9e7","observation_id":"d80910b9-69b0-4c14-92aa-dde4ef5b8f5e","resolution":{"observed_at":"2026-08-01T08:55:18.628945Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T08:55:18.712134Z","title":"The Monge-Ampère equation for(n− 1)-plurisubharmonic functions on a compact Kähler manifold","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2607.21024","last_updated":"2026-07-23T08:07:44Z","snapshot_observed_at":"2026-08-07T19:01:29.829642Z","submitted_at":"2026-07-23T08:07:44Z","title":"Liouville Rigidity for Real and Complex Degenerate Hessian Equations","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-01T08:55:18.712134Z"},"links":{"citing_paper":"/paper/2607.21024"},"observation_digest":"sha256:f35a996c1b85f141ec5df72d294401a0ebd3a1ed1fa3efcf4bf399f13ec2fb08","observation_id":"4e7429ea-6572-4067-8f14-19d813c3b4dd","resolution":{"observed_at":"2026-08-01T08:55:18.712134Z","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":"10.1007/bf02393303","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"On the Dirichlet problem for Hessian equations","venue":"Acta Mathematica","work_id":"8bf70ee1-fb63-4c70-9981-739b50ed5a20","year":1995},"citing_paper":{"arxiv_id":"2607.21024","last_updated":"2026-07-23T08:07:44Z","snapshot_observed_at":"2026-08-07T19:01:29.829642Z","submitted_at":"2026-07-23T08:07:44Z","title":"Liouville Rigidity for Real and Complex Degenerate Hessian Equations","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-01T08:55:18.827163Z"},"links":{"citing_paper":"/paper/2607.21024"},"observation_digest":"sha256:70ff834dc416a44305bd53ca78bb1f167dca9208ebd69bde9f61735133a1e3bf","observation_id":"19c075a0-1fef-4598-9466-b48582728fe0","resolution":{"observed_at":"2026-08-01T08:58:19.689829Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.12775/tmna","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T08:58:19.543487Z","title":"Hessian measures. I","venue":null,"work_id":"81c5efb7-a876-4bee-964c-397c4ef772f2","year":1997},"citing_paper":{"arxiv_id":"2607.21024","last_updated":"2026-07-23T08:07:44Z","snapshot_observed_at":"2026-08-07T19:01:29.829642Z","submitted_at":"2026-07-23T08:07:44Z","title":"Liouville Rigidity for Real and Complex Degenerate Hessian Equations","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-01T08:55:18.887445Z"},"links":{"citing_paper":"/paper/2607.21024"},"observation_digest":"sha256:68f087901b5dacd1d1b717c7834c690ac450bafef83b8c7505345f2073940f9f","observation_id":"ff7ba24a-eb22-4f6f-9a5c-4bdded2ab9f5","resolution":{"observed_at":"2026-08-01T08:58:19.630781Z","resolver_source":"doi_truncated","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T08:55:18.971865Z","title":"Hessian measures. II","venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2607.21024","last_updated":"2026-07-23T08:07:44Z","snapshot_observed_at":"2026-08-07T19:01:29.829642Z","submitted_at":"2026-07-23T08:07:44Z","title":"Liouville Rigidity for Real and Complex Degenerate Hessian Equations","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-01T08:55:18.971865Z"},"links":{"citing_paper":"/paper/2607.21024"},"observation_digest":"sha256:9a7c7674f25f9a3785ae0aeed21b93f44bc7aa62964ff2fbf6cd8bd61f3a8bc4","observation_id":"348f89fd-f0fa-490f-9755-98e93c8e2833","resolution":{"observed_at":"2026-08-01T08:55:18.971865Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T08:55:19.058915Z","title":"Hessian measures. III","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2607.21024","last_updated":"2026-07-23T08:07:44Z","snapshot_observed_at":"2026-08-07T19:01:29.829642Z","submitted_at":"2026-07-23T08:07:44Z","title":"Liouville Rigidity for Real and Complex Degenerate Hessian Equations","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-01T08:55:19.058915Z"},"links":{"citing_paper":"/paper/2607.21024"},"observation_digest":"sha256:2bbe1b0a8c5058296a2df8a38edab1b3809bf1e2e934658364ebd5da70ab1389","observation_id":"38e9e7c3-0bd4-4125-9815-b0caa96c4930","resolution":{"observed_at":"2026-08-01T08:55:19.058915Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T08:55:19.148559Z","title":"A class of fully nonlinear elliptic equations and related func- tionals","venue":null,"work_id":null,"year":1994},"citing_paper":{"arxiv_id":"2607.21024","last_updated":"2026-07-23T08:07:44Z","snapshot_observed_at":"2026-08-07T19:01:29.829642Z","submitted_at":"2026-07-23T08:07:44Z","title":"Liouville Rigidity for Real and Complex Degenerate Hessian Equations","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-01T08:55:19.148559Z"},"links":{"citing_paper":"/paper/2607.21024"},"observation_digest":"sha256:d60bcebd2c93d894a5d0844d41cc796178db5b1e305e967e72fefbd054ed5b94","observation_id":"ed4d3204-bc4f-4952-90f9-58b90736d9a5","resolution":{"observed_at":"2026-08-01T08:55:19.148559Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.2140/pjm.2017.291.485","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Hessian equations on closed Hermitian manifolds","venue":"Pacific Journal of Mathematics","work_id":"b321b601-5206-4a1d-a31c-fccb5e628342","year":2017},"citing_paper":{"arxiv_id":"2607.21024","last_updated":"2026-07-23T08:07:44Z","snapshot_observed_at":"2026-08-07T19:01:29.829642Z","submitted_at":"2026-07-23T08:07:44Z","title":"Liouville Rigidity for Real and Complex Degenerate Hessian Equations","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-01T08:55:19.212287Z"},"links":{"citing_paper":"/paper/2607.21024"},"observation_digest":"sha256:8cccd6d0eb2c1194401317621fe4d886f6035090be93e7f3b201dcb53ffd61e2","observation_id":"d62db74f-4c4a-476a-bc5d-be7e07d4060c","resolution":{"observed_at":"2026-08-01T08:58:19.506918Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2607.21024","last_updated":"2026-07-23T08:07:44Z","latest_version":1,"primary_category":"math.AP","snapshot_observed_at":"2026-08-07T19:01:29.829642Z","submitted_at":"2026-07-23T08:07:44Z","title":"Liouville Rigidity for Real and Complex Degenerate Hessian Equations"},"reference_resolution":{"displayed":47,"state_counts":{"malformed_identifier":8,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":22,"verified_exact":17,"verified_fuzzy":0},"total_outbound_references":47},"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":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"thesis":"As of 9 August 2026, this Paper Citation Record lists 47 of 47 outbound references and 0 inbound Pith citation observations for arXiv:2607.21024."}