{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:OZOFOUEYJUTRNASZQPDWLLBSVS","short_pith_number":"pith:OZOFOUEY","canonical_record":{"source":{"id":"2411.15311","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-11-22T19:08:38Z","cross_cats_sorted":[],"title_canon_sha256":"6d4e6714f2e247318c5af5fe832b5a5f1dcca66b2a15a8737d2922924ce20d6f","abstract_canon_sha256":"721ea9f0bc5c08dc7274431532638515977450229754ad8e9faf57412a3a81a1"},"schema_version":"1.0"},"canonical_sha256":"765c5750984d2716825983c765ac32acb40a285cfe2fff6d88046ff51ec57d8a","source":{"kind":"arxiv","id":"2411.15311","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.15311","created_at":"2026-07-05T09:39:32Z"},{"alias_kind":"arxiv_version","alias_value":"2411.15311v1","created_at":"2026-07-05T09:39:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.15311","created_at":"2026-07-05T09:39:32Z"},{"alias_kind":"pith_short_12","alias_value":"OZOFOUEYJUTR","created_at":"2026-07-05T09:39:32Z"},{"alias_kind":"pith_short_16","alias_value":"OZOFOUEYJUTRNASZ","created_at":"2026-07-05T09:39:32Z"},{"alias_kind":"pith_short_8","alias_value":"OZOFOUEY","created_at":"2026-07-05T09:39:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:OZOFOUEYJUTRNASZQPDWLLBSVS","target":"record","payload":{"canonical_record":{"source":{"id":"2411.15311","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-11-22T19:08:38Z","cross_cats_sorted":[],"title_canon_sha256":"6d4e6714f2e247318c5af5fe832b5a5f1dcca66b2a15a8737d2922924ce20d6f","abstract_canon_sha256":"721ea9f0bc5c08dc7274431532638515977450229754ad8e9faf57412a3a81a1"},"schema_version":"1.0"},"canonical_sha256":"765c5750984d2716825983c765ac32acb40a285cfe2fff6d88046ff51ec57d8a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:39:32.828604Z","signature_b64":"A4JJ1uzAcZxewIFoWkwweWy4U4AY9c924vz+skegwI6rKqBvCaS+TfxzMZ44YsIUm7JSPbPxQiakeWKS9G5jBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"765c5750984d2716825983c765ac32acb40a285cfe2fff6d88046ff51ec57d8a","last_reissued_at":"2026-07-05T09:39:32.828150Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:39:32.828150Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2411.15311","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":"2026-07-05T09:39:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ndon1Xiah7jcBRmcnrvbFuqGP3Dot78mz/KjbwvlQJMdZnG5hHct0iH/OjgQwk1Ui3If9i1YCz0SeRg4yp9MAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T05:26:56.629594Z"},"content_sha256":"ca64f03faa05ca00fdadd50123193d46d4a1b1b89df4f7d187f1c13f95efb708","schema_version":"1.0","event_id":"sha256:ca64f03faa05ca00fdadd50123193d46d4a1b1b89df4f7d187f1c13f95efb708"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:OZOFOUEYJUTRNASZQPDWLLBSVS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Global fractional Sobolev regularity for fully nonlinear elliptic equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Claudemir Alcantara, Makson Santos","submitted_at":"2024-11-22T19:08:38Z","abstract_excerpt":"We investigate fractional regularity estimates up to the boundary for solutions to fully nonlinear elliptic equations with measurable ingredients. Specifically, under the assumption of uniform ellipticity of the operator, we demonstrate that viscosity solutions to a second-order operator satisfy a fractional Laplacian equation. This result implies that the solutions are globally of class $W^{\\gamma, p}$, for $\\gamma \\in (1,2)$, with appropriate estimates. Consequently, these solutions exhibit differentiability of order strictly greater than one, without requiring any additional assumptions reg"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.15311","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.15311/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T09:39:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Cz2QB5dUjMnOmu/dmJKxySTvDIyOChRM2084IJk0kclf5BVi2FLLMWUDYTQ6yaUkVd+gZlFXHtGjOisqc/ifAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T05:26:56.630685Z"},"content_sha256":"849ac23030877b5b173b2a60c6e2eaef3d5b35709dff78b85b9feab4caaf1602","schema_version":"1.0","event_id":"sha256:849ac23030877b5b173b2a60c6e2eaef3d5b35709dff78b85b9feab4caaf1602"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OZOFOUEYJUTRNASZQPDWLLBSVS/bundle.json","state_url":"https://pith.science