{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:VG6INHD3AJIBITRAB7WVNI3OPQ","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":"08bb116763eea5ee2285740d0f7146f5a2ce9fd1660eaa4c81f75014efc52eae","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-12-30T17:59:46Z","title_canon_sha256":"e4d19143050715f4a8ca46cdbc7a09d8281e5553d82c075b452d02daeaae531d"},"schema_version":"1.0","source":{"id":"1512.09038","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.09038","created_at":"2026-05-18T00:43:43Z"},{"alias_kind":"arxiv_version","alias_value":"1512.09038v2","created_at":"2026-05-18T00:43:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.09038","created_at":"2026-05-18T00:43:43Z"},{"alias_kind":"pith_short_12","alias_value":"VG6INHD3AJIB","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"VG6INHD3AJIBITRA","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"VG6INHD3","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:732144a187fe01a9b241ae7363299a8e264e32574760dd4141600b53bf1e480c","target":"graph","created_at":"2026-05-18T00:43:43Z","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":"Consider a compact Riemannian manifold with boundary. In this short note we prove that under certain positive curvature assumptions on the manifold and its boundary the Steklov eigenvalues of the manifold are controlled by the Laplace eigenvalues of the boundary. Additionally, in two dimensions we obtain an upper bound for these Steklov eigenvalues in terms of topology of the surface without any curvature restrictions.","authors_text":"Mikhail A. Karpukhin","cross_cats":["math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-12-30T17:59:46Z","title":"Bounds between Laplace and Steklov eigenvalues on nonnegatively curved manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.09038","kind":"arxiv","version":2},"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:d53e2aea2143cfe60b9a373266d4cb79d5a5b280edc456d5f7a9f70fcfbf416b","target":"record","created_at":"2026-05-18T00:43:43Z","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":"08bb116763eea5ee2285740d0f7146f5a2ce9fd1660eaa4c81f75014efc52eae","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-12-30T17:59:46Z","title_canon_sha256":"e4d19143050715f4a8ca46cdbc7a09d8281e5553d82c075b452d02daeaae531d"},"schema_version":"1.0","source":{"id":"1512.09038","kind":"arxiv","version":2}},"canonical_sha256":"a9bc869c7b0250144e200fed56a36e7c3fb258e25ca22171c054fea216cd3525","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a9bc869c7b0250144e200fed56a36e7c3fb258e25ca22171c054fea216cd3525","first_computed_at":"2026-05-18T00:43:43.715418Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:43.715418Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MkHyRoN9Eg31nbsAc18NFF3bEW90ax/tm7WWRYNAZIsQuk1E0sW1gTRaUGvc4QYWwUOV3gd3BddGNBaJnFnJAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:43.715982Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.09038","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d53e2aea2143cfe60b9a373266d4cb79d5a5b280edc456d5f7a9f70fcfbf416b","sha256:732144a187fe01a9b241ae7363299a8e264e32574760dd4141600b53bf1e480c"],"state_sha256":"5df17db27b80c5a15347aadfd29ce9df12cac65fa6b9ff73ad4d5514dcd24170"}