{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:JDQZ5JIZNVAFCQ7JQI44YWHQRE","short_pith_number":"pith:JDQZ5JIZ","canonical_record":{"source":{"id":"1603.05565","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-03-17T16:27:07Z","cross_cats_sorted":[],"title_canon_sha256":"9e618eb3095b482b24ee946ab0e6902897e9452dd930e627d3be60ec3a93aae2","abstract_canon_sha256":"efef5b6f0f2a43624184be624e1e86f7c9999613c8273c73f310015e3b24fa74"},"schema_version":"1.0"},"canonical_sha256":"48e19ea5196d405143e98239cc58f0893a7aa581f119b7fd3a4a18e55b16e3b0","source":{"kind":"arxiv","id":"1603.05565","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.05565","created_at":"2026-05-18T01:18:56Z"},{"alias_kind":"arxiv_version","alias_value":"1603.05565v1","created_at":"2026-05-18T01:18:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.05565","created_at":"2026-05-18T01:18:56Z"},{"alias_kind":"pith_short_12","alias_value":"JDQZ5JIZNVAF","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"JDQZ5JIZNVAFCQ7J","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"JDQZ5JIZ","created_at":"2026-05-18T12:30:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:JDQZ5JIZNVAFCQ7JQI44YWHQRE","target":"record","payload":{"canonical_record":{"source":{"id":"1603.05565","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-03-17T16:27:07Z","cross_cats_sorted":[],"title_canon_sha256":"9e618eb3095b482b24ee946ab0e6902897e9452dd930e627d3be60ec3a93aae2","abstract_canon_sha256":"efef5b6f0f2a43624184be624e1e86f7c9999613c8273c73f310015e3b24fa74"},"schema_version":"1.0"},"canonical_sha256":"48e19ea5196d405143e98239cc58f0893a7aa581f119b7fd3a4a18e55b16e3b0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:56.084635Z","signature_b64":"vS0x5EM07lPW6qSYukzkwIeqEomLqQrwCom4x4lKhZlVstTTMRVju6wzIUosU1juo9OWiAHPfSgT+P1skrNkCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"48e19ea5196d405143e98239cc58f0893a7aa581f119b7fd3a4a18e55b16e3b0","last_reissued_at":"2026-05-18T01:18:56.084093Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:56.084093Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.05565","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":"2026-05-18T01:18:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MTePIfdUbNi0pdCRcgX1txeNsALRoIVbmqDvqaEdPShdA/9lVgMP0HiXNWluTH4liPRnWnSUiEGkkknmtFTRAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T10:38:57.070353Z"},"content_sha256":"64bd92deabfa0f96ba9246bfb0b14ca03d7a682f0ccbed5f5f9d4940df047a19","schema_version":"1.0","event_id":"sha256:64bd92deabfa0f96ba9246bfb0b14ca03d7a682f0ccbed5f5f9d4940df047a19"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:JDQZ5JIZNVAFCQ7JQI44YWHQRE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fractional differentiability for solutions of nonlinear elliptic equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Albert Clop, Antonia Passarelli di Napoli, Antonio L. Bais\\'on, Joan Orobitg, Raffaella Giova","submitted_at":"2016-03-17T16:27:07Z","abstract_excerpt":"We study nonlinear elliptic equations in divergence form $${\\operatorname{div}}{\\mathcal A}(x,Du)={\\operatorname{div}}G.$$ When ${\\mathcal A}$ has linear growth in $Du$, and assuming that $x\\mapsto{\\mathcal A}(x,\\xi)$ enjoys $B^\\alpha_{\\frac{n}\\alpha, q}$ smoothness, local well-posedness is found in $B^\\alpha_{p,q}$ for certain values of $p\\in[2,\\frac{n}{\\alpha})$ and $q\\in[1,\\infty]$. In the particular case ${\\mathcal A}(x,\\xi)=A(x)\\xi$, $G=0$ and $A\\in B^\\alpha_{\\frac{n}\\alpha,q}$, $1\\leq q\\leq\\infty$, we obtain $Du\\in B^\\alpha_{p,q}$ for each $p<\\frac{n}\\alpha$. Our main tool in the proof i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.05565","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":"2026-05-18T01:18:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i74T9uI9U89gp8wC1pNrHGGVf7k4UsEjds4gPRDn2XtbR2BMYWTa8N38EqRwrvzOA6kHuH9ZgOnFNzjqDneuCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T10:38:57.070704Z"},"content_sha256":"8af885321eae4c5ad8be1dee983e391e2e3a7fba91e804ffe3eed53ec97f0f1c","schema_version":"1.0","event_id":"sha256:8af885321eae4c5ad8be1dee983e391e2e3a7fba91e804ffe3eed53ec97f0f1c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JDQZ5JIZNVAFCQ7JQI44YWHQRE/bundle.json","state_url":"https