{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:LVXJYRKZNBQV4KMS6FNLJVWHOV","short_pith_number":"pith:LVXJYRKZ","canonical_record":{"source":{"id":"1307.0234","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-06-30T19:36:15Z","cross_cats_sorted":[],"title_canon_sha256":"f572e0fdb5253b11709a6d914daa3af23b8ce4b6c42ca38542cbc396332b03fb","abstract_canon_sha256":"b772c8714e9ece82e9e155193cf6a8acb9c168d024b03631c41143b50cf8eadb"},"schema_version":"1.0"},"canonical_sha256":"5d6e9c455968615e2992f15ab4d6c7754edffb4fb8b64b0eda9dd9a7bb49a638","source":{"kind":"arxiv","id":"1307.0234","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.0234","created_at":"2026-05-18T03:19:33Z"},{"alias_kind":"arxiv_version","alias_value":"1307.0234v1","created_at":"2026-05-18T03:19:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.0234","created_at":"2026-05-18T03:19:33Z"},{"alias_kind":"pith_short_12","alias_value":"LVXJYRKZNBQV","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"LVXJYRKZNBQV4KMS","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"LVXJYRKZ","created_at":"2026-05-18T12:27:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:LVXJYRKZNBQV4KMS6FNLJVWHOV","target":"record","payload":{"canonical_record":{"source":{"id":"1307.0234","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-06-30T19:36:15Z","cross_cats_sorted":[],"title_canon_sha256":"f572e0fdb5253b11709a6d914daa3af23b8ce4b6c42ca38542cbc396332b03fb","abstract_canon_sha256":"b772c8714e9ece82e9e155193cf6a8acb9c168d024b03631c41143b50cf8eadb"},"schema_version":"1.0"},"canonical_sha256":"5d6e9c455968615e2992f15ab4d6c7754edffb4fb8b64b0eda9dd9a7bb49a638","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:19:33.900510Z","signature_b64":"HZOU4FbdXaUMMms+6d9L7YQJ9lEYXV85TgZx+NdqudDiobBPiUT/OeDbNvx7q3MrlGlbvpUiOoScZ+PL29q5BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5d6e9c455968615e2992f15ab4d6c7754edffb4fb8b64b0eda9dd9a7bb49a638","last_reissued_at":"2026-05-18T03:19:33.900029Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:19:33.900029Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.0234","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":"2026-05-18T03:19:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g/3sMQDba1Jm7fYFhs7eZkzJdGN5DNWdG6ZpVqGjaBqQ6HolEXmAPYbCQUoob5hTDJtN02LN5SV/T5i6UTJ/Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T04:53:40.035180Z"},"content_sha256":"5127a54cd17673e7b9d1e698cdf8b2070761d9e62095ba5651a34dd812c4e4fc","schema_version":"1.0","event_id":"sha256:5127a54cd17673e7b9d1e698cdf8b2070761d9e62095ba5651a34dd812c4e4fc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:LVXJYRKZNBQV4KMS6FNLJVWHOV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Regularity and Bernstein-type results for nonlocal minimal surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alessio Figalli, Enrico Valdinoci","submitted_at":"2013-06-30T19:36:15Z","abstract_excerpt":"We prove that, in every dimension, Lipschitz nonlocal minimal surfaces are smooth. Also, we extend to the nonlocal setting a famous theorem of De Giorgi stating that the validity of Bernstein's theorem in dimension $n+1$ is a consequence of the nonexistence of $n$-dimensional singular minimal cones in $\\R^n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.0234","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":"2026-05-18T03:19:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cUW6MHSdgHPQGY68INMUgrAgC2fyUJ62Tno8i4bJFCdx8OGm5roFCR5Fn3r1BIQzDEAZg9Wj7V2HLfQ5xAgSBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T04:53:40.035855Z"},"content_sha256":"c1535a0a9cde2d02483e6b5ae0889e8961da26cf985c857f8118e4503e36b651","schema_version":"1.0","event_id":"sha256:c1535a0a9cde2d02483e6b5ae0889e8961da26cf985c857f8118e4503e36b651"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LVXJYRKZNBQV4KMS6FNLJVWHOV/bundle.json","state_url":