{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:LSU4SIVQIEZBLD3PCXBBH5O7TT","short_pith_number":"pith:LSU4SIVQ","schema_version":"1.0","canonical_sha256":"5ca9c922b04132158f6f15c213f5df9ce866c34e0ec88b1dc18d004af28467b3","source":{"kind":"arxiv","id":"1705.08951","version":1},"attestation_state":"computed","paper":{"title":"Steklov problem on differential forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.SP","authors_text":"Mikhail Karpukhin","submitted_at":"2017-05-24T20:13:59Z","abstract_excerpt":"In this paper we study spectral properties of Dirichlet-to-Neumann map on differential forms obtained by a slight modification of the definition due to Belishev and Sharafutdinov. The resulting operator $\\Lambda$ is shown to be self-adjoint on the subspace of coclosed forms and to have purely discrete spectrum there.We investigate properies of eigenvalues of $\\Lambda$ and prove a Hersch-Payne-Schiffer type inequality relating products of those eigenvalues to eigenvalues of Hodge Laplacian on the boundary. Moreover, non-trivial eigenvalues of $\\Lambda$ are always at least as large as eigenvalue"},"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":"1705.08951","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2017-05-24T20:13:59Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"12fd0e7a98a04f5ad5ebe0e6d21c2f3f719200328f9c84d3e947a126bf045683","abstract_canon_sha256":"bbd5a5db940667c52e56822a857364bba89bfabe64c94ce48c869a8d20ea5bac"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:40.874896Z","signature_b64":"SEHH8fIK4wXVyt06VaFPDkv632qH6zDrw4h7o7Ge0WM9tVHVIJ4Luc52Pk0ANFm4E4BbgV855IOHyR/qf8E8Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5ca9c922b04132158f6f15c213f5df9ce866c34e0ec88b1dc18d004af28467b3","last_reissued_at":"2026-05-18T00:43:40.874291Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:40.874291Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Steklov problem on differential forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.SP","authors_text":"Mikhail Karpukhin","submitted_at":"2017-05-24T20:13:59Z","abstract_excerpt":"In this paper we study spectral properties of Dirichlet-to-Neumann map on differential forms obtained by a slight modification of the definition due to Belishev and Sharafutdinov. The resulting operator $\\Lambda$ is shown to be self-adjoint on the subspace of coclosed forms and to have purely discrete spectrum there.We investigate properies of eigenvalues of $\\Lambda$ and prove a Hersch-Payne-Schiffer type inequality relating products of those eigenvalues to eigenvalues of Hodge Laplacian on the boundary. Moreover, non-trivial eigenvalues of $\\Lambda$ are always at least as large as eigenvalue"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.08951","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":"1705.08951","created_at":"2026-05-18T00:43:40.874382+00:00"},{"alias_kind":"arxiv_version","alias_value":"1705.08951v1","created_at":"2026-05-18T00:43:40.874382+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.08951","created_at":"2026-05-18T00:43:40.874382+00:00"},{"alias_kind":"pith_short_12","alias_value":"LSU4SIVQIEZB","created_at":"2026-05-18T12:31:28.150371+00:00"},{"alias_kind":"pith_short_16","alias_value":"LSU4SIVQIEZBLD3P","created_at":"2026-05-18T12:31:28.150371+00:00"},{"alias_kind":"pith_short_8","alias_value":"LSU4SIVQ","created_at":"2026-05-18T12:31:28.150371+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/LSU4SIVQIEZBLD3PCXBBH5O7TT","json":"https://pith.science/pith/LSU4SIVQIEZBLD3PCXBBH5O7TT.json","graph_json":"https://pith.science/api/pith-number/LSU4SIVQIEZBLD3PCXBBH5O7TT/graph.json","events_json":"https://pith.science/api/pith-number/LSU4SIVQIEZBLD3PCXBBH5O7TT/events.json","paper":"https://pith.science/paper/LSU4SIVQ"},"agent_actions":{"view_html":"https://pith.science/pith/LSU4SIVQIEZBLD3PCXBBH5O7TT","download_json":"https://pith.science/pith/LSU4SIVQIEZBLD3PCXBBH5O7TT.json","view_paper":"https://pith.science/paper/LSU4SIVQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1705.08951&json=true","fetch_graph":"https://pith.science/api/pith-number/LSU4SIVQIEZBLD3PCXBBH5O7TT/graph.json","fetch_events":"https://pith.science/api/pith-number/LSU4SIVQIEZBLD3PCXBBH5O7TT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LSU4SIVQIEZBLD3PCXBBH5O7TT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LSU4SIVQIEZBLD3PCXBBH5O7TT/action/storage_attestation","attest_author":"https://pith.science/pith/LSU4SIVQIEZBLD3PCXBBH5O7TT/action/author_attestation","sign_citation":"https://pith.science/pith/LSU4SIVQIEZBLD3PCXBBH5O7TT/action/citation_signature","submit_replication":"https://pith.science/pith/LSU4SIVQIEZBLD3PCXBBH5O7TT/action/replication_record"}},"created_at":"2026-05-18T00:43:40.874382+00:00","updated_at":"2026-05-18T00:43:40.874382+00:00"}