{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:XBG6CV7UODOAXMUF7WGMNRRPIR","short_pith_number":"pith:XBG6CV7U","canonical_record":{"source":{"id":"1506.04684","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-06-15T17:58:44Z","cross_cats_sorted":[],"title_canon_sha256":"78a025b8a97b29053028e37cebabbd194e98cddd2b41b3059e172a9c208cabb8","abstract_canon_sha256":"e33e49ed636be6df12e75344e02df293beafa69f38438cbce3564440aa56bd98"},"schema_version":"1.0"},"canonical_sha256":"b84de157f470dc0bb285fd8cc6c62f4475a8c4be23af66d6fdb416c46f2be6f3","source":{"kind":"arxiv","id":"1506.04684","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.04684","created_at":"2026-05-18T00:45:04Z"},{"alias_kind":"arxiv_version","alias_value":"1506.04684v2","created_at":"2026-05-18T00:45:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.04684","created_at":"2026-05-18T00:45:04Z"},{"alias_kind":"pith_short_12","alias_value":"XBG6CV7UODOA","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"XBG6CV7UODOAXMUF","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"XBG6CV7U","created_at":"2026-05-18T12:29:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:XBG6CV7UODOAXMUF7WGMNRRPIR","target":"record","payload":{"canonical_record":{"source":{"id":"1506.04684","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-06-15T17:58:44Z","cross_cats_sorted":[],"title_canon_sha256":"78a025b8a97b29053028e37cebabbd194e98cddd2b41b3059e172a9c208cabb8","abstract_canon_sha256":"e33e49ed636be6df12e75344e02df293beafa69f38438cbce3564440aa56bd98"},"schema_version":"1.0"},"canonical_sha256":"b84de157f470dc0bb285fd8cc6c62f4475a8c4be23af66d6fdb416c46f2be6f3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:04.311922Z","signature_b64":"UZQ+feqspfjcN+FmNZ8uyKZ35v5qULoLZyDZfNehwF3Mu3hqAq9Qf7z9VkJWG+IsrkXXn6P0fy+ZF350CvLaCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b84de157f470dc0bb285fd8cc6c62f4475a8c4be23af66d6fdb416c46f2be6f3","last_reissued_at":"2026-05-18T00:45:04.311573Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:04.311573Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.04684","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":"2026-05-18T00:45:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ps4qyi98d4w1IKqKuVsgBir5XOW2kypovfOHzToaBmmurMqyYbX8wO/BTbph5z4+DS5O/1cVuJpnndu2ioEHAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T16:42:13.784184Z"},"content_sha256":"93f54b3972928e439b3efa1f97b45b7f1c9196adc22f29f0873838baae46e8cc","schema_version":"1.0","event_id":"sha256:93f54b3972928e439b3efa1f97b45b7f1c9196adc22f29f0873838baae46e8cc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:XBG6CV7UODOAXMUF7WGMNRRPIR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Global regularity for the free boundary in the obstacle problem for the fractional Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alessio Figalli, Bego\\~na Barrios, Xavier Ros-Oton","submitted_at":"2015-06-15T17:58:44Z","abstract_excerpt":"We study the regularity of the free boundary in the obstacle problem for the fractional Laplacian under the assumption that the obstacle $\\varphi$ satisfies $\\Delta \\varphi\\leq 0$ near the contact region. Our main result establishes that the free boundary consists of a set of regular points, which is known to be a $(n-1)$-dimensional $C^{1,\\alpha}$ manifold by the results in \\cite{CSS}, and a set of singular points, which we prove to be contained in a union of $k$-dimensional $C^1$-submanifold, $k=0,\\ldots,n-1$.\n  Such a complete result on the structure of the free boundary was known only in t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.04684","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":"2026-05-18T00:45:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SFdeZdlIQDkck31RZrmv3f7cVuDESyA4y5y7ENdnk164eCopvNRE5+cSabTR6Vt/vS6GR1iCg+a+9u3uU2TEAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T16:42:13.784558Z"},"content_sha256":"354789ac63eca39175c7b6230a4dd7c594ce65466fcbe43aa39424af1d287141","schema_version":"1.0","event_id":"sha256:354789ac63eca39175c7b6230a4dd7c594ce65466fcbe43aa39424af1d287141"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XBG6CV7UODOAXMUF7WGMNRRPIR/bundle.json","state_url":"https://