{"as_of":"2026-08-18T22:57:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:aa38405efdc9b4705dd3e0d72f17dad3c6d99d0ed99e6ccbb47f1e79b9db4d2b","coverage":[{"denominator":33,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":33,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-15T16:42:26.612284Z","state":"measured"},{"denominator":33,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":33,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-18T06:34:40.430872+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/2509.03217/citation-record","integrity":"/paper/2509.03217/integrity","json":"/paper/2509.03217/citation-record.json","paper":"/paper/2509.03217"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T16:42:26.430485Z","title":"Caffarelli and Xavier Cabr\\'e, Fully nonlinear elliptic equations, American Mathematical Society Colloquium Publications, vol","venue":null,"work_id":null,"year":1995},"citing_paper":{"arxiv_id":"2509.03217","last_updated":"2025-09-03T11:12:24Z","snapshot_observed_at":"2026-08-15T16:30:51.318863Z","submitted_at":"2025-09-03T11:12:24Z","title":"Hessian Estimates for the Sigma-2 Equation with Variable Right-Hand Side Terms in Dimension 4","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-15T16:42:26.430485Z"},"links":{"citing_paper":"/paper/2509.03217"},"observation_digest":"sha256:a7f0549d423792bff8cb5e94254e231dcc84001660e4a9337733996ebaeb8d7d","observation_id":"35b604ab-ba94-44d1-b9b8-c82d9d7ffc0b","resolution":{"observed_at":"2026-08-15T16:42:26.430485Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T16:42:27.143152Z","title":"PDE 9 (2016), no","venue":null,"work_id":"ddbd3ffb-633f-468b-a71f-3124a0ae54b6","year":2016},"citing_paper":{"arxiv_id":"2509.03217","last_updated":"2025-09-03T11:12:24Z","snapshot_observed_at":"2026-08-15T16:30:51.318863Z","submitted_at":"2025-09-03T11:12:24Z","title":"Hessian Estimates for the Sigma-2 Equation with Variable Right-Hand Side Terms in Dimension 4","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-15T16:42:26.436586Z"},"links":{"citing_paper":"/paper/2509.03217"},"observation_digest":"sha256:b698c40aee6523c765f760b59936e830a8fd4678b104f2841c37518a94b3fe7d","observation_id":"2068fb46-cdcc-40f6-b29a-357186b4a010","resolution":{"observed_at":"2026-08-15T16:42:27.148987Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2408.14850","last_updated":"2024-08-29T01:14:08Z","snapshot_observed_at":"2026-08-16T13:23:35.667293Z","submitted_at":"2024-08-27T08:05:07Z","title":"An Integral Approach to Prescribing Scalar Curvature Equations","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2408.14850","snapshot_observed_at":"2026-08-15T16:42:26.441995Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2509.03217","last_updated":"2025-09-03T11:12:24Z","snapshot_observed_at":"2026-08-15T16:30:51.318863Z","submitted_at":"2025-09-03T11:12:24Z","title":"Hessian Estimates for the Sigma-2 Equation with Variable Right-Hand Side Terms in Dimension 4","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-15T16:42:26.441995Z"},"links":{"cited_paper":"/paper/2408.14850","citing_paper":"/paper/2509.03217"},"observation_digest":"sha256:232a8a24d06a65222f1db815a33cfdfdd84e93314cb55ab6aa2c02ffc3131bbe","observation_id":"7fc28e45-6a43-4306-902d-9764d51c057c","resolution":{"observed_at":"2026-08-15T16:42:26.441995Z","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":"2026-08-15T16:42:26.447235Z","title":"Caffarelli, L","venue":null,"work_id":null,"year":1985},"citing_paper":{"arxiv_id":"2509.03217","last_updated":"2025-09-03T11:12:24Z","snapshot_observed_at":"2026-08-15T16:30:51.318863Z","submitted_at":"2025-09-03T11:12:24Z","title":"Hessian