{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:AW7TUGVCRZPW4CM6IDDOYQZQCA","short_pith_number":"pith:AW7TUGVC","canonical_record":{"source":{"id":"1610.04200","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-13T19:02:49Z","cross_cats_sorted":[],"title_canon_sha256":"94238c37d4d68f5c993f93f9a055cd6bacf6c87189f457f5f7a70246901cec58","abstract_canon_sha256":"47e260c91e91bf19183a0946c1654c1722b1b0955b441b237e9d2ce2cce1f1be"},"schema_version":"1.0"},"canonical_sha256":"05bf3a1aa28e5f6e099e40c6ec4330103708d03a06a65da2d3a511db9f894a4f","source":{"kind":"arxiv","id":"1610.04200","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.04200","created_at":"2026-05-18T00:49:06Z"},{"alias_kind":"arxiv_version","alias_value":"1610.04200v2","created_at":"2026-05-18T00:49:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.04200","created_at":"2026-05-18T00:49:06Z"},{"alias_kind":"pith_short_12","alias_value":"AW7TUGVCRZPW","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"AW7TUGVCRZPW4CM6","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"AW7TUGVC","created_at":"2026-05-18T12:30:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:AW7TUGVCRZPW4CM6IDDOYQZQCA","target":"record","payload":{"canonical_record":{"source":{"id":"1610.04200","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-13T19:02:49Z","cross_cats_sorted":[],"title_canon_sha256":"94238c37d4d68f5c993f93f9a055cd6bacf6c87189f457f5f7a70246901cec58","abstract_canon_sha256":"47e260c91e91bf19183a0946c1654c1722b1b0955b441b237e9d2ce2cce1f1be"},"schema_version":"1.0"},"canonical_sha256":"05bf3a1aa28e5f6e099e40c6ec4330103708d03a06a65da2d3a511db9f894a4f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:49:06.484543Z","signature_b64":"5g7D+yte2kA6OvkNg0dM/pHfMKhId8q0lvmVDE60FvQpcLW65KM8c7Wa8DCa3Rfb1eYaHi//Mg/Ul014CF0DDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"05bf3a1aa28e5f6e099e40c6ec4330103708d03a06a65da2d3a511db9f894a4f","last_reissued_at":"2026-05-18T00:49:06.484041Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:49:06.484041Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.04200","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":"2026-05-18T00:49:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dAZGyW1W7SyOS9tIhKD3rzyYfs0a8fV9VeG7F80MEq+ibFK3l61OwIs8a3K1eYChwGhQ+McmMxjwfLyGx05pDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T12:01:35.841709Z"},"content_sha256":"e9ba8948016be8948d241791fd3a83deaf32d926cc4e845c8bf124842c3efdca","schema_version":"1.0","event_id":"sha256:e9ba8948016be8948d241791fd3a83deaf32d926cc4e845c8bf124842c3efdca"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:AW7TUGVCRZPW4CM6IDDOYQZQCA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The obstacle problem for the fractional Laplacian with critical drift","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Xavier Fern\\'andez-Real, Xavier Ros-Oton","submitted_at":"2016-10-13T19:02:49Z","abstract_excerpt":"We study the obstacle problem for the fractional Laplacian with drift, $\\min\\left\\{(-\\Delta)^s u + b \\cdot \\nabla u,\\,u -\\varphi\\right\\} = 0$ in $\\mathbb{R}^n$, in the critical regime $s = \\frac{1}{2}$.\n  Our main result establishes the $C^{1,\\alpha}$ regularity of the free boundary around any regular point $x_0$, with an expansion of the form \\[ u(x)-\\varphi(x) = c_0\\big((x-x_0)\\cdot e\\big)_+^{1+\\tilde\\gamma(x_0)} + o\\left(|x-x_0|^{1+\\tilde\\gamma(x_0)+\\sigma}\\right), \\] \\[ \\tilde{\\gamma}(x_0) = \\frac{1}{2}+\\frac{1}{\\pi} \\arctan (b\\cdot e), \\] where $e \\in \\mathbb{S}^{n-1}$ is the normal vecto"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.04200","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":"2026-05-18T00:49:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XPL0SoZnOCjMo3fjSq0Nf/z463NpI3u7XCUVnDhEGsQpCdj/lx2fIDtENqC60dTTAzdWxwnljGEfWYpch1RmCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T12:01:35.842047Z"},"content_sha256":"b781a96a4168d9561e47a91ca02b56717744739ccac8e840a45c6dce0cb9c43f","schema_version":"1.0","event_id":"sha256:b781a96a4168d9561e47a91ca02b56717744739ccac8e840a45c6dce0cb9c43f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AW7TUGVCRZPW4CM6IDDOYQZQCA/bundle.json","state_url