pith.science/pith/XBG6CV7UODOAXMUF7WGMNRRPIR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XBG6CV7UODOAXMUF7WGMNRRPIR/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":"2026-06-09T16:42:13Z","links":{"resolver":"https://pith.science/pith/XBG6CV7UODOAXMUF7WGMNRRPIR","bundle":"https://pith.science/pith/XBG6CV7UODOAXMUF7WGMNRRPIR/bundle.json","state":"https://pith.science/pith/XBG6CV7UODOAXMUF7WGMNRRPIR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XBG6CV7UODOAXMUF7WGMNRRPIR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:XBG6CV7UODOAXMUF7WGMNRRPIR","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":"e33e49ed636be6df12e75344e02df293beafa69f38438cbce3564440aa56bd98","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-06-15T17:58:44Z","title_canon_sha256":"78a025b8a97b29053028e37cebabbd194e98cddd2b41b3059e172a9c208cabb8"},"schema_version":"1.0","source":{"id":"1506.04684","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.04684","created_at":"2026-05-18T00:45:04Z"},{"alias_kind":"arxiv_version","alias_value":"1506.04684v2","created_at":"2026-05-18T00:45:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.04684","created_at":"2026-05-18T00:45:04Z"},{"alias_kind":"pith_short_12","alias_value":"XBG6CV7UODOA","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"XBG6CV7UODOAXMUF","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"XBG6CV7U","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:354789ac63eca39175c7b6230a4dd7c594ce65466fcbe43aa39424af1d287141","target":"graph","created_at":"2026-05-18T00:45:04Z","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 the regularity of the free boundary in the obstacle problem for the fractional Laplacian under the assumption that the obstacle $\\varphi$ satisfies $\\Delta \\varphi\\leq 0$ near the contact region. Our main result establishes that the free boundary consists of a set of regular points, which is known to be a $(n-1)$-dimensional $C^{1,\\alpha}$ manifold by the results in \\cite{CSS}, and a set of singular points, which we prove to be contained in a union of $k$-dimensional $C^1$-submanifold, $k=0,\\ldots,n-1$.\n  Such a complete result on the structure of the free boundary was known only in t","authors_text":"Alessio Figalli, Bego\\~na Barrios, Xavier Ros-Oton","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-06-15T17:58:44Z","title":"Global regularity for the free boundary in the obstacle problem for the fractional Laplacian"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.04684","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":"sha256:93f54b3972928e439b3efa1f97b45b7f1c9196adc22f29f0873838baae46e8cc","target":"record","created_at":"2026-05-18T00:45:04Z","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":"e33e49ed636be6df12e75344e02df293beafa69f38438cbce3564440aa56bd98","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-06-15T17:58:44Z","title_canon_sha256":"78a025b8a97b29053028e37cebabbd194e98cddd2b41b3059e172a9c208cabb8"},"schema_version":"1.0","source":{"id":"1506.04684","kind":"arxiv","version":2}},"canonical_sha256":"b84de157f470dc0bb285fd8cc6c62f4475a8c4be23af66d6fdb416c46f2be6f3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b84de157f470dc0bb285fd8cc6c62f4475a8c4be23af66d6fdb416c46f2be6f3","first_computed_at":"2026-05-18T00:45:04.311573Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:04.311573Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UZQ+feqspfjcN+FmNZ8uyKZ35v5qULoLZyDZfNehwF3Mu3hqAq9Qf7z9VkJWG+IsrkXXn6P0fy+ZF350CvLaCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:04.311922Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.04684","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:93f54b3972928e439b3efa1f97b45b7f1c9196adc22f29f0873838baae46e8cc","sha256:354789ac63eca39175c7b6230a4dd7c594ce65466fcbe43aa39424af1d287141"],"state_sha256":"06d0d6a8b7d460bf108313fd16c5cc85ada89d721c8e3f73914c00da530021bf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bPo5IEzUQT2Ua6Q3yJNKzV9zjNqZb9WXAe6lIV2dtXOYXBvALDg8wMh1tS2HLM51emELpws3o9Hqa1o7PytgDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T16:42:13.786457Z","bundle_sha256":"d8d577549cd47db4724d02eb03bf19cd57e804ae26af75f981c973fafb9ec637"}}