Estimates for the Sigma-2 Equation with Variable Right-Hand Side Terms in Dimension 4","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-15T16:42:26.447235Z"},"links":{"citing_paper":"/paper/2509.03217"},"observation_digest":"sha256:f97436f947c1037c0416232bb088a7623731f925303e4424989e8e75b475465d","observation_id":"f7bf72d3-8a8c-462a-8556-5b11c86062f7","resolution":{"observed_at":"2026-08-15T16:42:26.447235Z","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":"2026-08-15T16:42:26.455541Z","title":"Trudinger, An A lexsandrov type theorem for k -convex functions , Bull","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2509.03217","last_updated":"2025-09-03T11:12:24Z","snapshot_observed_at":"2026-08-15T16:30:51.318863Z","submitted_at":"2025-09-03T11:12:24Z","title":"Hessian Estimates for the Sigma-2 Equation with Variable Right-Hand Side Terms in Dimension 4","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-15T16:42:26.455541Z"},"links":{"citing_paper":"/paper/2509.03217"},"observation_digest":"sha256:6ff0d5617d3d6dc579b20c08e154bdadbc7cc2cbfd4bc03acc2db9dd333a3a01","observation_id":"1982cdd7-306b-4953-ad97-3a233fd7f2c4","resolution":{"observed_at":"2026-08-15T16:42:26.455541Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T16:42:27.106883Z","title":"Pure Appl","venue":null,"work_id":"15a09825-05a2-4935-a59e-e959c164b4f3","year":2001},"citing_paper":{"arxiv_id":"2509.03217","last_updated":"2025-09-03T11:12:24Z","snapshot_observed_at":"2026-08-15T16:30:51.318863Z","submitted_at":"2025-09-03T11:12:24Z","title":"Hessian Estimates for the Sigma-2 Equation with Variable Right-Hand Side Terms in Dimension 4","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-15T16:42:26.462580Z"},"links":{"citing_paper":"/paper/2509.03217"},"observation_digest":"sha256:f9f6b671bfd15cf54329370538486705ece943b9a572a460bcc73059a035be52","observation_id":"c25fd6a0-f421-402f-bf96-529215a0f8c5","resolution":{"observed_at":"2026-08-15T16:42:27.112073Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T16:42:26.468515Z","title":"Evans and Ronald F","venue":null,"work_id":null,"year":1992},"citing_paper":{"arxiv_id":"2509.03217","last_updated":"2025-09-03T11:12:24Z","snapshot_observed_at":"2026-08-15T16:30:51.318863Z","submitted_at":"2025-09-03T11:12:24Z","title":"Hessian Estimates for the Sigma-2 Equation with Variable Right-Hand Side Terms in Dimension 4","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-15T16:42:26.468515Z"},"links":{"citing_paper":"/paper/2509.03217"},"observation_digest":"sha256:931bed03a4b45e73bef536666b1455b3f3f90e3b021ecf0e61f7928aceb8c3ac","observation_id":"05e86f53-089c-4f7a-a550-3d4b72a7dab8","resolution":{"observed_at":"2026-08-15T16:42:26.468515Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2509.01138","last_updated":"2025-09-01T05:14:56Z","snapshot_observed_at":"2026-08-05T13:08:30.801255Z","submitted_at":"2025-09-01T05:14:56Z","title":"A generalization of Savin's small perturbation theorem for fully nonlinear elliptic equations and applications","version":1},"cited_work":{"arxiv_id":"2509.01138","doi":null,"metadata_source":"pith","pith_arxiv_id":"2509.01138","snapshot_observed_at":"2026-08-15T16:42:26.674183Z","title":"A generalization of Savin's small perturbation theorem for fully nonlinear elliptic equations and applications","venue":"math.AP","work_id":"2243aace-ad31-4404-9b36-793f8ae5c768","year":2025},"citing_paper":{"arxiv_id":"2509.03217","last_updated":"2025-09-03T11:12:24Z","snapshot_observed_at":"2026-08-15T16:30:51.318863Z","submitted_at":"2025-09-03T11:12:24Z","title":"Hessian