{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:UEVCOJRKIVTXOZCCYANMHVDQHE","short_pith_number":"pith:UEVCOJRK","canonical_record":{"source":{"id":"1103.3677","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-03-18T17:56:02Z","cross_cats_sorted":[],"title_canon_sha256":"70e7cdddb2e8baaae293cc267eef8fad666bb858fa6b54466659f587412f43ee","abstract_canon_sha256":"9055996e6cb1bdb9313006222c6d4a0acf4d535b4698fb6cb2d35b4c84906711"},"schema_version":"1.0"},"canonical_sha256":"a12a27262a4567776442c01ac3d470392dee9fa6037b402bd966bb6f13eb063b","source":{"kind":"arxiv","id":"1103.3677","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.3677","created_at":"2026-05-18T04:26:32Z"},{"alias_kind":"arxiv_version","alias_value":"1103.3677v1","created_at":"2026-05-18T04:26:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.3677","created_at":"2026-05-18T04:26:32Z"},{"alias_kind":"pith_short_12","alias_value":"UEVCOJRKIVTX","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"UEVCOJRKIVTXOZCC","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"UEVCOJRK","created_at":"2026-05-18T12:26:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:UEVCOJRKIVTXOZCCYANMHVDQHE","target":"record","payload":{"canonical_record":{"source":{"id":"1103.3677","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-03-18T17:56:02Z","cross_cats_sorted":[],"title_canon_sha256":"70e7cdddb2e8baaae293cc267eef8fad666bb858fa6b54466659f587412f43ee","abstract_canon_sha256":"9055996e6cb1bdb9313006222c6d4a0acf4d535b4698fb6cb2d35b4c84906711"},"schema_version":"1.0"},"canonical_sha256":"a12a27262a4567776442c01ac3d470392dee9fa6037b402bd966bb6f13eb063b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:26:32.201858Z","signature_b64":"ic40jYRRXeOihkvfJaRdyKjnX+2pB6SiRXdXdZxn3hirL+4y1YG0FuBrF92va0TN0N5DeTiH2AFzHm9Ce12UCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a12a27262a4567776442c01ac3d470392dee9fa6037b402bd966bb6f13eb063b","last_reissued_at":"2026-05-18T04:26:32.201360Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:26:32.201360Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1103.3677","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:26:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AM1UUn/K7p2pVzsFWMmYio987vgUHBG6LbwjT2c9NL2CyVLeWV0H/h9fjAXPITyF4k1CKICNxhoR6W+QlkgBCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T03:51:34.518249Z"},"content_sha256":"df0bd9eaeadc33a603dfa4695733bce2e51bdce28e442730ac9dab59bc9be3a1","schema_version":"1.0","event_id":"sha256:df0bd9eaeadc33a603dfa4695733bce2e51bdce28e442730ac9dab59bc9be3a1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:UEVCOJRKIVTXOZCCYANMHVDQHE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Partial regularity of solutions of fully nonlinear uniformly elliptic equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Charles K. Smart, Luis Silvestre, Scott N. Armstrong","submitted_at":"2011-03-18T17:56:02Z","abstract_excerpt":"We prove that a viscosity solution of a uniformly elliptic, fully nonlinear equation is $C^{2,\\alpha}$ on the compliment of a closed set of Hausdorff dimension at most $\\epsilon$ less than the dimension. The equation is assumed to be $C^1$, and the constant $\\epsilon > 0$ depends only on the dimension and the ellipticity constants. The argument combines the $W^{2,\\epsilon}$ estimates of Lin with a result of Savin on the $C^{2,\\alpha}$ regularity of viscosity solutions which are close to quadratic polynomials."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.3677","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:26:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7PJI0f47wrRutNAbZmd3vGiS2GnfsR2LSi0OfYCh2nBPY2WVdxa9JlHPU1ZNUzlUJdZvSbq9uFwGh5i2hOhhCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T03:51:34.518975Z"},"content_sha256":"585f4c7448adc51f64ef0d5a9ef2afb66330a4eaaaee609ffd3c4a989c90fe46","schema_version":"1.0","event_id":"sha256:585f4c7448adc51f64ef0d5a9ef2afb66330a4eaaaee609ffd3c4a989c90fe46"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UEVCOJRKIVTXOZCCYANMHVDQHE/bundle.json","state_url":"https://pith