{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:MPCSWTBSUQ2AYEWLOFRRQRPBEJ","short_pith_number":"pith:MPCSWTBS","canonical_record":{"source":{"id":"1601.07211","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-01-26T22:36:48Z","cross_cats_sorted":[],"title_canon_sha256":"e3e88327cbc3351d765ba35489d94ad2b00a709d14e216ba01cdfb7c12f087a3","abstract_canon_sha256":"05f1572d9285b46c05b64f15a2877aa00b58c11a958e134549332438bac0c78f"},"schema_version":"1.0"},"canonical_sha256":"63c52b4c32a4340c12cb71631845e1224a2b3deb03f044ffa993e0db51526e8e","source":{"kind":"arxiv","id":"1601.07211","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.07211","created_at":"2026-05-18T01:16:06Z"},{"alias_kind":"arxiv_version","alias_value":"1601.07211v2","created_at":"2026-05-18T01:16:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.07211","created_at":"2026-05-18T01:16:06Z"},{"alias_kind":"pith_short_12","alias_value":"MPCSWTBSUQ2A","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"MPCSWTBSUQ2AYEWL","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"MPCSWTBS","created_at":"2026-05-18T12:30:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:MPCSWTBSUQ2AYEWLOFRRQRPBEJ","target":"record","payload":{"canonical_record":{"source":{"id":"1601.07211","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-01-26T22:36:48Z","cross_cats_sorted":[],"title_canon_sha256":"e3e88327cbc3351d765ba35489d94ad2b00a709d14e216ba01cdfb7c12f087a3","abstract_canon_sha256":"05f1572d9285b46c05b64f15a2877aa00b58c11a958e134549332438bac0c78f"},"schema_version":"1.0"},"canonical_sha256":"63c52b4c32a4340c12cb71631845e1224a2b3deb03f044ffa993e0db51526e8e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:06.702662Z","signature_b64":"DCI5box4xBTfun13boXvFL7tuUl8YIbcegzZNZlfieo30YWKCBi/ApBhR2ISpTa+IYHGAAt2OyDq1iVAwLAvDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"63c52b4c32a4340c12cb71631845e1224a2b3deb03f044ffa993e0db51526e8e","last_reissued_at":"2026-05-18T01:16:06.702150Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:06.702150Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.07211","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":"2026-05-18T01:16:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u/2gHa/Dwdn+VV9Oa/C0EK3ad0xlBySlVfOM+CCUzkF4D/JjYaIXDarAeGKoX/Ok00w7KdV9CnlVMiZgr6laDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T13:14:25.707577Z"},"content_sha256":"19aa409526164e8ce9e95f6c5ca9f51399ef85d1f1ec258e2adf6c6f4a73b85e","schema_version":"1.0","event_id":"sha256:19aa409526164e8ce9e95f6c5ca9f51399ef85d1f1ec258e2adf6c6f4a73b85e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:MPCSWTBSUQ2AYEWLOFRRQRPBEJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A regularity result for the p-laplacian near uniform ellipticity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Berardino Sciunzi, Carlo Mercuri, Giuseppe Riey","submitted_at":"2016-01-26T22:36:48Z","abstract_excerpt":"We consider weak solutions to a class of Dirichlet boundary value problems invloving the $p$-Laplace operator, and prove that the second weak derivatives are in $L^{q}$ with $q$ as large as it is desirable, provided $p$ is sufficiently close to $p_0=2$. We show that this phenomenon is driven by the classical Calder\\'on-Zygmund constant. As a byproduct of our analysis we show that $C^{1,\\alpha}$ regularity improves up to $C^{1,1^-}$, when p is close enough to 2. This result we believe it is particularly interesting in higher dimensions $n>2,$ when optimal $C^{1,\\alpha}$ regularity is related to"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.07211","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":"2026-05-18T01:16:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W0OLb0oU1Rf2QER39Vh/B0EyVQp2UFxqeAHol/7gtrtevC1nN4GR3j04O5215qzb/3WrcWY0JyChoFzzmJf8AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T13:14:25.707921Z"},"content_sha256":"2deaf5396aae9e559e77f00f70f48b3012f5e455567b84304cd91a09f38215c6","schema_version":"1.0","event_id":"sha256:2deaf5396aae9e559e77f00f70f48b3012f5e455567b84304cd91a09f38215c6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MPCSWTBSUQ2AYEWLOFRRQRPBEJ/bundle.json","state_url":"https://