Estimates for the Sigma-2 Equation with Variable Right-Hand Side Terms in Dimension 4","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-15T16:42:26.475454Z"},"links":{"cited_paper":"/paper/2509.01138","citing_paper":"/paper/2509.03217"},"observation_digest":"sha256:013df2a3a1e994f416b13bb7cf168fd669a3fadc7a44f2f2b9fa7bd385067473","observation_id":"8b5c4c38-b835-4cc1-848c-acb643a44f52","resolution":{"observed_at":"2026-08-15T16:42:26.681409Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T16:42:27.082160Z","title":null,"venue":null,"work_id":"979bca77-d088-417e-bb3a-efa721216e11","year":2019},"citing_paper":{"arxiv_id":"2509.03217","last_updated":"2025-09-03T11:12:24Z","snapshot_observed_at":"2026-08-15T16:30:51.318863Z","submitted_at":"2025-09-03T11:12:24Z","title":"Hessian Estimates for the Sigma-2 Equation with Variable Right-Hand Side Terms in Dimension 4","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-15T16:42:26.481697Z"},"links":{"citing_paper":"/paper/2509.03217"},"observation_digest":"sha256:4c71e801f20439be33ecf256d751f9bde1848dd9fb415f1ddf9f8a0e3d3a6397","observation_id":"2ea23a9b-2fc8-4a13-980e-14ef1b226bc3","resolution":{"observed_at":"2026-08-15T16:42:27.086719Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T16:42:26.487461Z","title":"Trudinger, Elliptic partial differential equations of second order, Classics in Mathematics, Springer-Verlag, Berlin, 2001, Reprint of the 1998 edition","venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2509.03217","last_updated":"2025-09-03T11:12:24Z","snapshot_observed_at":"2026-08-15T16:30:51.318863Z","submitted_at":"2025-09-03T11:12:24Z","title":"Hessian Estimates for the Sigma-2 Equation with Variable Right-Hand Side Terms in Dimension 4","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-15T16:42:26.487461Z"},"links":{"citing_paper":"/paper/2509.03217"},"observation_digest":"sha256:f90ae2c5e3be18ebf563752feb60f2ba6c44cd932240098dfc2df3dc1a575504","observation_id":"ec05a46a-fe56-4dcf-a04e-d0936f535b09","resolution":{"observed_at":"2026-08-15T16:42:26.487461Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T16:42:27.056063Z","title":"Analyse Math","venue":null,"work_id":"c43628b2-a9b3-41e8-bcd3-870435b312de","year":1959},"citing_paper":{"arxiv_id":"2509.03217","last_updated":"2025-09-03T11:12:24Z","snapshot_observed_at":"2026-08-15T16:30:51.318863Z","submitted_at":"2025-09-03T11:12:24Z","title":"Hessian Estimates for the Sigma-2 Equation with Variable Right-Hand Side Terms in Dimension 4","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-15T16:42:26.494806Z"},"links":{"citing_paper":"/paper/2509.03217"},"observation_digest":"sha256:380a6d4e6278f74bb1a746d250ea6c75c10ac1a83163e51e636ab663aba64316","observation_id":"99487958-eb8c-4767-a930-94d943106559","resolution":{"observed_at":"2026-08-15T16:42:27.060639Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T16:42:27.039243Z","title":"Blaine Lawson, Jr., Calibrated geometries, Acta Math","venue":null,"work_id":"1ef19a82-8d92-4d06-8711-cad235e93de7","year":1982},"citing_paper":{"arxiv_id":"2509.03217","last_updated":"2025-09-03T11:12:24Z","snapshot_observed_at":"2026-08-15T16:30:51.318863Z","submitted_at":"2025-09-03T11:12:24Z","title":"Hessian Estimates for the Sigma-2 Equation with Variable Right-Hand Side Terms in Dimension 