{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:GJFUP2623E22O3WFZBV2W3RWZ4","short_pith_number":"pith:GJFUP262","canonical_record":{"source":{"id":"1107.3228","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-07-16T12:58:11Z","cross_cats_sorted":[],"title_canon_sha256":"95515affbbf3187e61c926a2ae7b0614883bbb3c7133e18a2a932f9723b07d86","abstract_canon_sha256":"50692538be668296107c080f0d7adbef23494488caf748bc4749e51554d78f83"},"schema_version":"1.0"},"canonical_sha256":"324b47ebdad935a76ec5c86bab6e36cf0e69c7e9a08d28a14df96eb339bc1eec","source":{"kind":"arxiv","id":"1107.3228","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.3228","created_at":"2026-05-18T04:05:05Z"},{"alias_kind":"arxiv_version","alias_value":"1107.3228v2","created_at":"2026-05-18T04:05:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.3228","created_at":"2026-05-18T04:05:05Z"},{"alias_kind":"pith_short_12","alias_value":"GJFUP2623E22","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"GJFUP2623E22O3WF","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"GJFUP262","created_at":"2026-05-18T12:26:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:GJFUP2623E22O3WFZBV2W3RWZ4","target":"record","payload":{"canonical_record":{"source":{"id":"1107.3228","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-07-16T12:58:11Z","cross_cats_sorted":[],"title_canon_sha256":"95515affbbf3187e61c926a2ae7b0614883bbb3c7133e18a2a932f9723b07d86","abstract_canon_sha256":"50692538be668296107c080f0d7adbef23494488caf748bc4749e51554d78f83"},"schema_version":"1.0"},"canonical_sha256":"324b47ebdad935a76ec5c86bab6e36cf0e69c7e9a08d28a14df96eb339bc1eec","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:05:05.217909Z","signature_b64":"qgy9VnBbqEh9zHXy1i/aT4aipAjmx9i5BOKpqL6/ajAex7b1//dN0YyReP7blQ1s4/DJ7MAjkWbXE29GavwdCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"324b47ebdad935a76ec5c86bab6e36cf0e69c7e9a08d28a14df96eb339bc1eec","last_reissued_at":"2026-05-18T04:05:05.217263Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:05:05.217263Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1107.3228","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:05:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"455z8ginneW+ONDsAlAxxJePgfsqAxXmVT/wg1RKxk0YgNsABquGeo0WD+RvJD64med6OYgKvB5dwt14IICuDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T08:02:52.131185Z"},"content_sha256":"2b67e831c72294100f0d0839ad448a7b641ab17b5687741292d5e831049e8210","schema_version":"1.0","event_id":"sha256:2b67e831c72294100f0d0839ad448a7b641ab17b5687741292d5e831049e8210"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:GJFUP2623E22O3WFZBV2W3RWZ4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lipschitz Regularity of Solutions for Mixed Integro-Differential Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Adina Ciomaga (CMLA), Cyril Imbert (CEREMADE, DMA), Emmanuel Chasseigne (LMPT), Guy Barles (LMPT)","submitted_at":"2011-07-16T12:58:11Z","abstract_excerpt":"We establish new Hoelder and Lipschitz estimates for viscosity solutions of a large class of elliptic and parabolic nonlinear integro-differential equations, by the classical Ishii-Lions's method. We thus extend the Hoelder regularity results recently obtained by Barles, Chasseigne and Imbert (2011). In addition, we deal with a new class of nonlocal equations that we term mixed integro-differential equations. These equations are particularly interesting, as they are degenerate both in the local and nonlocal term, but their overall behavior is driven by the local-nonlocal interaction, e.g. the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.3228","kind":"arxiv","version":2},"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":"2026-05-18T04:05:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nxQxzEWCYOXg62j4Hs9dvNqrDaZzE4lS0iofO76xsd5uiFn+7CyffkOVU/v1tLiVnYIxRBya4Dm2bKqjkN/uAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T08:02:52.131851Z"},"content_sha256":"417afee488e154024485aa87a52e7760bf933e00ce59bd952cfca7744f92418c","schema_version":"1.0","event_id":"sha256:417afee488e154024485aa87a52e7760bf933e00ce59bd952cfca7744f92418c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GJFUP2623E22O3WFZBV2W3RWZ4/bundle.json","state_url":"https