{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:NBRFE3JBSLKA6LIGDERRX3PYDZ","short_pith_number":"pith:NBRFE3JB","schema_version":"1.0","canonical_sha256":"6862526d2192d40f2d0619231bedf81e40af20a6804b7a92e667538e8e8a44b3","source":{"kind":"arxiv","id":"1810.00711","version":2},"attestation_state":"computed","paper":{"title":"The Steklov and Laplacian spectra of Riemannian manifolds with boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.SP","authors_text":"Alexandre Girouard, Asma Hassannezhad, Bruno Colbois","submitted_at":"2018-10-01T14:08:44Z","abstract_excerpt":"Given two compact Riemannian manifolds with boundary $M_1$ and $M_2$ such that their respective boundaries $\\Sigma_1$ and $\\Sigma_2$ admit neighborhoods $\\Omega_1$ and $\\Omega_2$ which are isometric, we prove the existence of a constant $C$, which depends only on the geometry of $\\Omega_1\\cong\\Omega_2$, such that $|\\sigma_k(M_1)-\\sigma_k(M_2)|\\leq C$ for each $k\\in\\mathbb{N}$. This follows from a quantitative relationship between the Steklov eigenvalues $\\sigma_k$ of a compact Riemannian manifold $M$ and the eigenvalues $\\lambda_k$ of the Laplacian on its boundary. Our main result states that "},"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":"1810.00711","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2018-10-01T14:08:44Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"b168c871a2443b26e7c8cc4f5924014540434fa753d5158747fd7f8d679bb00e","abstract_canon_sha256":"d9640421f6e21ba74e57216cd263a232c4e1c391fac7d07282ab89fc45d72b1d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:05.184239Z","signature_b64":"tEdqISEjCmv5qFo2Vg3ymIjHgnU4DcCupyyDfDdXgmkG/swotrVGqj64tu5dZL3n0W+cLfQYLwL210Tpmop3AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6862526d2192d40f2d0619231bedf81e40af20a6804b7a92e667538e8e8a44b3","last_reissued_at":"2026-05-17T23:56:05.183612Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:05.183612Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Steklov and Laplacian spectra of Riemannian manifolds with boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.SP","authors_text":"Alexandre Girouard, Asma Hassannezhad, Bruno Colbois","submitted_at":"2018-10-01T14:08:44Z","abstract_excerpt":"Given two compact Riemannian manifolds with boundary $M_1$ and $M_2$ such that their respective boundaries $\\Sigma_1$ and $\\Sigma_2$ admit neighborhoods $\\Omega_1$ and $\\Omega_2$ which are isometric, we prove the existence of a constant $C$, which depends only on the geometry of $\\Omega_1\\cong\\Omega_2$, such that $|\\sigma_k(M_1)-\\sigma_k(M_2)|\\leq C$ for each $k\\in\\mathbb{N}$. This follows from a quantitative relationship between the Steklov eigenvalues $\\sigma_k$ of a compact Riemannian manifold $M$ and the eigenvalues $\\lambda_k$ of the Laplacian on its boundary. Our main result states that "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.00711","kind":"arxiv","version":2},"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":"1810.00711","created_at":"2026-05-17T23:56:05.183696+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.00711v2","created_at":"2026-05-17T23:56:05.183696+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.00711","created_at":"2026-05-17T23:56:05.183696+00:00"},{"alias_kind":"pith_short_12","alias_value":"NBRFE3JBSLKA","created_at":"2026-05-18T12:32:40.477152+00:00"},{"alias_kind":"pith_short_16","alias_value":"NBRFE3JBSLKA6LIG","created_at":"2026-05-18T12:32:40.477152+00:00"},{"alias_kind":"pith_short_8","alias_value":"NBRFE3JB","created_at":"2026-05-18T12:32:40.477152+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/NBRFE3JBSLKA6LIGDERRX3PYDZ","json":"https://pith.science/pith/NBRFE3JBSLKA6LIGDERRX3PYDZ.json","graph_json":"https://pith.science/api/pith-number/NBRFE3JBSLKA6LIGDERRX3PYDZ/graph.json","events_json":"https://pith.science/api/pith-number/NBRFE3JBSLKA6LIGDERRX3PYDZ/events.json","paper":"https://pith.science/paper/NBRFE3JB"},"agent_actions":{"view_html":"https://pith.science/pith/NBRFE3JBSLKA6LIGDERRX3PYDZ","download_json":"https://pith.science/pith/NBRFE3JBSLKA6LIGDERRX3PYDZ.json","view_paper":"https://pith.science/paper/NBRFE3JB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.00711&json=true","fetch_graph":"https://pith.science/api/pith-number/NBRFE3JBSLKA6LIGDERRX3PYDZ/graph.json","fetch_events":"https://pith.science/api/pith-number/NBRFE3JBSLKA6LIGDERRX3PYDZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NBRFE3JBSLKA6LIGDERRX3PYDZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NBRFE3JBSLKA6LIGDERRX3PYDZ/action/storage_attestation","attest_author":"https://pith.science/pith/NBRFE3JBSLKA6LIGDERRX3PYDZ/action/author_attestation","sign_citation":"https://pith.science/pith/NBRFE3JBSLKA6LIGDERRX3PYDZ/action/citation_signature","submit_replication":"https://pith.science/pith/NBRFE3JBSLKA6LIGDERRX3PYDZ/action/replication_record"}},"created_at":"2026-05-17T23:56:05.183696+00:00","updated_at":"2026-05-17T23:56:05.183696+00:00"}