4","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-15T16:42:26.501038Z"},"links":{"citing_paper":"/paper/2509.03217"},"observation_digest":"sha256:a78dabcabd617756c68c5e44d7988e7979d621c9e1ffff038cecc08b4c2cdfc1","observation_id":"becf415c-dcc4-437f-8e02-12a9a131a349","resolution":{"observed_at":"2026-08-15T16:42:27.045180Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T16:42:27.019974Z","title":"1, Courant Institute of Mathematical Sciences, New York; American Mathematical Society, Providence, RI, 2011","venue":null,"work_id":"6aa2d68d-585f-484e-aa36-8dd3c583213e","year":2011},"citing_paper":{"arxiv_id":"2509.03217","last_updated":"2025-09-03T11:12:24Z","snapshot_observed_at":"2026-08-15T16:30:51.318863Z","submitted_at":"2025-09-03T11:12:24Z","title":"Hessian Estimates for the Sigma-2 Equation with Variable Right-Hand Side Terms in Dimension 4","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-15T16:42:26.506075Z"},"links":{"citing_paper":"/paper/2509.03217"},"observation_digest":"sha256:96bf846c1a82546d95582dd3c223334276dedfcffeec354097c3984c99de88e6","observation_id":"05bb76af-809f-4174-beec-bdd879ea163c","resolution":{"observed_at":"2026-08-15T16:42:27.026094Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T16:42:27.003664Z","title":"Labutin, Potential estimates for a class of fully nonlinear elliptic equations, Duke Math","venue":null,"work_id":"4f92da90-72d0-4738-bbd5-585f69be02bb","year":2002},"citing_paper":{"arxiv_id":"2509.03217","last_updated":"2025-09-03T11:12:24Z","snapshot_observed_at":"2026-08-15T16:30:51.318863Z","submitted_at":"2025-09-03T11:12:24Z","title":"Hessian Estimates for the Sigma-2 Equation with Variable Right-Hand Side Terms in Dimension 4","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-15T16:42:26.511182Z"},"links":{"citing_paper":"/paper/2509.03217"},"observation_digest":"sha256:87dc7021bf98f69874bae3bbcda1b1a21764f939f57ae5b88fa45d5e7ddd3c0d","observation_id":"c9fe0e9d-fdc9-427e-8e1b-b29f534d2a77","resolution":{"observed_at":"2026-08-15T16:42:27.008360Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T16:42:26.987948Z","title":null,"venue":null,"work_id":"c1361bc5-30db-4ecc-b909-c5febb4084a3","year":2021},"citing_paper":{"arxiv_id":"2509.03217","last_updated":"2025-09-03T11:12:24Z","snapshot_observed_at":"2026-08-15T16:30:51.318863Z","submitted_at":"2025-09-03T11:12:24Z","title":"Hessian Estimates for the Sigma-2 Equation with Variable Right-Hand Side Terms in Dimension 4","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-15T16:42:26.516175Z"},"links":{"citing_paper":"/paper/2509.03217"},"observation_digest":"sha256:51e230a2475e6485fa6751872f2fbad6f412b6b09d6fe35d9a7ac84147108cb3","observation_id":"8d3a1682-c747-4c5b-9c46-d7aaccedc298","resolution":{"observed_at":"2026-08-15T16:42:26.993068Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T16:42:26.971524Z","title":"Trudinger, On some inequalities for elementary symmetric functions, Bull","venue":null,"work_id":"f0f7e5b0-cc9a-4c70-a686-5031a67f50fb","year":1994},"citing_paper":{"arxiv_id":"2509.03217","last_updated":"2025-09-03T11:12:24Z","snapshot_observed_at":"2026-08-15T16:30:51.318863Z","submitted_at":"2025-09-03T11:12:24Z","title":"Hessian Estimates for the Sigma-2 Equation with Variable Right-Hand Side Terms in Dimension 4","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-15T16:42:26.521186Z"},"links":{"citing_paper":"/paper/2509.03217"},"observation_digest":"sha256:005360969e714637ac243984e4b93392767a10ec0e2e2ad549427d55e9126fbd","observation_id":"10cc223d-da87-4a75-bdae-64fa653ee9ea","resolution":{"observed_at":"2026-08-15T16:42:26.977044Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2405.07199","last_updated":"2024-05-12T07:55:26Z","snapshot_observed_at":"2026-08-16T13:53:26.703061Z","submitted_at":"2024-05-12T07:55:26Z","title":"Pointwise