{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:RCZK2GTZZJVPURAGBEOIJ5IFF2","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":"8ffd29cd6c1dffdc9fff843c1c05df9728f9e668fd01832310f996f1183cdab8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-01-23T08:31:47Z","title_canon_sha256":"29a217ac4ce81300c54f4e90a98b41cf6b91d1b3fa831cb7247bd1f07b187ed2"},"schema_version":"1.0","source":{"id":"1801.07435","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.07435","created_at":"2026-05-18T00:25:12Z"},{"alias_kind":"arxiv_version","alias_value":"1801.07435v1","created_at":"2026-05-18T00:25:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.07435","created_at":"2026-05-18T00:25:12Z"},{"alias_kind":"pith_short_12","alias_value":"RCZK2GTZZJVP","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"RCZK2GTZZJVPURAG","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"RCZK2GTZ","created_at":"2026-05-18T12:32:50Z"}],"graph_snapshots":[{"event_id":"sha256:d65e36a0c3469bd6b41c32e72fed5ac2fe3f812c9a112f817d2e84d432c507e1","target":"graph","created_at":"2026-05-18T00:25:12Z","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":"In this paper we prove that the second (non-trivial) Neumann eigenvalue of the Laplace operator on smooth domains of R N with prescribed measure m attains its maximum on the union of two disjoint balls of measure m 2. As a consequence, the P{\\'o}lya conjecture for the Neumann eigenvalues holds for the second eigenvalue and for arbitrary domains. We moreover prove that a relaxed form of the same inequality holds in the context of non-smooth domains and densities.","authors_text":"Antoine Henrot (EDP), Dorin Bucur (LAMA)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-01-23T08:31:47Z","title":"Maximization of the second non-trivial Neumann eigenvalue"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.07435","kind":"arxiv","version":1},"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:a51d78d9435d9b8cdb3aa96beceb1f8d5eeab2fde9614945146637229a4d65e0","target":"record","created_at":"2026-05-18T00:25:12Z","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":"8ffd29cd6c1dffdc9fff843c1c05df9728f9e668fd01832310f996f1183cdab8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-01-23T08:31:47Z","title_canon_sha256":"29a217ac4ce81300c54f4e90a98b41cf6b91d1b3fa831cb7247bd1f07b187ed2"},"schema_version":"1.0","source":{"id":"1801.07435","kind":"arxiv","version":1}},"canonical_sha256":"88b2ad1a79ca6afa4406091c84f5052e90033814e6b705b0cb953ef6f3d0def1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"88b2ad1a79ca6afa4406091c84f5052e90033814e6b705b0cb953ef6f3d0def1","first_computed_at":"2026-05-18T00:25:12.814283Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:25:12.814283Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CIPs5Tczebrgq163P9ZgOstfGh/ielJzCf9uBk7FBWWvcXO4cAQQ9s+AkHu898g5F5Y/nyx+9lTB0exWg7eYAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:25:12.814903Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.07435","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a51d78d9435d9b8cdb3aa96beceb1f8d5eeab2fde9614945146637229a4d65e0","sha256:d65e36a0c3469bd6b41c32e72fed5ac2fe3f812c9a112f817d2e84d432c507e1"],"state_sha256":"893e1fffd3a8aaaeb282c1e3e834a9582a1027cb1986d331c5686b5b2b4f1624"}