{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:SVEYJNOG3AAD7VHDNQDTA7PG27","short_pith_number":"pith:SVEYJNOG","schema_version":"1.0","canonical_sha256":"954984b5c6d8003fd4e36c07307de6d7f458cbfa049a41ff32dd668e01974ac4","source":{"kind":"arxiv","id":"1503.06904","version":4},"attestation_state":"computed","paper":{"title":"The PPW conjecture in curved spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Nick Edelen","submitted_at":"2015-03-24T03:47:49Z","abstract_excerpt":"In Euclidean and Hyperbolic space, and the hemisphere in $S^n$, geodesic balls maximize the gap $\\lambda_2 - \\lambda_1$ of Dirichlet eigenvalues, amoung domains with fixed $\\lambda_1$. We prove an upper bound on $\\lambda_2 - \\lambda_1$ for domains in manifolds with certain curvature bounds. The inequality is sharp on geodesic balls in spaceforms."},"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":"1503.06904","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-03-24T03:47:49Z","cross_cats_sorted":[],"title_canon_sha256":"32ed63c90376960d8dcca193a5ce25a168878165ac96cd9892db5e09fe89ec89","abstract_canon_sha256":"ae07fb4ba0fc6ddf91b924aa32e03deeb92ccda41315f72eecf6b2d4719a1744"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:54:09.116164Z","signature_b64":"td9Czen/5yJIw3CV7hXanrD8rgX8hZ0fI+LPU2NiuBAxyTFGwn4eWAK9XnRAIPjhlkuwOBlqEcQn5YqGP2lyBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"954984b5c6d8003fd4e36c07307de6d7f458cbfa049a41ff32dd668e01974ac4","last_reissued_at":"2026-05-18T00:54:09.115783Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:54:09.115783Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The PPW conjecture in curved spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Nick Edelen","submitted_at":"2015-03-24T03:47:49Z","abstract_excerpt":"In Euclidean and Hyperbolic space, and the hemisphere in $S^n$, geodesic balls maximize the gap $\\lambda_2 - \\lambda_1$ of Dirichlet eigenvalues, amoung domains with fixed $\\lambda_1$. We prove an upper bound on $\\lambda_2 - \\lambda_1$ for domains in manifolds with certain curvature bounds. The inequality is sharp on geodesic balls in spaceforms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.06904","kind":"arxiv","version":4},"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":"1503.06904","created_at":"2026-05-18T00:54:09.115842+00:00"},{"alias_kind":"arxiv_version","alias_value":"1503.06904v4","created_at":"2026-05-18T00:54:09.115842+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.06904","created_at":"2026-05-18T00:54:09.115842+00:00"},{"alias_kind":"pith_short_12","alias_value":"SVEYJNOG3AAD","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_16","alias_value":"SVEYJNOG3AAD7VHD","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_8","alias_value":"SVEYJNOG","created_at":"2026-05-18T12:29:42.218222+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/SVEYJNOG3AAD7VHDNQDTA7PG27","json":"https://pith.science/pith/SVEYJNOG3AAD7VHDNQDTA7PG27.json","graph_json":"https://pith.science/api/pith-number/SVEYJNOG3AAD7VHDNQDTA7PG27/graph.json","events_json":"https://pith.science/api/pith-number/SVEYJNOG3AAD7VHDNQDTA7PG27/events.json","paper":"https://pith.science/paper/SVEYJNOG"},"agent_actions":{"view_html":"https://pith.science/pith/SVEYJNOG3AAD7VHDNQDTA7PG27","download_json":"https://pith.science/pith/SVEYJNOG3AAD7VHDNQDTA7PG27.json","view_paper":"https://pith.science/paper/SVEYJNOG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1503.06904&json=true","fetch_graph":"https://pith.science/api/pith-number/SVEYJNOG3AAD7VHDNQDTA7PG27/graph.json","fetch_events":"https://pith.science/api/pith-number/SVEYJNOG3AAD7VHDNQDTA7PG27/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SVEYJNOG3AAD7VHDNQDTA7PG27/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SVEYJNOG3AAD7VHDNQDTA7PG27/action/storage_attestation","attest_author":"https://pith.science/pith/SVEYJNOG3AAD7VHDNQDTA7PG27/action/author_attestation","sign_citation":"https://pith.science/pith/SVEYJNOG3AAD7VHDNQDTA7PG27/action/citation_signature","submit_replication":"https://pith.science/pith/SVEYJNOG3AAD7VHDNQDTA7PG27/action/replication_record"}},"created_at":"2026-05-18T00:54:09.115842+00:00","updated_at":"2026-05-18T00:54:09.115842+00:00"}