pith.science/pith/MPCSWTBSUQ2AYEWLOFRRQRPBEJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MPCSWTBSUQ2AYEWLOFRRQRPBEJ/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":"2026-06-08T13:14:25Z","links":{"resolver":"https://pith.science/pith/MPCSWTBSUQ2AYEWLOFRRQRPBEJ","bundle":"https://pith.science/pith/MPCSWTBSUQ2AYEWLOFRRQRPBEJ/bundle.json","state":"https://pith.science/pith/MPCSWTBSUQ2AYEWLOFRRQRPBEJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MPCSWTBSUQ2AYEWLOFRRQRPBEJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:MPCSWTBSUQ2AYEWLOFRRQRPBEJ","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":"05f1572d9285b46c05b64f15a2877aa00b58c11a958e134549332438bac0c78f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-01-26T22:36:48Z","title_canon_sha256":"e3e88327cbc3351d765ba35489d94ad2b00a709d14e216ba01cdfb7c12f087a3"},"schema_version":"1.0","source":{"id":"1601.07211","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.07211","created_at":"2026-05-18T01:16:06Z"},{"alias_kind":"arxiv_version","alias_value":"1601.07211v2","created_at":"2026-05-18T01:16:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.07211","created_at":"2026-05-18T01:16:06Z"},{"alias_kind":"pith_short_12","alias_value":"MPCSWTBSUQ2A","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"MPCSWTBSUQ2AYEWL","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"MPCSWTBS","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:2deaf5396aae9e559e77f00f70f48b3012f5e455567b84304cd91a09f38215c6","target":"graph","created_at":"2026-05-18T01:16:06Z","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 consider weak solutions to a class of Dirichlet boundary value problems invloving the $p$-Laplace operator, and prove that the second weak derivatives are in $L^{q}$ with $q$ as large as it is desirable, provided $p$ is sufficiently close to $p_0=2$. We show that this phenomenon is driven by the classical Calder\\'on-Zygmund constant. As a byproduct of our analysis we show that $C^{1,\\alpha}$ regularity improves up to $C^{1,1^-}$, when p is close enough to 2. This result we believe it is particularly interesting in higher dimensions $n>2,$ when optimal $C^{1,\\alpha}$ regularity is related to","authors_text":"Berardino Sciunzi, Carlo Mercuri, Giuseppe Riey","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-01-26T22:36:48Z","title":"A regularity result for the p-laplacian near uniform ellipticity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.07211","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":"sha256:19aa409526164e8ce9e95f6c5ca9f51399ef85d1f1ec258e2adf6c6f4a73b85e","target":"record","created_at":"2026-05-18T01:16:06Z","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":"05f1572d9285b46c05b64f15a2877aa00b58c11a958e134549332438bac0c78f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-01-26T22:36:48Z","title_canon_sha256":"e3e88327cbc3351d765ba35489d94ad2b00a709d14e216ba01cdfb7c12f087a3"},"schema_version":"1.0","source":{"id":"1601.07211","kind":"arxiv","version":2}},"canonical_sha256":"63c52b4c32a4340c12cb71631845e1224a2b3deb03f044ffa993e0db51526e8e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"63c52b4c32a4340c12cb71631845e1224a2b3deb03f044ffa993e0db51526e8e","first_computed_at":"2026-05-18T01:16:06.702150Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:16:06.702150Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DCI5box4xBTfun13boXvFL7tuUl8YIbcegzZNZlfieo30YWKCBi/ApBhR2ISpTa+IYHGAAt2OyDq1iVAwLAvDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:16:06.702662Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.07211","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:19aa409526164e8ce9e95f6c5ca9f51399ef85d1f1ec258e2adf6c6f4a73b85e","sha256:2deaf5396aae9e559e77f00f70f48b3012f5e455567b84304cd91a09f38215c6"],"state_sha256":"b7bc38c523b36b201ca7aa24653949ebfc1e034c4f5a7bd089b9f107e7d31353"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gC70t5RJXqt/SMNCuCzbpeawGeZtmm3ct9+1DkmFztH5D91kPyYjNNQGBUbBzOR0VBz1NaBIB4RYkE/xIvSFDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T13:14:25.709914Z","bundle_sha256":"7886243980c6e839db19fa194fd102af16206e2a6d3cb89a884b432463adcdd3"}}