{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:IR2JIF2W32BF3GZ2JHO6KYCGTC","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":"ced523c77c77c2d0d2da4d07856fc782462895e462a031fdd41b02961b782a66","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-21T13:54:37Z","title_canon_sha256":"771cafa41aa0cdc93e51d983c89d78ea3667f95145ee83ec2b3072ad4d936710"},"schema_version":"1.0","source":{"id":"1411.5872","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.5872","created_at":"2026-05-18T02:28:20Z"},{"alias_kind":"arxiv_version","alias_value":"1411.5872v2","created_at":"2026-05-18T02:28:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.5872","created_at":"2026-05-18T02:28:20Z"},{"alias_kind":"pith_short_12","alias_value":"IR2JIF2W32BF","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"IR2JIF2W32BF3GZ2","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"IR2JIF2W","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:761acbbbfe07b16ceb08f63b147064d1d588b8890d2ee05caed4dfd6db756af3","target":"graph","created_at":"2026-05-18T02:28:20Z","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":"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","authors_text":"F. Brock, F. Chiacchio, G. di Blasio","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-21T13:54:37Z","title":"Optimal Szeg\\\"o-Weinberger type inequalities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.5872","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":"sha256:36b72df8dadb547d6afec368c8d20f86d607a7f6b63d98e398a93c07e9fa9b1d","target":"record","created_at":"2026-05-18T02:28:20Z","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":"ced523c77c77c2d0d2da4d07856fc782462895e462a031fdd41b02961b782a66","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-21T13:54:37Z","title_canon_sha256":"771cafa41aa0cdc93e51d983c89d78ea3667f95145ee83ec2b3072ad4d936710"},"schema_version":"1.0","source":{"id":"1411.5872","kind":"arxiv","version":2}},"canonical_sha256":"4474941756de825d9b3a49dde56046989e840db6644fc8d1987eeee028d306e7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4474941756de825d9b3a49dde56046989e840db6644fc8d1987eeee028d306e7","first_computed_at":"2026-05-18T02:28:20.353749Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:20.353749Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FsoaOSCeZezM3kN9dO1gTVGxTm7cj1NCCLIlha/VrKILtlWRDshml2MnbKGPh8lVdpeGIngPxyJvaZcQO2m6BA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:20.354410Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.5872","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:36b72df8dadb547d6afec368c8d20f86d607a7f6b63d98e398a93c07e9fa9b1d","sha256:761acbbbfe07b16ceb08f63b147064d1d588b8890d2ee05caed4dfd6db756af3"],"state_sha256":"3f0a60bb428a4b97356e043917256a4e4096e6a65d21618bdb38a8b7bbba2895"}