regularity for locally uniformly elliptic equations and applications","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2405.07199","snapshot_observed_at":"2026-08-15T16:42:26.526103Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2509.03217","last_updated":"2025-09-03T11:12:24Z","snapshot_observed_at":"2026-08-15T16:30:51.318863Z","submitted_at":"2025-09-03T11:12:24Z","title":"Hessian Estimates for the Sigma-2 Equation with Variable Right-Hand Side Terms in Dimension 4","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-15T16:42:26.526103Z"},"links":{"cited_paper":"/paper/2405.07199","citing_paper":"/paper/2509.03217"},"observation_digest":"sha256:d0a4aabd846171b3681722a228335a8ade839ded62d7c94bc283e745bdcb69b8","observation_id":"4e4d8674-4e39-4ce9-b277-6e63e1b76f50","resolution":{"observed_at":"2026-08-15T16:42:26.526103Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T16:42:26.956033Z","title":null,"venue":null,"work_id":"edee3362-86bb-44b9-a489-62e9e40689ca","year":2019},"citing_paper":{"arxiv_id":"2509.03217","last_updated":"2025-09-03T11:12:24Z","snapshot_observed_at":"2026-08-15T16:30:51.318863Z","submitted_at":"2025-09-03T11:12:24Z","title":"Hessian Estimates for the Sigma-2 Equation with Variable Right-Hand Side Terms in Dimension 4","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-15T16:42:26.531637Z"},"links":{"citing_paper":"/paper/2509.03217"},"observation_digest":"sha256:887bdb3c9453b803eea891cd90a75da3e1136abb2ea97199c5cc41e7c8cfda00","observation_id":"c7ba01d0-4f04-4949-aab5-374279586462","resolution":{"observed_at":"2026-08-15T16:42:26.960874Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T16:42:26.939651Z","title":null,"venue":null,"work_id":"b832ee77-d330-4e68-864d-fbdef9454173","year":1971},"citing_paper":{"arxiv_id":"2509.03217","last_updated":"2025-09-03T11:12:24Z","snapshot_observed_at":"2026-08-15T16:30:51.318863Z","submitted_at":"2025-09-03T11:12:24Z","title":"Hessian Estimates for the Sigma-2 Equation with Variable Right-Hand Side Terms in Dimension 4","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-15T16:42:26.536630Z"},"links":{"citing_paper":"/paper/2509.03217"},"observation_digest":"sha256:71756ae1db165866af3b4bb1486c2d67f0f2f673e5fdc9a28b758ada088cb724","observation_id":"04f6a306-40f4-4130-929c-e7c12a63ffd2","resolution":{"observed_at":"2026-08-15T16:42:26.944249Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T16:42:26.921329Z","title":null,"venue":null,"work_id":"44a019d1-d745-4bf1-9a5c-dbc40ba26645","year":1978},"citing_paper":{"arxiv_id":"2509.03217","last_updated":"2025-09-03T11:12:24Z","snapshot_observed_at":"2026-08-15T16:30:51.318863Z","submitted_at":"2025-09-03T11:12:24Z","title":"Hessian Estimates for the Sigma-2 Equation with Variable Right-Hand Side Terms in Dimension 4","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-15T16:42:26.542737Z"},"links":{"citing_paper":"/paper/2509.03217"},"observation_digest":"sha256:d8f5e7f1a11924662785626e9545da4c3855091bff80501076a7d7ef0a9c0fce","observation_id":"461547f3-5df7-48d2-ad0a-ada8d1ebe09e","resolution":{"observed_at":"2026-08-15T16:42:26.927356Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T16:42:26.905035Z","title":null,"venue":null,"work_id":"364418a4-476a-4fe9-8f8d-9136e4f4272d","year":2024},"citing_paper":{"arxiv_id":"2509.03217","last_updated":"2025-09-03T11:12:24Z","snapshot_observed_at":"2026-08-15T16:30:51.318863Z","submitted_at":"2025-09-03T11:12:24Z","title":"Hessian