{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:D5ASESLUS3Z5OSZHIXDN5GILM2","short_pith_number":"pith:D5ASESLU","canonical_record":{"source":{"id":"1212.4030","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-12-17T15:39:54Z","cross_cats_sorted":[],"title_canon_sha256":"bcd7920c4700ca0bbe8c58f2f6999ff24a17f68b8913773251633a0e1e1b460f","abstract_canon_sha256":"f1506d84d0746d4dac85188af1c00616a2cc5cca9318bb70c3be083968faa5f3"},"schema_version":"1.0"},"canonical_sha256":"1f4122497496f3d74b2745c6de990b66b1a99efb5ce79741bdbeb3540271779e","source":{"kind":"arxiv","id":"1212.4030","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.4030","created_at":"2026-05-18T03:38:21Z"},{"alias_kind":"arxiv_version","alias_value":"1212.4030v1","created_at":"2026-05-18T03:38:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.4030","created_at":"2026-05-18T03:38:21Z"},{"alias_kind":"pith_short_12","alias_value":"D5ASESLUS3Z5","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"D5ASESLUS3Z5OSZH","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"D5ASESLU","created_at":"2026-05-18T12:27:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:D5ASESLUS3Z5OSZHIXDN5GILM2","target":"record","payload":{"canonical_record":{"source":{"id":"1212.4030","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-12-17T15:39:54Z","cross_cats_sorted":[],"title_canon_sha256":"bcd7920c4700ca0bbe8c58f2f6999ff24a17f68b8913773251633a0e1e1b460f","abstract_canon_sha256":"f1506d84d0746d4dac85188af1c00616a2cc5cca9318bb70c3be083968faa5f3"},"schema_version":"1.0"},"canonical_sha256":"1f4122497496f3d74b2745c6de990b66b1a99efb5ce79741bdbeb3540271779e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:38:21.703060Z","signature_b64":"q8ct9Aeq0XssYft7H+PkyhdNYhcj7L0JIu/hwUwx8XyZbQdId9q3MV8JxO0Hg2ImxWvEUmEyFB6R049g4xqEDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1f4122497496f3d74b2745c6de990b66b1a99efb5ce79741bdbeb3540271779e","last_reissued_at":"2026-05-18T03:38:21.702366Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:38:21.702366Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1212.4030","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":"2026-05-18T03:38:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1p1p73K3mNU0YwwflQfpBoq6LSjH1TytX7BbmK/Jg4wjFguPT1RgSUrhZOvpgMoz3u0kSQs79bFd3FRIZAWFCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T00:22:14.671097Z"},"content_sha256":"08a947beaba01eb29cd377a72abb8d2ae0210970a1d7ba333bd86587eec987dd","schema_version":"1.0","event_id":"sha256:08a947beaba01eb29cd377a72abb8d2ae0210970a1d7ba333bd86587eec987dd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:D5ASESLUS3Z5OSZHIXDN5GILM2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Regularity for solutions of non local parabolic equations II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gonzalo Davila, Hector A. Chang Lara","submitted_at":"2012-12-17T15:39:54Z","abstract_excerpt":"We prove boundary regularity and a compactness result for parabolic nonlocal equations of the form $u_t-Iu=f$, where the operator $I$ is not necessarily translation invariant. As a consequence of this and the regularity results for translation invariant case, we obtain $C^{1,\\alpha}$ interior estimates in space for non translation invariant operators under some hypothesis on the time regularity of the boundary data."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.4030","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":"2026-05-18T03:38:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qm72e9MVqAcHeh4/y+0uT+9Q3pP8F9Aj/QcyLC9X36gQD4XQNwXHa/Kx3XHPFgQ8sHyVB/2I+Hh8EAhEsbk4AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T00:22:14.671451Z"},"content_sha256":"6789201413d3dcdea0e03aba3d1db14b0c605c02ed21f163c24d668327cc6911","schema_version":"1.0","event_id":"sha256:6789201413d3dcdea0e03aba3d1db14b0c605c02ed21f163c24d668327cc6911"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D5ASESLUS3Z5OSZHIXDN5GILM2/bundle.json","state_url":