{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:IR2JIF2W32BF3GZ2JHO6KYCGTC","short_pith_number":"pith:IR2JIF2W","schema_version":"1.0","canonical_sha256":"4474941756de825d9b3a49dde56046989e840db6644fc8d1987eeee028d306e7","source":{"kind":"arxiv","id":"1411.5872","version":2},"attestation_state":"computed","paper":{"title":"Optimal Szeg\\\"o-Weinberger type inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"F. Brock, F. Chiacchio, G. di Blasio","submitted_at":"2014-11-21T13:54:37Z","abstract_excerpt":"Denote with $\\mu_{1}(\\Omega;e^{h\\left(|x|\\right)})$ the first nontrivial eigenvalue of the Neumann problem \\begin{equation*} \\left\\{\\begin{array}{lll} -\\text{div}\\left(e^{h\\left(|x|\\right)}\\nabla u\\right) =\\mu e^{h\\left(|x|\\right)}u & \\text{in} & \\Omega & & \\frac{\\partial u}{\\partial \\nu}=0 & \\text{on} & \\partial \\Omega , \\end{array} \\right. \\end{equation*} where $\\Omega $ is a bounded and Lipschitz domain in $\\mathbb{R}^{N}$. Under suitable assumption on $h$ we prove that the ball centered at the origin is the unique set maximizing $\\mu_{1}(\\Omega;e^{h\\left(|x|\\right)})$ among all Lipschitz b"},"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":"1411.5872","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-21T13:54:37Z","cross_cats_sorted":[],"title_canon_sha256":"771cafa41aa0cdc93e51d983c89d78ea3667f95145ee83ec2b3072ad4d936710","abstract_canon_sha256":"ced523c77c77c2d0d2da4d07856fc782462895e462a031fdd41b02961b782a66"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:28:20.354410Z","signature_b64":"FsoaOSCeZezM3kN9dO1gTVGxTm7cj1NCCLIlha/VrKILtlWRDshml2MnbKGPh8lVdpeGIngPxyJvaZcQO2m6BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4474941756de825d9b3a49dde56046989e840db6644fc8d1987eeee028d306e7","last_reissued_at":"2026-05-18T02:28:20.353749Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:28:20.353749Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Optimal Szeg\\\"o-Weinberger type inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"F. Brock, F. Chiacchio, G. di Blasio","submitted_at":"2014-11-21T13:54:37Z","abstract_excerpt":"Denote with $\\mu_{1}(\\Omega;e^{h\\left(|x|\\right)})$ the first nontrivial eigenvalue of the Neumann problem \\begin{equation*} \\left\\{\\begin{array}{lll} -\\text{div}\\left(e^{h\\left(|x|\\right)}\\nabla u\\right) =\\mu e^{h\\left(|x|\\right)}u & \\text{in} & \\Omega & & \\frac{\\partial u}{\\partial \\nu}=0 & \\text{on} & \\partial \\Omega , \\end{array} \\right. \\end{equation*} where $\\Omega $ is a bounded and Lipschitz domain in $\\mathbb{R}^{N}$. Under suitable assumption on $h$ we prove that the ball centered at the origin is the unique set maximizing $\\mu_{1}(\\Omega;e^{h\\left(|x|\\right)})$ among all Lipschitz b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.5872","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":"1411.5872","created_at":"2026-05-18T02:28:20.353886+00:00"},{"alias_kind":"arxiv_version","alias_value":"1411.5872v2","created_at":"2026-05-18T02:28:20.353886+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.5872","created_at":"2026-05-18T02:28:20.353886+00:00"},{"alias_kind":"pith_short_12","alias_value":"IR2JIF2W32BF","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_16","alias_value":"IR2JIF2W32BF3GZ2","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_8","alias_value":"IR2JIF2W","created_at":"2026-05-18T12:28:33.132498+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/IR2JIF2W32BF3GZ2JHO6KYCGTC","json":"https://pith.science/pith/IR2JIF2W32BF3GZ2JHO6KYCGTC.json","graph_json":"https://pith.science/api/pith-number/IR2JIF2W32BF3GZ2JHO6KYCGTC/graph.json","events_json":"https://pith.science/api/pith-number/IR2JIF2W32BF3GZ2JHO6KYCGTC/events.json","paper":"https://pith.science/paper/IR2JIF2W"},"agent_actions":{"view_html":"https://pith.science/pith/IR2JIF2W32BF3GZ2JHO6KYCGTC","download_json":"https://pith.science/pith/IR2JIF2W32BF3GZ2JHO6KYCGTC.json","view_paper":"https://pith.science/paper/IR2JIF2W","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1411.5872&json=true","fetch_graph":"https://pith.science/api/pith-number/IR2JIF2W32BF3GZ2JHO6KYCGTC/graph.json","fetch_events":"https://pith.science/api/pith-number/IR2JIF2W32BF3GZ2JHO6KYCGTC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IR2JIF2W32BF3GZ2JHO6KYCGTC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IR2JIF2W32BF3GZ2JHO6KYCGTC/action/storage_attestation","attest_author":"https://pith.science/pith/IR2JIF2W32BF3GZ2JHO6KYCGTC/action/author_attestation","sign_citation":"https://pith.science/pith/IR2JIF2W32BF3GZ2JHO6KYCGTC/action/citation_signature","submit_replication":"https://pith.science/pith/IR2JIF2W32BF3GZ2JHO6KYCGTC/action/replication_record"}},"created_at":"2026-05-18T02:28:20.353886+00:00","updated_at":"2026-05-18T02:28:20.353886+00:00"}