{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:AW7TUGVCRZPW4CM6IDDOYQZQCA","short_pith_number":"pith:AW7TUGVC","schema_version":"1.0","canonical_sha256":"05bf3a1aa28e5f6e099e40c6ec4330103708d03a06a65da2d3a511db9f894a4f","source":{"kind":"arxiv","id":"1610.04200","version":2},"attestation_state":"computed","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"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"},"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"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1610.04200","created_at":"2026-05-18T00:49:06.484119+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.04200v2","created_at":"2026-05-18T00:49:06.484119+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.04200","created_at":"2026-05-18T00:49:06.484119+00:00"},{"alias_kind":"pith_short_12","alias_value":"AW7TUGVCRZPW","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_16","alias_value":"AW7TUGVCRZPW4CM6","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_8","alias_value":"AW7TUGVC","created_at":"2026-05-18T12:30:07.202191+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/AW7TUGVCRZPW4CM6IDDOYQZQCA","json":"https://pith.science/pith/AW7TUGVCRZPW4CM6IDDOYQZQCA.json","graph_json":"https://pith.science/api/pith-number/AW7TUGVCRZPW4CM6IDDOYQZQCA/graph.json","events_json":"https://pith.science/api/pith-number/AW7TUGVCRZPW4CM6IDDOYQZQCA/events.json","paper":"https://pith.science/paper/AW7TUGVC"},"agent_actions":{"view_html":"https://pith.science/pith/AW7TUGVCRZPW4CM6IDDOYQZQCA","download_json":"https://pith.science/pith/AW7TUGVCRZPW4CM6IDDOYQZQCA.json","view_paper":"https://pith.science/paper/AW7TUGVC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.04200&json=true","fetch_graph":"https://pith.science/api/pith-number/AW7TUGVCRZPW4CM6IDDOYQZQCA/graph.json","fetch_events":"https://pith.science/api/pith-number/AW7TUGVCRZPW4CM6IDDOYQZQCA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AW7TUGVCRZPW4CM6IDDOYQZQCA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AW7TUGVCRZPW4CM6IDDOYQZQCA/action/storage_attestation","attest_author":"https://pith.science/pith/AW7TUGVCRZPW4CM6IDDOYQZQCA/action/author_attestation","sign_citation":"https://pith.science/pith/AW7TUGVCRZPW4CM6IDDOYQZQCA/action/citation_signature","submit_replication":"https://pith.science/pith/AW7TUGVCRZPW4CM6IDDOYQZQCA/action/replication_record"}},"created_at":"2026-05-18T00:49:06.484119+00:00","updated_at":"2026-05-18T00:49:06.484119+00:00"}