":"https://pith.science/pith/AW7TUGVCRZPW4CM6IDDOYQZQCA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AW7TUGVCRZPW4CM6IDDOYQZQCA/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":"2026-06-29T12:01:35Z","links":{"resolver":"https://pith.science/pith/AW7TUGVCRZPW4CM6IDDOYQZQCA","bundle":"https://pith.science/pith/AW7TUGVCRZPW4CM6IDDOYQZQCA/bundle.json","state":"https://pith.science/pith/AW7TUGVCRZPW4CM6IDDOYQZQCA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AW7TUGVCRZPW4CM6IDDOYQZQCA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:AW7TUGVCRZPW4CM6IDDOYQZQCA","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":"47e260c91e91bf19183a0946c1654c1722b1b0955b441b237e9d2ce2cce1f1be","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-13T19:02:49Z","title_canon_sha256":"94238c37d4d68f5c993f93f9a055cd6bacf6c87189f457f5f7a70246901cec58"},"schema_version":"1.0","source":{"id":"1610.04200","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.04200","created_at":"2026-05-18T00:49:06Z"},{"alias_kind":"arxiv_version","alias_value":"1610.04200v2","created_at":"2026-05-18T00:49:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.04200","created_at":"2026-05-18T00:49:06Z"},{"alias_kind":"pith_short_12","alias_value":"AW7TUGVCRZPW","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"AW7TUGVCRZPW4CM6","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"AW7TUGVC","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:b781a96a4168d9561e47a91ca02b56717744739ccac8e840a45c6dce0cb9c43f","target":"graph","created_at":"2026-05-18T00:49:06Z","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 study the obstacle problem for the fractional Laplacian with drift, $\\min\\left\\{(-\\Delta)^s u + b \\cdot \\nabla u,\\,u -\\varphi\\right\\} = 0$ in $\\mathbb{R}^n$, in the critical regime $s = \\frac{1}{2}$.\n  Our main result establishes the $C^{1,\\alpha}$ regularity of the free boundary around any regular point $x_0$, with an expansion of the form \\[ u(x)-\\varphi(x) = c_0\\big((x-x_0)\\cdot e\\big)_+^{1+\\tilde\\gamma(x_0)} + o\\left(|x-x_0|^{1+\\tilde\\gamma(x_0)+\\sigma}\\right), \\] \\[ \\tilde{\\gamma}(x_0) = \\frac{1}{2}+\\frac{1}{\\pi} \\arctan (b\\cdot e), \\] where $e \\in \\mathbb{S}^{n-1}$ is the normal vecto","authors_text":"Xavier Fern\\'andez-Real, Xavier Ros-Oton","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-13T19:02:49Z","title":"The obstacle problem for the fractional Laplacian with critical drift"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.04200","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:e9ba8948016be8948d241791fd3a83deaf32d926cc4e845c8bf124842c3efdca","target":"record","created_at":"2026-05-18T00:49:06Z","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":"47e260c91e91bf19183a0946c1654c1722b1b0955b441b237e9d2ce2cce1f1be","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-13T19:02:49Z","title_canon_sha256":"94238c37d4d68f5c993f93f9a055cd6bacf6c87189f457f5f7a70246901cec58"},"schema_version":"1.0","source":{"id":"1610.04200","kind":"arxiv","version":2}},"canonical_sha256":"05bf3a1aa28e5f6e099e40c6ec4330103708d03a06a65da2d3a511db9f894a4f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"05bf3a1aa28e5f6e099e40c6ec4330103708d03a06a65da2d3a511db9f894a4f","first_computed_at":"2026-05-18T00:49:06.484041Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:49:06.484041Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5g7D+yte2kA6OvkNg0dM/pHfMKhId8q0lvmVDE60FvQpcLW65KM8c7Wa8DCa3Rfb1eYaHi//Mg/Ul014CF0DDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:49:06.484543Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.04200","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e9ba8948016be8948d241791fd3a83deaf32d926cc4e845c8bf124842c3efdca","sha256:b781a96a4168d9561e47a91ca02b56717744739ccac8e840a45c6dce0cb9c43f"],"state_sha256":"12ec55fe80c5b99023f3a01336a7b6aac1496042e84b01d5026ae92bb4719eb1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kivY/LyeyShUZzXLHrhId1q4i0R7yyKnSDNYAvemQszjevDHeDBTQA7I+OjI3IYJ2WHiQxZOEjt41cjnQmL4Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T12:01:35.843924Z","bundle_sha256":"8edc632b6df2e3c642320ffdb71b52b4c23a21f86129cec2a6a0f66481efee36"}}