"https://pith.science/pith/LVXJYRKZNBQV4KMS6FNLJVWHOV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LVXJYRKZNBQV4KMS6FNLJVWHOV/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":"2026-06-05T04:53:40Z","links":{"resolver":"https://pith.science/pith/LVXJYRKZNBQV4KMS6FNLJVWHOV","bundle":"https://pith.science/pith/LVXJYRKZNBQV4KMS6FNLJVWHOV/bundle.json","state":"https://pith.science/pith/LVXJYRKZNBQV4KMS6FNLJVWHOV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LVXJYRKZNBQV4KMS6FNLJVWHOV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:LVXJYRKZNBQV4KMS6FNLJVWHOV","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":"b772c8714e9ece82e9e155193cf6a8acb9c168d024b03631c41143b50cf8eadb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-06-30T19:36:15Z","title_canon_sha256":"f572e0fdb5253b11709a6d914daa3af23b8ce4b6c42ca38542cbc396332b03fb"},"schema_version":"1.0","source":{"id":"1307.0234","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.0234","created_at":"2026-05-18T03:19:33Z"},{"alias_kind":"arxiv_version","alias_value":"1307.0234v1","created_at":"2026-05-18T03:19:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.0234","created_at":"2026-05-18T03:19:33Z"},{"alias_kind":"pith_short_12","alias_value":"LVXJYRKZNBQV","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"LVXJYRKZNBQV4KMS","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"LVXJYRKZ","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:c1535a0a9cde2d02483e6b5ae0889e8961da26cf985c857f8118e4503e36b651","target":"graph","created_at":"2026-05-18T03:19:33Z","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, in every dimension, Lipschitz nonlocal minimal surfaces are smooth. Also, we extend to the nonlocal setting a famous theorem of De Giorgi stating that the validity of Bernstein's theorem in dimension $n+1$ is a consequence of the nonexistence of $n$-dimensional singular minimal cones in $\\R^n$.","authors_text":"Alessio Figalli, Enrico Valdinoci","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-06-30T19:36:15Z","title":"Regularity and Bernstein-type results for nonlocal minimal surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.0234","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":"sha256:5127a54cd17673e7b9d1e698cdf8b2070761d9e62095ba5651a34dd812c4e4fc","target":"record","created_at":"2026-05-18T03:19:33Z","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":"b772c8714e9ece82e9e155193cf6a8acb9c168d024b03631c41143b50cf8eadb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-06-30T19:36:15Z","title_canon_sha256":"f572e0fdb5253b11709a6d914daa3af23b8ce4b6c42ca38542cbc396332b03fb"},"schema_version":"1.0","source":{"id":"1307.0234","kind":"arxiv","version":1}},"canonical_sha256":"5d6e9c455968615e2992f15ab4d6c7754edffb4fb8b64b0eda9dd9a7bb49a638","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5d6e9c455968615e2992f15ab4d6c7754edffb4fb8b64b0eda9dd9a7bb49a638","first_computed_at":"2026-05-18T03:19:33.900029Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:19:33.900029Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HZOU4FbdXaUMMms+6d9L7YQJ9lEYXV85TgZx+NdqudDiobBPiUT/OeDbNvx7q3MrlGlbvpUiOoScZ+PL29q5BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:19:33.900510Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.0234","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5127a54cd17673e7b9d1e698cdf8b2070761d9e62095ba5651a34dd812c4e4fc","sha256:c1535a0a9cde2d02483e6b5ae0889e8961da26cf985c857f8118e4503e36b651"],"state_sha256":"53a2141df8aedfd97a4daccc78ab8dd3f4e3464c7cdaa3920f25b05be03dd180"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j2z9Y5OxOrSn09BuXmU0lVUglD+y9hqwFotLQDuzVTM7VWFzVuzINEIsk6AifxJsIx0q2Bv3XeBa4tt5AxH5Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T04:53:40.039093Z","bundle_sha256":"1c98c6c854a1b0c8c0438e5f47673de9a8f49d9a28513c1c18ccd908085944dc"}}