://pith.science/pith/GJFUP2623E22O3WFZBV2W3RWZ4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GJFUP2623E22O3WFZBV2W3RWZ4/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":"2026-05-26T08:02:52Z","links":{"resolver":"https://pith.science/pith/GJFUP2623E22O3WFZBV2W3RWZ4","bundle":"https://pith.science/pith/GJFUP2623E22O3WFZBV2W3RWZ4/bundle.json","state":"https://pith.science/pith/GJFUP2623E22O3WFZBV2W3RWZ4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GJFUP2623E22O3WFZBV2W3RWZ4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:GJFUP2623E22O3WFZBV2W3RWZ4","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":"50692538be668296107c080f0d7adbef23494488caf748bc4749e51554d78f83","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-07-16T12:58:11Z","title_canon_sha256":"95515affbbf3187e61c926a2ae7b0614883bbb3c7133e18a2a932f9723b07d86"},"schema_version":"1.0","source":{"id":"1107.3228","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.3228","created_at":"2026-05-18T04:05:05Z"},{"alias_kind":"arxiv_version","alias_value":"1107.3228v2","created_at":"2026-05-18T04:05:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.3228","created_at":"2026-05-18T04:05:05Z"},{"alias_kind":"pith_short_12","alias_value":"GJFUP2623E22","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"GJFUP2623E22O3WF","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"GJFUP262","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:417afee488e154024485aa87a52e7760bf933e00ce59bd952cfca7744f92418c","target":"graph","created_at":"2026-05-18T04:05:05Z","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 Hoelder and Lipschitz estimates for viscosity solutions of a large class of elliptic and parabolic nonlinear integro-differential equations, by the classical Ishii-Lions's method. We thus extend the Hoelder regularity results recently obtained by Barles, Chasseigne and Imbert (2011). In addition, we deal with a new class of nonlocal equations that we term mixed integro-differential equations. These equations are particularly interesting, as they are degenerate both in the local and nonlocal term, but their overall behavior is driven by the local-nonlocal interaction, e.g. the ","authors_text":"Adina Ciomaga (CMLA), Cyril Imbert (CEREMADE, DMA), Emmanuel Chasseigne (LMPT), Guy Barles (LMPT)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-07-16T12:58:11Z","title":"Lipschitz Regularity of Solutions for Mixed Integro-Differential Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.3228","kind":"arxiv","version":2},"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":"sha256:2b67e831c72294100f0d0839ad448a7b641ab17b5687741292d5e831049e8210","target":"record","created_at":"2026-05-18T04:05:05Z","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":"50692538be668296107c080f0d7adbef23494488caf748bc4749e51554d78f83","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-07-16T12:58:11Z","title_canon_sha256":"95515affbbf3187e61c926a2ae7b0614883bbb3c7133e18a2a932f9723b07d86"},"schema_version":"1.0","source":{"id":"1107.3228","kind":"arxiv","version":2}},"canonical_sha256":"324b47ebdad935a76ec5c86bab6e36cf0e69c7e9a08d28a14df96eb339bc1eec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"324b47ebdad935a76ec5c86bab6e36cf0e69c7e9a08d28a14df96eb339bc1eec","first_computed_at":"2026-05-18T04:05:05.217263Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:05:05.217263Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qgy9VnBbqEh9zHXy1i/aT4aipAjmx9i5BOKpqL6/ajAex7b1//dN0YyReP7blQ1s4/DJ7MAjkWbXE29GavwdCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:05:05.217909Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.3228","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2b67e831c72294100f0d0839ad448a7b641ab17b5687741292d5e831049e8210","sha256:417afee488e154024485aa87a52e7760bf933e00ce59bd952cfca7744f92418c"],"state_sha256":"15b6cd00cdf3e7617ef4a4e6dd45d989d32bf4d0aced5f7a08f69080f8b22f84"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fVZ+OI/pBFcaxSFgU+g+9UXimZM90PyTQjZJ/PvRI7UpH25QWPZmSDWpAQGKSE2PwUs/BCecVxIuCKhtCu37AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T08:02:52.135041Z","bundle_sha256":"b6cab7094b10313bb03f833150292252f4e8c1a2f9d90f0ef758ea6a2dc50e2a"}}