{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:5AD32JYLLQWOXHCTJDRQHLJ4WD","short_pith_number":"pith:5AD32JYL","canonical_record":{"source":{"id":"1601.05882","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-01-22T06:00:35Z","cross_cats_sorted":[],"title_canon_sha256":"76fddd131257c817904a6f1394a160332abf400c31c15b186f47e03a39e5f157","abstract_canon_sha256":"33922a2f06483e0b2fb6ebf3f22db59bae9ae36a12ade25b80f96f8e1042f205"},"schema_version":"1.0"},"canonical_sha256":"e807bd270b5c2ceb9c5348e303ad3cb0d8331a7fa97c7ca1ac846e30e4bc8a34","source":{"kind":"arxiv","id":"1601.05882","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.05882","created_at":"2026-05-18T01:22:09Z"},{"alias_kind":"arxiv_version","alias_value":"1601.05882v1","created_at":"2026-05-18T01:22:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.05882","created_at":"2026-05-18T01:22:09Z"},{"alias_kind":"pith_short_12","alias_value":"5AD32JYLLQWO","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"5AD32JYLLQWOXHCT","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"5AD32JYL","created_at":"2026-05-18T12:29:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:5AD32JYLLQWOXHCTJDRQHLJ4WD","target":"record","payload":{"canonical_record":{"source":{"id":"1601.05882","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-01-22T06:00:35Z","cross_cats_sorted":[],"title_canon_sha256":"76fddd131257c817904a6f1394a160332abf400c31c15b186f47e03a39e5f157","abstract_canon_sha256":"33922a2f06483e0b2fb6ebf3f22db59bae9ae36a12ade25b80f96f8e1042f205"},"schema_version":"1.0"},"canonical_sha256":"e807bd270b5c2ceb9c5348e303ad3cb0d8331a7fa97c7ca1ac846e30e4bc8a34","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:09.901739Z","signature_b64":"CsaHV1WZou6k0vE5IpFn6w4p7/LazN6yVDCoj9WNedkmg9a4Ct3Zes9lV616Ide/EWKdbP0qcIAjXFxGjxDqDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e807bd270b5c2ceb9c5348e303ad3cb0d8331a7fa97c7ca1ac846e30e4bc8a34","last_reissued_at":"2026-05-18T01:22:09.901196Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:09.901196Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.05882","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":"2026-05-18T01:22:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZnnkI59ASivDHaic9ou9aBpOoKUqJCc6mnHe/PFaNpJTGULosHli9iNpLcf7QwG6i9eiQV6Vero4tNACshHXCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T12:04:28.675338Z"},"content_sha256":"a84dab5bbdd731fd238dd2ed0eb15a6de7759ba78489f608601548b2fe38fb51","schema_version":"1.0","event_id":"sha256:a84dab5bbdd731fd238dd2ed0eb15a6de7759ba78489f608601548b2fe38fb51"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:5AD32JYLLQWOXHCTJDRQHLJ4WD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"$W^{\\sigma,\\epsilon}$-estimates for nonlocal elliptic equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hui Yu","submitted_at":"2016-01-22T06:00:35Z","abstract_excerpt":"We prove that the fractional derivatives of solutions to a class of nonlocal fully nonlinear elliptic equations are epsilon-integrable. We follow Fanghua Lin's original approach to the analogous problem for second order equations, by first proving a potential estimate, then combining this estimate with the ABP-type estimate by N. Guillen and R. Schwab to control the size of the superlevel sets of the fractional derivatives of solutions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.05882","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":"2026-05-18T01:22:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5Efaj9IUPvxJgBno78jEW9Sgi+iun1j08LpT4/sd6PhlNQobYAjaotWYTQUDfGVRVCSP+3XwMDh4A6JmoVdPBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T12:04:28.675915Z"},"content_sha256":"cf9d1fff350b03ec4c9a460ace45ed0d3993583ff2d48a151f2796b01a723d35","schema_version":"1.0","event_id":"sha256:cf9d1fff350b03ec4c9a460ace45ed0d3993583ff2d48a151f2796b01a723d35"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5AD32JYLLQWOXHCTJDRQHLJ4WD/bundle.json","state