{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:KHF3KHEAYGJJFTRRF7L7AQC5T2","short_pith_number":"pith:KHF3KHEA","schema_version":"1.0","canonical_sha256":"51cbb51c80c19292ce312fd7f0405d9eb9595a2afbbe9969b9ac4acfe1c268f9","source":{"kind":"arxiv","id":"1608.01236","version":2},"attestation_state":"computed","paper":{"title":"Sharp Poincar\\'e inequalities in a class of non-convex sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.SP","authors_text":"B. Brandolini, E. B. Dryden, F. Chiacchio, J. J. Langford","submitted_at":"2016-08-03T16:06:40Z","abstract_excerpt":"Let $\\gamma$ be a smooth, non-closed, simple curve whose image is symmetric with respect to the $y$-axis, and let $D$ be a planar domain consisting of the points on one side of $\\gamma$, within a suitable distance $\\delta$ of $\\gamma$. Denote by $\\mu_1^{odd}(D)$ the smallest nontrivial Neumann eigenvalue having a corresponding eigenfunction that is odd with respect to the $y$-axis. If $\\gamma$ satisfies some simple geometric conditions, then $\\mu_1^{odd}(D)$ can be sharply estimated from below in terms of the length of $\\gamma$, its curvature, and $\\delta$. Moreover, we give explicit condition"},"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":"1608.01236","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2016-08-03T16:06:40Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"9be3f9b3f2de48925cc7b0a44c353d70b2209b2c9bf8e29600b2a1d8784e4162","abstract_canon_sha256":"548934285818be781d3961b089ff47e648a0ac409dce39037461b275b30428a3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:04.425402Z","signature_b64":"aTa/DVcod8ck1q+gcHDxCvCqJK7BEQSgYkQ+IORTAweRDj4JGUbCuicOX01gSQvKTLBBA5Yll+OeOE/xFysTDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"51cbb51c80c19292ce312fd7f0405d9eb9595a2afbbe9969b9ac4acfe1c268f9","last_reissued_at":"2026-05-18T00:10:04.424687Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:04.424687Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sharp Poincar\\'e inequalities in a class of non-convex sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.SP","authors_text":"B. Brandolini, E. B. Dryden, F. Chiacchio, J. J. Langford","submitted_at":"2016-08-03T16:06:40Z","abstract_excerpt":"Let $\\gamma$ be a smooth, non-closed, simple curve whose image is symmetric with respect to the $y$-axis, and let $D$ be a planar domain consisting of the points on one side of $\\gamma$, within a suitable distance $\\delta$ of $\\gamma$. Denote by $\\mu_1^{odd}(D)$ the smallest nontrivial Neumann eigenvalue having a corresponding eigenfunction that is odd with respect to the $y$-axis. If $\\gamma$ satisfies some simple geometric conditions, then $\\mu_1^{odd}(D)$ can be sharply estimated from below in terms of the length of $\\gamma$, its curvature, and $\\delta$. Moreover, we give explicit condition"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.01236","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":"1608.01236","created_at":"2026-05-18T00:10:04.424795+00:00"},{"alias_kind":"arxiv_version","alias_value":"1608.01236v2","created_at":"2026-05-18T00:10:04.424795+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.01236","created_at":"2026-05-18T00:10:04.424795+00:00"},{"alias_kind":"pith_short_12","alias_value":"KHF3KHEAYGJJ","created_at":"2026-05-18T12:30:25.849896+00:00"},{"alias_kind":"pith_short_16","alias_value":"KHF3KHEAYGJJFTRR","created_at":"2026-05-18T12:30:25.849896+00:00"},{"alias_kind":"pith_short_8","alias_value":"KHF3KHEA","created_at":"2026-05-18T12:30:25.849896+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/KHF3KHEAYGJJFTRRF7L7AQC5T2","json":"https://pith.science/pith/KHF3KHEAYGJJFTRRF7L7AQC5T2.json","graph_json":"https://pith.science/api/pith-number/KHF3KHEAYGJJFTRRF7L7AQC5T2/graph.json","events_json":"https://pith.science/api/pith-number/KHF3KHEAYGJJFTRRF7L7AQC5T2/events.json","paper":"https://pith.science/paper/KHF3KHEA"},"agent_actions":{"view_html":"https://pith.science/pith/KHF3KHEAYGJJFTRRF7L7AQC5T2","download_json":"https://pith.science/pith/KHF3KHEAYGJJFTRRF7L7AQC5T2.json","view_paper":"https://pith.science/paper/KHF3KHEA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1608.01236&json=true","fetch_graph":"https://pith.science/api/pith-number/KHF3KHEAYGJJFTRRF7L7AQC5T2/graph.json","fetch_events":"https://pith.science/api/pith-number/KHF3KHEAYGJJFTRRF7L7AQC5T2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KHF3KHEAYGJJFTRRF7L7AQC5T2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KHF3KHEAYGJJFTRRF7L7AQC5T2/action/storage_attestation","attest_author":"https://pith.science/pith/KHF3KHEAYGJJFTRRF7L7AQC5T2/action/author_attestation","sign_citation":"https://pith.science/pith/KHF3KHEAYGJJFTRRF7L7AQC5T2/action/citation_signature","submit_replication":"https://pith.science/pith/KHF3KHEAYGJJFTRRF7L7AQC5T2/action/replication_record"}},"created_at":"2026-05-18T00:10:04.424795+00:00","updated_at":"2026-05-18T00:10:04.424795+00:00"}