.science/pith/UEVCOJRKIVTXOZCCYANMHVDQHE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UEVCOJRKIVTXOZCCYANMHVDQHE/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-09T03:51:34Z","links":{"resolver":"https://pith.science/pith/UEVCOJRKIVTXOZCCYANMHVDQHE","bundle":"https://pith.science/pith/UEVCOJRKIVTXOZCCYANMHVDQHE/bundle.json","state":"https://pith.science/pith/UEVCOJRKIVTXOZCCYANMHVDQHE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UEVCOJRKIVTXOZCCYANMHVDQHE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:UEVCOJRKIVTXOZCCYANMHVDQHE","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":"9055996e6cb1bdb9313006222c6d4a0acf4d535b4698fb6cb2d35b4c84906711","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-03-18T17:56:02Z","title_canon_sha256":"70e7cdddb2e8baaae293cc267eef8fad666bb858fa6b54466659f587412f43ee"},"schema_version":"1.0","source":{"id":"1103.3677","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.3677","created_at":"2026-05-18T04:26:32Z"},{"alias_kind":"arxiv_version","alias_value":"1103.3677v1","created_at":"2026-05-18T04:26:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.3677","created_at":"2026-05-18T04:26:32Z"},{"alias_kind":"pith_short_12","alias_value":"UEVCOJRKIVTX","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"UEVCOJRKIVTXOZCC","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"UEVCOJRK","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:585f4c7448adc51f64ef0d5a9ef2afb66330a4eaaaee609ffd3c4a989c90fe46","target":"graph","created_at":"2026-05-18T04:26:32Z","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 prove that a viscosity solution of a uniformly elliptic, fully nonlinear equation is $C^{2,\\alpha}$ on the compliment of a closed set of Hausdorff dimension at most $\\epsilon$ less than the dimension. The equation is assumed to be $C^1$, and the constant $\\epsilon > 0$ depends only on the dimension and the ellipticity constants. The argument combines the $W^{2,\\epsilon}$ estimates of Lin with a result of Savin on the $C^{2,\\alpha}$ regularity of viscosity solutions which are close to quadratic polynomials.","authors_text":"Charles K. Smart, Luis Silvestre, Scott N. Armstrong","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-03-18T17:56:02Z","title":"Partial regularity of solutions of fully nonlinear uniformly elliptic equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.3677","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:df0bd9eaeadc33a603dfa4695733bce2e51bdce28e442730ac9dab59bc9be3a1","target":"record","created_at":"2026-05-18T04:26:32Z","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":"9055996e6cb1bdb9313006222c6d4a0acf4d535b4698fb6cb2d35b4c84906711","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-03-18T17:56:02Z","title_canon_sha256":"70e7cdddb2e8baaae293cc267eef8fad666bb858fa6b54466659f587412f43ee"},"schema_version":"1.0","source":{"id":"1103.3677","kind":"arxiv","version":1}},"canonical_sha256":"a12a27262a4567776442c01ac3d470392dee9fa6037b402bd966bb6f13eb063b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a12a27262a4567776442c01ac3d470392dee9fa6037b402bd966bb6f13eb063b","first_computed_at":"2026-05-18T04:26:32.201360Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:26:32.201360Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ic40jYRRXeOihkvfJaRdyKjnX+2pB6SiRXdXdZxn3hirL+4y1YG0FuBrF92va0TN0N5DeTiH2AFzHm9Ce12UCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:26:32.201858Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.3677","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:df0bd9eaeadc33a603dfa4695733bce2e51bdce28e442730ac9dab59bc9be3a1","sha256:585f4c7448adc51f64ef0d5a9ef2afb66330a4eaaaee609ffd3c4a989c90fe46"],"state_sha256":"89123fc1af0ed5fa01dd2e81166f11bf3df9eb1855ac5f576bd0efd68562ca1f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2MhlQ1E8UIfLnk17otKbJNb/nOXwlPn4isEbnyr9Cy2GmAbXrKA2aEjT4V0MqWAa0cYtCuCJm56+IAdGtVgXAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T03:51:34.522773Z","bundle_sha256":"af40da7251d874f0a623b513d654803d746d157dc69dde29ba98fa1abdeb8845"}}