_url":"https://pith.science/pith/5AD32JYLLQWOXHCTJDRQHLJ4WD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5AD32JYLLQWOXHCTJDRQHLJ4WD/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":"2026-05-30T12:04:28Z","links":{"resolver":"https://pith.science/pith/5AD32JYLLQWOXHCTJDRQHLJ4WD","bundle":"https://pith.science/pith/5AD32JYLLQWOXHCTJDRQHLJ4WD/bundle.json","state":"https://pith.science/pith/5AD32JYLLQWOXHCTJDRQHLJ4WD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5AD32JYLLQWOXHCTJDRQHLJ4WD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:5AD32JYLLQWOXHCTJDRQHLJ4WD","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":"33922a2f06483e0b2fb6ebf3f22db59bae9ae36a12ade25b80f96f8e1042f205","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-01-22T06:00:35Z","title_canon_sha256":"76fddd131257c817904a6f1394a160332abf400c31c15b186f47e03a39e5f157"},"schema_version":"1.0","source":{"id":"1601.05882","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.05882","created_at":"2026-05-18T01:22:09Z"},{"alias_kind":"arxiv_version","alias_value":"1601.05882v1","created_at":"2026-05-18T01:22:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.05882","created_at":"2026-05-18T01:22:09Z"},{"alias_kind":"pith_short_12","alias_value":"5AD32JYLLQWO","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"5AD32JYLLQWOXHCT","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"5AD32JYL","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:cf9d1fff350b03ec4c9a460ace45ed0d3993583ff2d48a151f2796b01a723d35","target":"graph","created_at":"2026-05-18T01:22:09Z","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 the fractional derivatives of solutions to a class of nonlocal fully nonlinear elliptic equations are epsilon-integrable. We follow Fanghua Lin's original approach to the analogous problem for second order equations, by first proving a potential estimate, then combining this estimate with the ABP-type estimate by N. Guillen and R. Schwab to control the size of the superlevel sets of the fractional derivatives of solutions.","authors_text":"Hui Yu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-01-22T06:00:35Z","title":"$W^{\\sigma,\\epsilon}$-estimates for nonlocal elliptic equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.05882","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:a84dab5bbdd731fd238dd2ed0eb15a6de7759ba78489f608601548b2fe38fb51","target":"record","created_at":"2026-05-18T01:22:09Z","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":"33922a2f06483e0b2fb6ebf3f22db59bae9ae36a12ade25b80f96f8e1042f205","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-01-22T06:00:35Z","title_canon_sha256":"76fddd131257c817904a6f1394a160332abf400c31c15b186f47e03a39e5f157"},"schema_version":"1.0","source":{"id":"1601.05882","kind":"arxiv","version":1}},"canonical_sha256":"e807bd270b5c2ceb9c5348e303ad3cb0d8331a7fa97c7ca1ac846e30e4bc8a34","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e807bd270b5c2ceb9c5348e303ad3cb0d8331a7fa97c7ca1ac846e30e4bc8a34","first_computed_at":"2026-05-18T01:22:09.901196Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:09.901196Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CsaHV1WZou6k0vE5IpFn6w4p7/LazN6yVDCoj9WNedkmg9a4Ct3Zes9lV616Ide/EWKdbP0qcIAjXFxGjxDqDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:09.901739Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.05882","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a84dab5bbdd731fd238dd2ed0eb15a6de7759ba78489f608601548b2fe38fb51","sha256:cf9d1fff350b03ec4c9a460ace45ed0d3993583ff2d48a151f2796b01a723d35"],"state_sha256":"142de6cdc6868cda31b31c09308e8439838e0223b5f2ae7f437f381f3c1f4b6e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p426NV2KbmwwCDTvUYKnXZdoY+Wi5f+fhkNi2xjVbZir8hVcCrMO0ASglsDwmQqcXg0AZ/Mqfj8N+bgI7rnGDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T12:04:28.678571Z","bundle_sha256":"543e6d43b6d7c8833bd51b8c1023cd51f001a5945543789b1fd9dee26c789764"}}