Estimates for the Sigma-2 Equation with Variable Right-Hand Side Terms in Dimension 4","version":1},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-15T16:42:26.548584Z"},"links":{"citing_paper":"/paper/2509.03217"},"observation_digest":"sha256:c564adca733e096a2be51eb492ca2163732aa14220090144cf6b8012ca2847ad","observation_id":"e0663db7-683c-4123-91a1-2ac882c5d415","resolution":{"observed_at":"2026-08-15T16:42:26.910270Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T16:42:26.889685Z","title":"Partial Differential Equations 32 (2007), no","venue":null,"work_id":"8692567e-eb99-4cca-b668-d31c8dc3c9e4","year":2007},"citing_paper":{"arxiv_id":"2509.03217","last_updated":"2025-09-03T11:12:24Z","snapshot_observed_at":"2026-08-15T16:30:51.318863Z","submitted_at":"2025-09-03T11:12:24Z","title":"Hessian Estimates for the Sigma-2 Equation with Variable Right-Hand Side Terms in Dimension 4","version":1},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-15T16:42:26.554162Z"},"links":{"citing_paper":"/paper/2509.03217"},"observation_digest":"sha256:6c96c150c18fb51298d4518f27b0e534137da71d1d0fab452a24c53205ba9a61","observation_id":"b2089a52-c8f1-43c3-bbd1-0ef1babaae37","resolution":{"observed_at":"2026-08-15T16:42:26.894900Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T16:42:26.872162Z","title":null,"venue":null,"work_id":"5ceef10f-a97f-4189-9909-c87d75573002","year":2020},"citing_paper":{"arxiv_id":"2509.03217","last_updated":"2025-09-03T11:12:24Z","snapshot_observed_at":"2026-08-15T16:30:51.318863Z","submitted_at":"2025-09-03T11:12:24Z","title":"Hessian Estimates for the Sigma-2 Equation with Variable Right-Hand Side Terms in Dimension 4","version":1},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-15T16:42:26.560520Z"},"links":{"citing_paper":"/paper/2509.03217"},"observation_digest":"sha256:2e1db57fdd3439ea7b28bf5181b38a90fb42fb4996b578c737e86527953c1056","observation_id":"0cbe6bb5-a362-4d16-9f30-9e6209c86a06","resolution":{"observed_at":"2026-08-15T16:42:26.877387Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T16:42:26.856171Z","title":null,"venue":null,"work_id":"29b080e7-79ff-4343-a222-ba8c5814531e","year":2022},"citing_paper":{"arxiv_id":"2509.03217","last_updated":"2025-09-03T11:12:24Z","snapshot_observed_at":"2026-08-15T16:30:51.318863Z","submitted_at":"2025-09-03T11:12:24Z","title":"Hessian Estimates for the Sigma-2 Equation with Variable Right-Hand Side Terms in Dimension 4","version":1},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-08-15T16:42:26.565926Z"},"links":{"citing_paper":"/paper/2509.03217"},"observation_digest":"sha256:d56ca0363146af5395383e9d5f3910d802483d0a4a74ffba9d4f6687872bd5f4","observation_id":"0ec3c7a3-c438-4948-8914-387da731263b","resolution":{"observed_at":"2026-08-15T16:42:26.861246Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T16:42:26.839298Z","title":null,"venue":null,"work_id":"f21c3630-8e98-465e-adac-38ca23f22c5d","year":2025},"citing_paper":{"arxiv_id":"2509.03217","last_updated":"2025-09-03T11:12:24Z","snapshot_observed_at":"2026-08-15T16:30:51.318863Z","submitted_at":"2025-09-03T11:12:24Z","title":"Hessian Estimates for the Sigma-2 Equation with Variable Right-Hand Side Terms in Dimension 4","version":1},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-08-15T16:42:26.571321Z"},"links":{"citing_paper":"/paper/2509.03217"},"observation_digest":"sha256:948b27f1b7347a43e2a44b468759257b00a933edeef0c35bea4398b74b0f97a7","observation_id":"52b2bca5-f0cd-4f19-978b-a0478988fc41","resolution":{"observed_at":"2026-08-15T16:42:26.844553Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T16:42:26.576616Z","title":"Trudinger, Weak