{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:VWILGZNXD7DERM2AK7333BVHVH","short_pith_number":"pith:VWILGZNX","schema_version":"1.0","canonical_sha256":"ad90b365b71fc648b34057f7bd86a7a9c7030a34c05f0a2225c112b333a1f9d4","source":{"kind":"arxiv","id":"1902.10587","version":2},"attestation_state":"computed","paper":{"title":"Nontrivial solutions to Serrin's problem in annular domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Luciano Sciaraffia, Nikola Kamburov","submitted_at":"2019-02-27T15:27:57Z","abstract_excerpt":"We construct nontrivial smooth bounded domains $\\Omega \\subseteq \\mathbb{R}^n$ of the form $\\Omega_0 \\setminus \\overline{\\Omega}_1$, bifurcating from annuli, for which there exists a positive solution to the overdetermined boundary value problem \\[\n  -\\Delta u = 1, \\; u>0 \\quad \\text{in } \\Omega, \\qquad\n  u = 0 ,\\; \\partial_\\nu u = \\text{const} \\quad \\text{on } \\partial\\Omega_0, \\qquad\n  u = \\text{const} ,\\; \\partial_\\nu u = \\text{const} \\quad \\text{on } \\partial \\Omega_1, \\] where $\\nu$ stands for the inner unit normal to $\\partial\\Omega$. From results by Reichel and later by Sirakov, it was "},"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":"1902.10587","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-02-27T15:27:57Z","cross_cats_sorted":[],"title_canon_sha256":"5c58f34432e43c1141bf81c1ad989fe3c0101d863da2a47caf741f73e7c191e7","abstract_canon_sha256":"3047fc9a51a773c4d49068cdb0c3af0ceae2f82424815db021bfd94b12489db5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:00.855519Z","signature_b64":"6iCfKg0wTCbCZ2dJg6NZYXh08kO/W+l0Dp7QdbS/4/t/MHFxq7s2D26aguEgnGCEBI9Df42Y1Qa4UW8GRiGqBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ad90b365b71fc648b34057f7bd86a7a9c7030a34c05f0a2225c112b333a1f9d4","last_reissued_at":"2026-05-17T23:52:00.855030Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:00.855030Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nontrivial solutions to Serrin's problem in annular domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Luciano Sciaraffia, Nikola Kamburov","submitted_at":"2019-02-27T15:27:57Z","abstract_excerpt":"We construct nontrivial smooth bounded domains $\\Omega \\subseteq \\mathbb{R}^n$ of the form $\\Omega_0 \\setminus \\overline{\\Omega}_1$, bifurcating from annuli, for which there exists a positive solution to the overdetermined boundary value problem \\[\n  -\\Delta u = 1, \\; u>0 \\quad \\text{in } \\Omega, \\qquad\n  u = 0 ,\\; \\partial_\\nu u = \\text{const} \\quad \\text{on } \\partial\\Omega_0, \\qquad\n  u = \\text{const} ,\\; \\partial_\\nu u = \\text{const} \\quad \\text{on } \\partial \\Omega_1, \\] where $\\nu$ stands for the inner unit normal to $\\partial\\Omega$. From results by Reichel and later by Sirakov, it was "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.10587","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":"1902.10587","created_at":"2026-05-17T23:52:00.855102+00:00"},{"alias_kind":"arxiv_version","alias_value":"1902.10587v2","created_at":"2026-05-17T23:52:00.855102+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.10587","created_at":"2026-05-17T23:52:00.855102+00:00"},{"alias_kind":"pith_short_12","alias_value":"VWILGZNXD7DE","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_16","alias_value":"VWILGZNXD7DERM2A","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_8","alias_value":"VWILGZNX","created_at":"2026-05-18T12:33:30.264802+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/VWILGZNXD7DERM2AK7333BVHVH","json":"https://pith.science/pith/VWILGZNXD7DERM2AK7333BVHVH.json","graph_json":"https://pith.science/api/pith-number/VWILGZNXD7DERM2AK7333BVHVH/graph.json","events_json":"https://pith.science/api/pith-number/VWILGZNXD7DERM2AK7333BVHVH/events.json","paper":"https://pith.science/paper/VWILGZNX"},"agent_actions":{"view_html":"https://pith.science/pith/VWILGZNXD7DERM2AK7333BVHVH","download_json":"https://pith.science/pith/VWILGZNXD7DERM2AK7333BVHVH.json","view_paper":"https://pith.science/paper/VWILGZNX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1902.10587&json=true","fetch_graph":"https://pith.science/api/pith-number/VWILGZNXD7DERM2AK7333BVHVH/graph.json","fetch_events":"https://pith.science/api/pith-number/VWILGZNXD7DERM2AK7333BVHVH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VWILGZNXD7DERM2AK7333BVHVH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VWILGZNXD7DERM2AK7333BVHVH/action/storage_attestation","attest_author":"https://pith.science/pith/VWILGZNXD7DERM2AK7333BVHVH/action/author_attestation","sign_citation":"https://pith.science/pith/VWILGZNXD7DERM2AK7333BVHVH/action/citation_signature","submit_replication":"https://pith.science/pith/VWILGZNXD7DERM2AK7333BVHVH/action/replication_record"}},"created_at":"2026-05-17T23:52:00.855102+00:00","updated_at":"2026-05-17T23:52:00.855102+00:00"}