"https://pith.science/pith/D5ASESLUS3Z5OSZHIXDN5GILM2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D5ASESLUS3Z5OSZHIXDN5GILM2/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":"2026-06-29T00:22:14Z","links":{"resolver":"https://pith.science/pith/D5ASESLUS3Z5OSZHIXDN5GILM2","bundle":"https://pith.science/pith/D5ASESLUS3Z5OSZHIXDN5GILM2/bundle.json","state":"https://pith.science/pith/D5ASESLUS3Z5OSZHIXDN5GILM2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D5ASESLUS3Z5OSZHIXDN5GILM2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:D5ASESLUS3Z5OSZHIXDN5GILM2","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":"f1506d84d0746d4dac85188af1c00616a2cc5cca9318bb70c3be083968faa5f3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-12-17T15:39:54Z","title_canon_sha256":"bcd7920c4700ca0bbe8c58f2f6999ff24a17f68b8913773251633a0e1e1b460f"},"schema_version":"1.0","source":{"id":"1212.4030","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.4030","created_at":"2026-05-18T03:38:21Z"},{"alias_kind":"arxiv_version","alias_value":"1212.4030v1","created_at":"2026-05-18T03:38:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.4030","created_at":"2026-05-18T03:38:21Z"},{"alias_kind":"pith_short_12","alias_value":"D5ASESLUS3Z5","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"D5ASESLUS3Z5OSZH","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"D5ASESLU","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:6789201413d3dcdea0e03aba3d1db14b0c605c02ed21f163c24d668327cc6911","target":"graph","created_at":"2026-05-18T03:38:21Z","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 boundary regularity and a compactness result for parabolic nonlocal equations of the form $u_t-Iu=f$, where the operator $I$ is not necessarily translation invariant. As a consequence of this and the regularity results for translation invariant case, we obtain $C^{1,\\alpha}$ interior estimates in space for non translation invariant operators under some hypothesis on the time regularity of the boundary data.","authors_text":"Gonzalo Davila, Hector A. Chang Lara","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-12-17T15:39:54Z","title":"Regularity for solutions of non local parabolic equations II"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.4030","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":"sha256:08a947beaba01eb29cd377a72abb8d2ae0210970a1d7ba333bd86587eec987dd","target":"record","created_at":"2026-05-18T03:38:21Z","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":"f1506d84d0746d4dac85188af1c00616a2cc5cca9318bb70c3be083968faa5f3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-12-17T15:39:54Z","title_canon_sha256":"bcd7920c4700ca0bbe8c58f2f6999ff24a17f68b8913773251633a0e1e1b460f"},"schema_version":"1.0","source":{"id":"1212.4030","kind":"arxiv","version":1}},"canonical_sha256":"1f4122497496f3d74b2745c6de990b66b1a99efb5ce79741bdbeb3540271779e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1f4122497496f3d74b2745c6de990b66b1a99efb5ce79741bdbeb3540271779e","first_computed_at":"2026-05-18T03:38:21.702366Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:38:21.702366Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"q8ct9Aeq0XssYft7H+PkyhdNYhcj7L0JIu/hwUwx8XyZbQdId9q3MV8JxO0Hg2ImxWvEUmEyFB6R049g4xqEDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:38:21.703060Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.4030","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:08a947beaba01eb29cd377a72abb8d2ae0210970a1d7ba333bd86587eec987dd","sha256:6789201413d3dcdea0e03aba3d1db14b0c605c02ed21f163c24d668327cc6911"],"state_sha256":"88c1c1e106273029af946b195f95456b50b2f4f45870cffba60619d16bcea7e8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TAghdLe6T+rPbboGZAWSJjsW5yeOxh2/L8CelSVfJOo+/eLaySwO/X2weHtKJfgrdzFgvVbQ0q68igkEg21+BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T00:22:14.673241Z","bundle_sha256":"0deadc6cb124e8a729fee8f46418dbad13fb5c2f7260e086c6edef76c24c50c7"}}