/pith/OZOFOUEYJUTRNASZQPDWLLBSVS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OZOFOUEYJUTRNASZQPDWLLBSVS/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":"2026-08-13T05:26:56Z","links":{"resolver":"https://pith.science/pith/OZOFOUEYJUTRNASZQPDWLLBSVS","bundle":"https://pith.science/pith/OZOFOUEYJUTRNASZQPDWLLBSVS/bundle.json","state":"https://pith.science/pith/OZOFOUEYJUTRNASZQPDWLLBSVS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OZOFOUEYJUTRNASZQPDWLLBSVS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:OZOFOUEYJUTRNASZQPDWLLBSVS","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":"721ea9f0bc5c08dc7274431532638515977450229754ad8e9faf57412a3a81a1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-11-22T19:08:38Z","title_canon_sha256":"6d4e6714f2e247318c5af5fe832b5a5f1dcca66b2a15a8737d2922924ce20d6f"},"schema_version":"1.0","source":{"id":"2411.15311","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.15311","created_at":"2026-07-05T09:39:32Z"},{"alias_kind":"arxiv_version","alias_value":"2411.15311v1","created_at":"2026-07-05T09:39:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.15311","created_at":"2026-07-05T09:39:32Z"},{"alias_kind":"pith_short_12","alias_value":"OZOFOUEYJUTR","created_at":"2026-07-05T09:39:32Z"},{"alias_kind":"pith_short_16","alias_value":"OZOFOUEYJUTRNASZ","created_at":"2026-07-05T09:39:32Z"},{"alias_kind":"pith_short_8","alias_value":"OZOFOUEY","created_at":"2026-07-05T09:39:32Z"}],"graph_snapshots":[{"event_id":"sha256:849ac23030877b5b173b2a60c6e2eaef3d5b35709dff78b85b9feab4caaf1602","target":"graph","created_at":"2026-07-05T09:39:32Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2411.15311/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We investigate fractional regularity estimates up to the boundary for solutions to fully nonlinear elliptic equations with measurable ingredients. Specifically, under the assumption of uniform ellipticity of the operator, we demonstrate that viscosity solutions to a second-order operator satisfy a fractional Laplacian equation. This result implies that the solutions are globally of class $W^{\\gamma, p}$, for $\\gamma \\in (1,2)$, with appropriate estimates. Consequently, these solutions exhibit differentiability of order strictly greater than one, without requiring any additional assumptions reg","authors_text":"Claudemir Alcantara, Makson Santos","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-11-22T19:08:38Z","title":"Global fractional Sobolev regularity for fully nonlinear elliptic equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.15311","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:ca64f03faa05ca00fdadd50123193d46d4a1b1b89df4f7d187f1c13f95efb708","target":"record","created_at":"2026-07-05T09:39:32Z","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":"721ea9f0bc5c08dc7274431532638515977450229754ad8e9faf57412a3a81a1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-11-22T19:08:38Z","title_canon_sha256":"6d4e6714f2e247318c5af5fe832b5a5f1dcca66b2a15a8737d2922924ce20d6f"},"schema_version":"1.0","source":{"id":"2411.15311","kind":"arxiv","version":1}},"canonical_sha256":"765c5750984d2716825983c765ac32acb40a285cfe2fff6d88046ff51ec57d8a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"765c5750984d2716825983c765ac32acb40a285cfe2fff6d88046ff51ec57d8a","first_computed_at":"2026-07-05T09:39:32.828150Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:39:32.828150Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"A4JJ1uzAcZxewIFoWkwweWy4U4AY9c924vz+skegwI6rKqBvCaS+TfxzMZ44YsIUm7JSPbPxQiakeWKS9G5jBA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:39:32.828604Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.15311","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ca64f03faa05ca00fdadd50123193d46d4a1b1b89df4f7d187f1c13f95efb708","sha256:849ac23030877b5b173b2a60c6e2eaef3d5b35709dff78b85b9feab4caaf1602"],"state_sha256":"a676a2cf31a8c444a2ca0c3d7969335f13b1815d23fe424bd6bd72840c99a595"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BlCDu3QrzJJQaIhHhbONXlzVlNM+pbF1jmwb1EYRvUbaPdn7Zq4KPykY9Ki9zevSvqQeCiynNcGDTJk0P6TeCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T05:26:56.637495Z","bundle_sha256":"125351a9fb365297caca50a9c4ab2de1a4d60e972a337e9bb716a55b422bc19b"}}