{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:JQHQ3S5MHBU2GI5LT3ATG5DKHC","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"0e7c3c5152341ab23a131a101f4f6c379d6cae6c5a7714448ab4bddd1543d77a","cross_cats_sorted":["math.CV","math.DG"],"license":"","primary_cat":"math.AP","submitted_at":"2007-10-22T08:11:34Z","title_canon_sha256":"ec0b9d5cdbc7d827b03fb82784d41744609a3129715ecd259f00e96c58fd6b98"},"schema_version":"1.0","source":{"id":"0710.3991","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0710.3991","created_at":"2026-05-18T00:28:27Z"},{"alias_kind":"arxiv_version","alias_value":"0710.3991v1","created_at":"2026-05-18T00:28:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0710.3991","created_at":"2026-05-18T00:28:27Z"},{"alias_kind":"pith_short_12","alias_value":"JQHQ3S5MHBU2","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"JQHQ3S5MHBU2GI5L","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"JQHQ3S5M","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:402a9d33a60d1f2b5cf46f9d44bb30d7436c00e26642830b6c737f975bfff80a","target":"graph","created_at":"2026-05-18T00:28:27Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We study the Dirichlet problem for fully nonlinear, degenerate elliptic equations of the form f(Hess, u)=0 on a smoothly bounded domain D in R^n. In our approach the equation is replaced by a subset F of the space of symmetric nxn-matrices, with bdy(F) contined in the set {f=0}. We establish the existence and uniqueness of continuous solutions under an explicit geometric ``F-convexity'' assumption on the boundary bdy(F). The topological structure of F-convex domains is also studied and a theorem of Andreotti-Frankel type is proved for them. Two key ingredients in the analysis are the use of su","authors_text":"F. Reese Harvey, H. Blaine Lawson, jr","cross_cats":["math.CV","math.DG"],"headline":"","license":"","primary_cat":"math.AP","submitted_at":"2007-10-22T08:11:34Z","title":"Dirichlet Duality and the Nonlinear Dirichlet Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0710.3991","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:f38e8fdf69161261574e181c42d7585962a0b8e0d1e946ca2baa4c6ac946baf4","target":"record","created_at":"2026-05-18T00:28:27Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"0e7c3c5152341ab23a131a101f4f6c379d6cae6c5a7714448ab4bddd1543d77a","cross_cats_sorted":["math.CV","math.DG"],"license":"","primary_cat":"math.AP","submitted_at":"2007-10-22T08:11:34Z","title_canon_sha256":"ec0b9d5cdbc7d827b03fb82784d41744609a3129715ecd259f00e96c58fd6b98"},"schema_version":"1.0","source":{"id":"0710.3991","kind":"arxiv","version":1}},"canonical_sha256":"4c0f0dcbac3869a323ab9ec133746a38999f17c66c0cc80bc25378c6e4d81ee0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4c0f0dcbac3869a323ab9ec133746a38999f17c66c0cc80bc25378c6e4d81ee0","first_computed_at":"2026-05-18T00:28:27.911632Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:28:27.911632Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+DrIYEgUiNlus2p7/hwmV0ZEl+tB3+siXq4HBJuucnUYsMa2muQXa4/RbgkkWeOYR4DoVRM5l76MAmrqb57uBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:28:27.912242Z","signed_message":"canonical_sha256_bytes"},"source_id":"0710.3991","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f38e8fdf69161261574e181c42d7585962a0b8e0d1e946ca2baa4c6ac946baf4","sha256:402a9d33a60d1f2b5cf46f9d44bb30d7436c00e26642830b6c737f975bfff80a"],"state_sha256":"adfdc7ff98b5235cb1d69fefc5eb6d7fce42ef128b317101a56e782ec33a9bc2"}