solutions of H essian equations , Comm","venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"2509.03217","last_updated":"2025-09-03T11:12:24Z","snapshot_observed_at":"2026-08-15T16:30:51.318863Z","submitted_at":"2025-09-03T11:12:24Z","title":"Hessian Estimates for the Sigma-2 Equation with Variable Right-Hand Side Terms in Dimension 4","version":1},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-08-15T16:42:26.576616Z"},"links":{"citing_paper":"/paper/2509.03217"},"observation_digest":"sha256:35c378a8bde3e34aefcac06ae7b825bd3e9cd88e2b1c8b56061ab986961ce35d","observation_id":"0c737aaa-cff6-4182-97cb-633ebac6401d","resolution":{"observed_at":"2026-08-15T16:42:26.576616Z","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":"2026-08-15T16:42:26.582513Z","title":"Trudinger and Xu-Jia Wang, Hessian measures","venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2509.03217","last_updated":"2025-09-03T11:12:24Z","snapshot_observed_at":"2026-08-15T16:30:51.318863Z","submitted_at":"2025-09-03T11:12:24Z","title":"Hessian Estimates for the Sigma-2 Equation with Variable Right-Hand Side Terms in Dimension 4","version":1},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-08-15T16:42:26.582513Z"},"links":{"citing_paper":"/paper/2509.03217"},"observation_digest":"sha256:794440ce4847128ce63c1e74836f05c37d7c9d7b93798cc786f3a14a94a90dcf","observation_id":"48b3638c-dead-45ae-b137-67fe050e35c0","resolution":{"observed_at":"2026-08-15T16:42:26.582513Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T16:42:26.799123Z","title":null,"venue":null,"work_id":"b06f6b9c-996d-4418-a39a-2ea6fb4da5b6","year":1990},"citing_paper":{"arxiv_id":"2509.03217","last_updated":"2025-09-03T11:12:24Z","snapshot_observed_at":"2026-08-15T16:30:51.318863Z","submitted_at":"2025-09-03T11:12:24Z","title":"Hessian Estimates for the Sigma-2 Equation with Variable Right-Hand Side Terms in Dimension 4","version":1},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-08-15T16:42:26.587856Z"},"links":{"citing_paper":"/paper/2509.03217"},"observation_digest":"sha256:836135428bce458e05c8fefa37f322b9ec7d31b6a8b068b5a66c8ebe5a116132","observation_id":"db23c6a1-87d4-423b-9efd-35611707351c","resolution":{"observed_at":"2026-08-15T16:42:26.805338Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T16:42:26.780659Z","title":"1977, Springer, Dordrecht, 2009, pp","venue":null,"work_id":"cc9edca7-fdd9-40b6-8043-7f4e1ac6805d","year":1977},"citing_paper":{"arxiv_id":"2509.03217","last_updated":"2025-09-03T11:12:24Z","snapshot_observed_at":"2026-08-15T16:30:51.318863Z","submitted_at":"2025-09-03T11:12:24Z","title":"Hessian Estimates for the Sigma-2 Equation with Variable Right-Hand Side Terms in Dimension 4","version":1},"reference_index":29,"source":"arxiv_source","source_observed_at":"2026-08-15T16:42:26.592437Z"},"links":{"citing_paper":"/paper/2509.03217"},"observation_digest":"sha256:692e031fb4ba82555930158e5fc79a6f378d27dd2acc653a5e7914b0b1c75a11","observation_id":"24e80534-5343-4130-ba08-94364e753ada","resolution":{"observed_at":"2026-08-15T16:42:26.786578Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T16:42:26.762434Z","title":"Pure Appl","venue":null,"work_id":"0ed79ad3-19b0-47c7-bcfd-4c500c49a6c9","year":2009},"citing_paper":{"arxiv_id":"2509.03217","last_updated":"2025-09-03T11:12:24Z","snapshot_observed_at":"2026-08-15T16:30:51.318863Z","submitted_at":"2025-09-03T11:12:24Z","title":"Hessian