{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:NJRM2VA7OYT6PB2NVM77BBV4D2","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":"cdf7d5e8c1ab806c4f2626de53e25dacde72edf486a0cfd586d153d421f9345a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-08T18:48:56Z","title_canon_sha256":"6936155f6400358f0ac982c2cc21bb5af97a23c0a8c00914745d9bf495f88b84"},"schema_version":"1.0","source":{"id":"1705.03046","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.03046","created_at":"2026-05-18T00:44:50Z"},{"alias_kind":"arxiv_version","alias_value":"1705.03046v1","created_at":"2026-05-18T00:44:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.03046","created_at":"2026-05-18T00:44:50Z"},{"alias_kind":"pith_short_12","alias_value":"NJRM2VA7OYT6","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"NJRM2VA7OYT6PB2N","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"NJRM2VA7","created_at":"2026-05-18T12:31:31Z"}],"graph_snapshots":[{"event_id":"sha256:4c0fd5882c16ff121cfd0b186be341c0c22695b241d7e51db9cafb1e227560ac","target":"graph","created_at":"2026-05-18T00:44:50Z","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 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","authors_text":"Ariel M. Salort, Joao V. da Silva, Julio D. Rossi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-08T18:48:56Z","title":"Uniform stability of the ball with respect to the first Dirichlet and Neumann $\\infty-$eigenvalues"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.03046","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":"sha256:6619419dfc78ace29c5b0deefdb7465b255f365a0975c68681a9ee8ab7afd2e2","target":"record","created_at":"2026-05-18T00:44:50Z","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":"cdf7d5e8c1ab806c4f2626de53e25dacde72edf486a0cfd586d153d421f9345a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-08T18:48:56Z","title_canon_sha256":"6936155f6400358f0ac982c2cc21bb5af97a23c0a8c00914745d9bf495f88b84"},"schema_version":"1.0","source":{"id":"1705.03046","kind":"arxiv","version":1}},"canonical_sha256":"6a62cd541f7627e7874dab3ff086bc1eab2d1c588df649b0154e41efc35af71e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6a62cd541f7627e7874dab3ff086bc1eab2d1c588df649b0154e41efc35af71e","first_computed_at":"2026-05-18T00:44:50.844674Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:50.844674Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LImBqTRz80CskPSSvYVrcQwZSszFeY/trMgPdb569WSu6Y1Ig2qRR2WDoNpmfUfOojaBP2gQS7aI0gTfEabBDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:50.845309Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.03046","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6619419dfc78ace29c5b0deefdb7465b255f365a0975c68681a9ee8ab7afd2e2","sha256:4c0fd5882c16ff121cfd0b186be341c0c22695b241d7e51db9cafb1e227560ac"],"state_sha256":"81e733f0658235cd50915f42c9a549945efa30d13dc1af52942a301ef2121480"}