{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:JZKLAY4UGDIM2XTBC25AV7WQ7E","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":"dd27e37b5434ff122de34351e57d397b73d337bccde0704a3fc3d356e7ac8a10","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2016-02-19T08:53:28Z","title_canon_sha256":"7fd699ec8505696a6f0e57e19010aeef6682f090ea2c2f884bc2854b5b89048f"},"schema_version":"1.0","source":{"id":"1602.06078","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.06078","created_at":"2026-05-18T01:20:21Z"},{"alias_kind":"arxiv_version","alias_value":"1602.06078v1","created_at":"2026-05-18T01:20:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.06078","created_at":"2026-05-18T01:20:21Z"},{"alias_kind":"pith_short_12","alias_value":"JZKLAY4UGDIM","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"JZKLAY4UGDIM2XTB","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"JZKLAY4U","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:b162588b459f8398506576282f9849b425917769d2eb770e45eb0321b52fa77b","target":"graph","created_at":"2026-05-18T01:20:21Z","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":"We consider the Steklov eigenvalues of the Laplace operator as limiting Neumann eigenvalues in a problem of mass concentration at the boundary of a ball. We discuss the asymptotic behavior of the Neumann eigenvalues and find explicit formulas for their derivatives at the limiting problem. We deduce that the Neumann eigenvalues have a monotone behavior in the limit and that Steklov eigenvalues locally minimize the Neumann eigenvalues.","authors_text":"Luigi Provenzano, Pier Domenico Lamberti","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2016-02-19T08:53:28Z","title":"Neumann to Steklov eigenvalues: asymptotic and monotonicity results"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.06078","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":"sha256:08180d2ae972e63bffb7201dd623cb24cee7e5db3c4bd28842fcabae05519d98","target":"record","created_at":"2026-05-18T01:20:21Z","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":"dd27e37b5434ff122de34351e57d397b73d337bccde0704a3fc3d356e7ac8a10","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2016-02-19T08:53:28Z","title_canon_sha256":"7fd699ec8505696a6f0e57e19010aeef6682f090ea2c2f884bc2854b5b89048f"},"schema_version":"1.0","source":{"id":"1602.06078","kind":"arxiv","version":1}},"canonical_sha256":"4e54b0639430d0cd5e6116ba0afed0f936466a283ae722c9229730b0dd6e0580","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4e54b0639430d0cd5e6116ba0afed0f936466a283ae722c9229730b0dd6e0580","first_computed_at":"2026-05-18T01:20:21.705101Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:21.705101Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Y1GcuCqKkxkPcWSo3QFk7LzQibXbmxwpA+W6p1rsyqO5icWZAQdkKPc3I2G2rZm1fCPKpIKUM7MK9QH6hYtvAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:21.705678Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.06078","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:08180d2ae972e63bffb7201dd623cb24cee7e5db3c4bd28842fcabae05519d98","sha256:b162588b459f8398506576282f9849b425917769d2eb770e45eb0321b52fa77b"],"state_sha256":"fca6dcbf8879cdd2eafbb37522fb0b7728ebc4f4208d58918040431ffcecc86f"}