{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:RGK4BH3SPZQHWQDXQRYRH3WXS4","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":"d8e86e2250a536343a3271dbb705c5b30cda6c92624badb209123ad40a56dae5","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-06-18T22:08:27Z","title_canon_sha256":"0ae7ed4ee286efbf304a9beee0992f3c5cc0bd4b62864453805c3054ee211360"},"schema_version":"1.0","source":{"id":"1206.4089","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.4089","created_at":"2026-05-18T03:15:32Z"},{"alias_kind":"arxiv_version","alias_value":"1206.4089v3","created_at":"2026-05-18T03:15:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.4089","created_at":"2026-05-18T03:15:32Z"},{"alias_kind":"pith_short_12","alias_value":"RGK4BH3SPZQH","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"RGK4BH3SPZQHWQDX","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"RGK4BH3S","created_at":"2026-05-18T12:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:a32126a45466168c9eec3b3b801135b4376f8295bab40de6028d15f5ecfbb1e8","target":"graph","created_at":"2026-05-18T03:15:32Z","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 establish new, optimal gradient continuity estimates for solutions to a class of 2nd order partial differential equations, $\\mathscr{L}(X, \\nabla u, D^2 u) = f$, whose diffusion properties (ellipticity) degenerate along the \\textit{a priori} unknown singular set of an existing solution, $\\mathscr{S}(u) := \\{X : \\nabla u(X) = 0 \\}$. The innovative feature of our main result concerns its optimality -- the sharp, encoded smoothness aftereffects of the operator. Such a quantitative information usually plays a decisive role in the analysis of a number of analytic and geometric problems. Our resu","authors_text":"Dami\\~ao J. Ara\\'ujo, Eduardo V. Teixeira, Gleydson C. Ricarte","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-06-18T22:08:27Z","title":"Optimal gradient continuity for degenerate elliptic equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.4089","kind":"arxiv","version":3},"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":"sha256:5200b9dbeff4ca408ae3051a1cd19d88004393998be3d59cc9ec118f6abe17f7","target":"record","created_at":"2026-05-18T03:15:32Z","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":"d8e86e2250a536343a3271dbb705c5b30cda6c92624badb209123ad40a56dae5","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-06-18T22:08:27Z","title_canon_sha256":"0ae7ed4ee286efbf304a9beee0992f3c5cc0bd4b62864453805c3054ee211360"},"schema_version":"1.0","source":{"id":"1206.4089","kind":"arxiv","version":3}},"canonical_sha256":"8995c09f727e607b4077847113eed79728960d547f52a96ea0f3c6542f08093e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8995c09f727e607b4077847113eed79728960d547f52a96ea0f3c6542f08093e","first_computed_at":"2026-05-18T03:15:32.695560Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:15:32.695560Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"H/Ju4l5LiKU+QoqAYS3EUEmsrkeEMZKzem6ezWVRVE8TOz/J0g/a8/cV4XILNacQkMxIJ7Pwx7MdOOHX15KiCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:15:32.696283Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.4089","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5200b9dbeff4ca408ae3051a1cd19d88004393998be3d59cc9ec118f6abe17f7","sha256:a32126a45466168c9eec3b3b801135b4376f8295bab40de6028d15f5ecfbb1e8"],"state_sha256":"04f6d1d075a1405791675a2b3bac5524705573b79d41854eb61dde8853ed2a60"}