://pith.science/pith/JDQZ5JIZNVAFCQ7JQI44YWHQRE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JDQZ5JIZNVAFCQ7JQI44YWHQRE/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":"2026-06-20T10:38:57Z","links":{"resolver":"https://pith.science/pith/JDQZ5JIZNVAFCQ7JQI44YWHQRE","bundle":"https://pith.science/pith/JDQZ5JIZNVAFCQ7JQI44YWHQRE/bundle.json","state":"https://pith.science/pith/JDQZ5JIZNVAFCQ7JQI44YWHQRE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JDQZ5JIZNVAFCQ7JQI44YWHQRE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:JDQZ5JIZNVAFCQ7JQI44YWHQRE","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":"efef5b6f0f2a43624184be624e1e86f7c9999613c8273c73f310015e3b24fa74","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-03-17T16:27:07Z","title_canon_sha256":"9e618eb3095b482b24ee946ab0e6902897e9452dd930e627d3be60ec3a93aae2"},"schema_version":"1.0","source":{"id":"1603.05565","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.05565","created_at":"2026-05-18T01:18:56Z"},{"alias_kind":"arxiv_version","alias_value":"1603.05565v1","created_at":"2026-05-18T01:18:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.05565","created_at":"2026-05-18T01:18:56Z"},{"alias_kind":"pith_short_12","alias_value":"JDQZ5JIZNVAF","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"JDQZ5JIZNVAFCQ7J","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"JDQZ5JIZ","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:8af885321eae4c5ad8be1dee983e391e2e3a7fba91e804ffe3eed53ec97f0f1c","target":"graph","created_at":"2026-05-18T01:18:56Z","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 study nonlinear elliptic equations in divergence form $${\\operatorname{div}}{\\mathcal A}(x,Du)={\\operatorname{div}}G.$$ When ${\\mathcal A}$ has linear growth in $Du$, and assuming that $x\\mapsto{\\mathcal A}(x,\\xi)$ enjoys $B^\\alpha_{\\frac{n}\\alpha, q}$ smoothness, local well-posedness is found in $B^\\alpha_{p,q}$ for certain values of $p\\in[2,\\frac{n}{\\alpha})$ and $q\\in[1,\\infty]$. In the particular case ${\\mathcal A}(x,\\xi)=A(x)\\xi$, $G=0$ and $A\\in B^\\alpha_{\\frac{n}\\alpha,q}$, $1\\leq q\\leq\\infty$, we obtain $Du\\in B^\\alpha_{p,q}$ for each $p<\\frac{n}\\alpha$. Our main tool in the proof i","authors_text":"Albert Clop, Antonia Passarelli di Napoli, Antonio L. Bais\\'on, Joan Orobitg, Raffaella Giova","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-03-17T16:27:07Z","title":"Fractional differentiability for solutions of nonlinear elliptic equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.05565","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":"sha256:64bd92deabfa0f96ba9246bfb0b14ca03d7a682f0ccbed5f5f9d4940df047a19","target":"record","created_at":"2026-05-18T01:18:56Z","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":"efef5b6f0f2a43624184be624e1e86f7c9999613c8273c73f310015e3b24fa74","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-03-17T16:27:07Z","title_canon_sha256":"9e618eb3095b482b24ee946ab0e6902897e9452dd930e627d3be60ec3a93aae2"},"schema_version":"1.0","source":{"id":"1603.05565","kind":"arxiv","version":1}},"canonical_sha256":"48e19ea5196d405143e98239cc58f0893a7aa581f119b7fd3a4a18e55b16e3b0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"48e19ea5196d405143e98239cc58f0893a7aa581f119b7fd3a4a18e55b16e3b0","first_computed_at":"2026-05-18T01:18:56.084093Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:56.084093Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vS0x5EM07lPW6qSYukzkwIeqEomLqQrwCom4x4lKhZlVstTTMRVju6wzIUosU1juo9OWiAHPfSgT+P1skrNkCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:56.084635Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.05565","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:64bd92deabfa0f96ba9246bfb0b14ca03d7a682f0ccbed5f5f9d4940df047a19","sha256:8af885321eae4c5ad8be1dee983e391e2e3a7fba91e804ffe3eed53ec97f0f1c"],"state_sha256":"8d12d33602185dbb37b32bac507822d7a32243592c34db9cdf92e43165c354e5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B2q5IglspudDAAPmAaQbie6CSGadb9DgayjLG5DQ1xqbLQb24oV2VuWxylDIT0wBquHAAN6bQhhd/LlSwMpCBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T10:38:57.072598Z","bundle_sha256":"f3876e7e542a9a41a74a62b5ed58257731b6f50048c2ea2084e3384e59679fef"}}