{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:NJRM2VA7OYT6PB2NVM77BBV4D2","short_pith_number":"pith:NJRM2VA7","schema_version":"1.0","canonical_sha256":"6a62cd541f7627e7874dab3ff086bc1eab2d1c588df649b0154e41efc35af71e","source":{"kind":"arxiv","id":"1705.03046","version":1},"attestation_state":"computed","paper":{"title":"Uniform stability of the ball with respect to the first Dirichlet and Neumann $\\infty-$eigenvalues","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ariel M. Salort, Joao V. da Silva, Julio D. Rossi","submitted_at":"2017-05-08T18:48:56Z","abstract_excerpt":"In this note we analyze how perturbations of a ball $\\mathfrak{B}_r \\subset \\mathbb{R}^n$ behaves in terms of their first (non-trivial) Neumann and Dirichlet $\\infty-$eigenvalues when a volume constraint $\\\\mathscr{L}^n(\\Omega) = \\mathscr{L}^n(\\mathfrak{B}_r)$ is imposed. Our main result states that $\\Omega$ is uniformly close to a ball when it has first Neumann and Dirichlet eigenvalues close to the ones for the ball of the same volume $\\mathfrak{B}_r$. In fact, we show that, if $$\n  |\\lambda_{1,\\infty}^D(\\Omega) - \\lambda_{1,\\infty}^D(\\mathfrak{B}_r)| = \\delta_1 \\quad \\text{and} \\quad |\\lamb"},"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":"1705.03046","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-08T18:48:56Z","cross_cats_sorted":[],"title_canon_sha256":"6936155f6400358f0ac982c2cc21bb5af97a23c0a8c00914745d9bf495f88b84","abstract_canon_sha256":"cdf7d5e8c1ab806c4f2626de53e25dacde72edf486a0cfd586d153d421f9345a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:50.845309Z","signature_b64":"LImBqTRz80CskPSSvYVrcQwZSszFeY/trMgPdb569WSu6Y1Ig2qRR2WDoNpmfUfOojaBP2gQS7aI0gTfEabBDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6a62cd541f7627e7874dab3ff086bc1eab2d1c588df649b0154e41efc35af71e","last_reissued_at":"2026-05-18T00:44:50.844674Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:50.844674Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Uniform stability of the ball with respect to the first Dirichlet and Neumann $\\infty-$eigenvalues","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ariel M. Salort, Joao V. da Silva, Julio D. Rossi","submitted_at":"2017-05-08T18:48:56Z","abstract_excerpt":"In this note we analyze how perturbations of a ball $\\mathfrak{B}_r \\subset \\mathbb{R}^n$ behaves in terms of their first (non-trivial) Neumann and Dirichlet $\\infty-$eigenvalues when a volume constraint $\\\\mathscr{L}^n(\\Omega) = \\mathscr{L}^n(\\mathfrak{B}_r)$ is imposed. Our main result states that $\\Omega$ is uniformly close to a ball when it has first Neumann and Dirichlet eigenvalues close to the ones for the ball of the same volume $\\mathfrak{B}_r$. In fact, we show that, if $$\n  |\\lambda_{1,\\infty}^D(\\Omega) - \\lambda_{1,\\infty}^D(\\mathfrak{B}_r)| = \\delta_1 \\quad \\text{and} \\quad |\\lamb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.03046","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":"1705.03046","created_at":"2026-05-18T00:44:50.844769+00:00"},{"alias_kind":"arxiv_version","alias_value":"1705.03046v1","created_at":"2026-05-18T00:44:50.844769+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.03046","created_at":"2026-05-18T00:44:50.844769+00:00"},{"alias_kind":"pith_short_12","alias_value":"NJRM2VA7OYT6","created_at":"2026-05-18T12:31:31.346846+00:00"},{"alias_kind":"pith_short_16","alias_value":"NJRM2VA7OYT6PB2N","created_at":"2026-05-18T12:31:31.346846+00:00"},{"alias_kind":"pith_short_8","alias_value":"NJRM2VA7","created_at":"2026-05-18T12:31:31.346846+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/NJRM2VA7OYT6PB2NVM77BBV4D2","json":"https://pith.science/pith/NJRM2VA7OYT6PB2NVM77BBV4D2.json","graph_json":"https://pith.science/api/pith-number/NJRM2VA7OYT6PB2NVM77BBV4D2/graph.json","events_json":"https://pith.science/api/pith-number/NJRM2VA7OYT6PB2NVM77BBV4D2/events.json","paper":"https://pith.science/paper/NJRM2VA7"},"agent_actions":{"view_html":"https://pith.science/pith/NJRM2VA7OYT6PB2NVM77BBV4D2","download_json":"https://pith.science/pith/NJRM2VA7OYT6PB2NVM77BBV4D2.json","view_paper":"https://pith.science/paper/NJRM2VA7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1705.03046&json=true","fetch_graph":"https://pith.science/api/pith-number/NJRM2VA7OYT6PB2NVM77BBV4D2/graph.json","fetch_events":"https://pith.science/api/pith-number/NJRM2VA7OYT6PB2NVM77BBV4D2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NJRM2VA7OYT6PB2NVM77BBV4D2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NJRM2VA7OYT6PB2NVM77BBV4D2/action/storage_attestation","attest_author":"https://pith.science/pith/NJRM2VA7OYT6PB2NVM77BBV4D2/action/author_attestation","sign_citation":"https://pith.science/pith/NJRM2VA7OYT6PB2NVM77BBV4D2/action/citation_signature","submit_replication":"https://pith.science/pith/NJRM2VA7OYT6PB2NVM77BBV4D2/action/replication_record"}},"created_at":"2026-05-18T00:44:50.844769+00:00","updated_at":"2026-05-18T00:44:50.844769+00:00"}