Estimates for the Sigma-2 Equation with Variable Right-Hand Side Terms in Dimension 4","version":1},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-08-15T16:42:26.597095Z"},"links":{"citing_paper":"/paper/2509.03217"},"observation_digest":"sha256:d3535e8073f718f89f131be3f73521fbf1e45a7a920fd1e57653c8c4ec4fa65e","observation_id":"0d017b5d-fa56-482a-91b4-925893be27fe","resolution":{"observed_at":"2026-08-15T16:42:26.767908Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T16:42:26.745612Z","title":null,"venue":null,"work_id":"1a053b3a-1d67-4cf3-87f7-0e91aaecd79a","year":2020},"citing_paper":{"arxiv_id":"2509.03217","last_updated":"2025-09-03T11:12:24Z","snapshot_observed_at":"2026-08-15T16:30:51.318863Z","submitted_at":"2025-09-03T11:12:24Z","title":"Hessian Estimates for the Sigma-2 Equation with Variable Right-Hand Side Terms in Dimension 4","version":1},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-08-15T16:42:26.601831Z"},"links":{"citing_paper":"/paper/2509.03217"},"observation_digest":"sha256:b4abef4a012689ad1fcb5eac4abd85949e3aa59bcbc88bcecbd4f0deaba90cbd","observation_id":"fd21ec9b-103b-45ba-92cf-ebd4db8cc6a0","resolution":{"observed_at":"2026-08-15T16:42:26.751054Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T16:42:26.728432Z","title":null,"venue":null,"work_id":"6e4be451-f48d-43b0-bea2-328d1105ca9e","year":2024},"citing_paper":{"arxiv_id":"2509.03217","last_updated":"2025-09-03T11:12:24Z","snapshot_observed_at":"2026-08-15T16:30:51.318863Z","submitted_at":"2025-09-03T11:12:24Z","title":"Hessian Estimates for the Sigma-2 Equation with Variable Right-Hand Side Terms in Dimension 4","version":1},"reference_index":32,"source":"arxiv_source","source_observed_at":"2026-08-15T16:42:26.606857Z"},"links":{"citing_paper":"/paper/2509.03217"},"observation_digest":"sha256:2f02c0118add707fcea918640630ca726399ea5c4fff649d2e4097c66392c722","observation_id":"995e9be0-ec06-45d0-b56a-0407eb0f7525","resolution":{"observed_at":"2026-08-15T16:42:26.733509Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-15T16:42:26.711404Z","title":null,"venue":null,"work_id":"637d160a-416b-4190-98e5-d8b4945410d5","year":2024},"citing_paper":{"arxiv_id":"2509.03217","last_updated":"2025-09-03T11:12:24Z","snapshot_observed_at":"2026-08-15T16:30:51.318863Z","submitted_at":"2025-09-03T11:12:24Z","title":"Hessian Estimates for the Sigma-2 Equation with Variable Right-Hand Side Terms in Dimension 4","version":1},"reference_index":33,"source":"arxiv_source","source_observed_at":"2026-08-15T16:42:26.612284Z"},"links":{"citing_paper":"/paper/2509.03217"},"observation_digest":"sha256:91b0488d4341500ae2130aefd8fbe06139fab66e4e9e987ad537616741db85eb","observation_id":"cc53c8a4-5e6e-439f-95d3-c7c1be7854b3","resolution":{"observed_at":"2026-08-15T16:42:26.717179Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2509.03217","last_updated":"2025-09-03T11:12:24Z","latest_version":1,"primary_category":"math.AP","snapshot_observed_at":"2026-08-15T16:30:51.318863Z","submitted_at":"2025-09-03T11:12:24Z","title":"Hessian Estimates for the Sigma-2 Equation with Variable Right-Hand Side Terms in Dimension 4"},"reference_resolution":{"displayed":33,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":22,"verified_exact":1,"verified_fuzzy":10},"total_outbound_references":33},"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":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"thesis":"As of 18 August 2026, this Paper Citation Record lists 33 of 33 outbound references and 0 inbound Pith citation observations for arXiv:2509.03217."}