{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:YIR7OKT6O7MNDOYCIOBHDNTZSB","short_pith_number":"pith:YIR7OKT6","schema_version":"1.0","canonical_sha256":"c223f72a7e77d8d1bb02438271b679906e6dead3fdc663375a4a50184a18637a","source":{"kind":"arxiv","id":"1501.04520","version":1},"attestation_state":"computed","paper":{"title":"Reverse Cheeger inequality for planar convex sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.OC","authors_text":"Enea Parini","submitted_at":"2015-01-19T15:20:02Z","abstract_excerpt":"We prove the sharp inequality \\[ J(\\Omega) := \\frac{\\lambda_1(\\Omega)}{h_1(\\Omega)^2} < \\frac{\\pi^2}{4},\\] where $\\Omega$ is any planar, convex set, $\\lambda_1(\\Omega)$ is the first eigenvalue of the Laplacian under Dirichlet boundary conditions, and $h_1(\\Omega)$ is the Cheeger constant of $\\Omega$. The value on the right-hand side is optimal, and any sequence of convex sets with fixed volume and diameter tending to infinity is a maximizing sequence. Morever, we discuss the minimization of $J$ in the same class of subsets: we provide a lower bound which improves the generic bound given by Che"},"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":"1501.04520","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-01-19T15:20:02Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"8bad3d27e2d48bbf36f19b2045fba316ef78b5265ef1fd3e353223ab719c5858","abstract_canon_sha256":"e5bbe931f05737b2186d455e0b7709297f3c8a1a6636ea3c07d56863f4c3b0b7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:08.812579Z","signature_b64":"6yCkA0Nna6MK5MSryFojZ+bVfR8JvPk1/G37ujFb9NNRPiLNqmiZKaW8JIQapHUI217232F5xK5m8Pk7ou2vDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c223f72a7e77d8d1bb02438271b679906e6dead3fdc663375a4a50184a18637a","last_reissued_at":"2026-05-18T02:29:08.811942Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:08.811942Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Reverse Cheeger inequality for planar convex sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.OC","authors_text":"Enea Parini","submitted_at":"2015-01-19T15:20:02Z","abstract_excerpt":"We prove the sharp inequality \\[ J(\\Omega) := \\frac{\\lambda_1(\\Omega)}{h_1(\\Omega)^2} < \\frac{\\pi^2}{4},\\] where $\\Omega$ is any planar, convex set, $\\lambda_1(\\Omega)$ is the first eigenvalue of the Laplacian under Dirichlet boundary conditions, and $h_1(\\Omega)$ is the Cheeger constant of $\\Omega$. The value on the right-hand side is optimal, and any sequence of convex sets with fixed volume and diameter tending to infinity is a maximizing sequence. Morever, we discuss the minimization of $J$ in the same class of subsets: we provide a lower bound which improves the generic bound given by Che"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.04520","kind":"arxiv","version":1},"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":"1501.04520","created_at":"2026-05-18T02:29:08.812032+00:00"},{"alias_kind":"arxiv_version","alias_value":"1501.04520v1","created_at":"2026-05-18T02:29:08.812032+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.04520","created_at":"2026-05-18T02:29:08.812032+00:00"},{"alias_kind":"pith_short_12","alias_value":"YIR7OKT6O7MN","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_16","alias_value":"YIR7OKT6O7MNDOYC","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_8","alias_value":"YIR7OKT6","created_at":"2026-05-18T12:29:50.041715+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/YIR7OKT6O7MNDOYCIOBHDNTZSB","json":"https://pith.science/pith/YIR7OKT6O7MNDOYCIOBHDNTZSB.json","graph_json":"https://pith.science/api/pith-number/YIR7OKT6O7MNDOYCIOBHDNTZSB/graph.json","events_json":"https://pith.science/api/pith-number/YIR7OKT6O7MNDOYCIOBHDNTZSB/events.json","paper":"https://pith.science/paper/YIR7OKT6"},"agent_actions":{"view_html":"https://pith.science/pith/YIR7OKT6O7MNDOYCIOBHDNTZSB","download_json":"https://pith.science/pith/YIR7OKT6O7MNDOYCIOBHDNTZSB.json","view_paper":"https://pith.science/paper/YIR7OKT6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1501.04520&json=true","fetch_graph":"https://pith.science/api/pith-number/YIR7OKT6O7MNDOYCIOBHDNTZSB/graph.json","fetch_events":"https://pith.science/api/pith-number/YIR7OKT6O7MNDOYCIOBHDNTZSB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YIR7OKT6O7MNDOYCIOBHDNTZSB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YIR7OKT6O7MNDOYCIOBHDNTZSB/action/storage_attestation","attest_author":"https://pith.science/pith/YIR7OKT6O7MNDOYCIOBHDNTZSB/action/author_attestation","sign_citation":"https://pith.science/pith/YIR7OKT6O7MNDOYCIOBHDNTZSB/action/citation_signature","submit_replication":"https://pith.science/pith/YIR7OKT6O7MNDOYCIOBHDNTZSB/action/replication_record"}},"created_at":"2026-05-18T02:29:08.812032+00:00","updated_at":"2026-05-18T02:29:08.812032+00:00"}