{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:CNQQIM7GV565DIFQINSXLS36RR","short_pith_number":"pith:CNQQIM7G","schema_version":"1.0","canonical_sha256":"13610433e6af7dd1a0b0436575cb7e8c42a7ed0a47b6972c69adfc00125b1615","source":{"kind":"arxiv","id":"1506.06583","version":1},"attestation_state":"computed","paper":{"title":"On eigenvalue asymptotics for strong delta-interactions supported by surfaces with boundaries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.SP","quant-ph"],"primary_cat":"math-ph","authors_text":"Ch. K\\\"uhn, J. Dittrich, K. Pankrashkin, P. Exner","submitted_at":"2015-06-22T13:06:06Z","abstract_excerpt":"Let $S\\subset\\mathbb{R}^3$ be a $C^4$-smooth relatively compact orientable surface with a sufficiently regular boundary. For $\\beta\\in\\mathbb{R}_+$, let $E_j(\\beta)$ denote the $j$th negative eigenvalue of the operator associated with the quadratic form \\[ H^1(\\mathbb{R}^3)\\ni u\\mapsto \\iiint_{\\mathbb{R}^3} |\\nabla u|^2dx -\\beta \\iint_S |u|^2d\\sigma, \\] where $\\sigma$ is the two-dimensional Hausdorff measure on $S$. We show that for each fixed $j$ one has the asymptotic expansion \\[ E_j(\\beta)=-\\dfrac{\\beta^2}{4}+\\mu^D_j+ o(1) \\;\\text{ as }\\; \\beta\\to+\\infty\\,, \\] where $\\mu_j^D$ is the $j$th "},"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":"1506.06583","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-06-22T13:06:06Z","cross_cats_sorted":["math.MP","math.SP","quant-ph"],"title_canon_sha256":"fd83388aa4281e3284104ee92069767e2ce5e4f2e926939922d517265b53e2e0","abstract_canon_sha256":"0bb2ebd80231ec9f221a578c8395c68275794dd6f255a1871f253aaa9dd8fa42"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:16.065986Z","signature_b64":"l2/Z1oVYEim7F/SNkFLukcaOFpTbs1sPuSczlKjSl0gb+7qPEonpVYlE6OBXgC+j8wUY3BntV1HD/gFEbNHdCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"13610433e6af7dd1a0b0436575cb7e8c42a7ed0a47b6972c69adfc00125b1615","last_reissued_at":"2026-05-18T01:19:16.065606Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:16.065606Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On eigenvalue asymptotics for strong delta-interactions supported by surfaces with boundaries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.SP","quant-ph"],"primary_cat":"math-ph","authors_text":"Ch. K\\\"uhn, J. Dittrich, K. Pankrashkin, P. Exner","submitted_at":"2015-06-22T13:06:06Z","abstract_excerpt":"Let $S\\subset\\mathbb{R}^3$ be a $C^4$-smooth relatively compact orientable surface with a sufficiently regular boundary. For $\\beta\\in\\mathbb{R}_+$, let $E_j(\\beta)$ denote the $j$th negative eigenvalue of the operator associated with the quadratic form \\[ H^1(\\mathbb{R}^3)\\ni u\\mapsto \\iiint_{\\mathbb{R}^3} |\\nabla u|^2dx -\\beta \\iint_S |u|^2d\\sigma, \\] where $\\sigma$ is the two-dimensional Hausdorff measure on $S$. We show that for each fixed $j$ one has the asymptotic expansion \\[ E_j(\\beta)=-\\dfrac{\\beta^2}{4}+\\mu^D_j+ o(1) \\;\\text{ as }\\; \\beta\\to+\\infty\\,, \\] where $\\mu_j^D$ is the $j$th "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.06583","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":"1506.06583","created_at":"2026-05-18T01:19:16.065663+00:00"},{"alias_kind":"arxiv_version","alias_value":"1506.06583v1","created_at":"2026-05-18T01:19:16.065663+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.06583","created_at":"2026-05-18T01:19:16.065663+00:00"},{"alias_kind":"pith_short_12","alias_value":"CNQQIM7GV565","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_16","alias_value":"CNQQIM7GV565DIFQ","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_8","alias_value":"CNQQIM7G","created_at":"2026-05-18T12:29:17.054201+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/CNQQIM7GV565DIFQINSXLS36RR","json":"https://pith.science/pith/CNQQIM7GV565DIFQINSXLS36RR.json","graph_json":"https://pith.science/api/pith-number/CNQQIM7GV565DIFQINSXLS36RR/graph.json","events_json":"https://pith.science/api/pith-number/CNQQIM7GV565DIFQINSXLS36RR/events.json","paper":"https://pith.science/paper/CNQQIM7G"},"agent_actions":{"view_html":"https://pith.science/pith/CNQQIM7GV565DIFQINSXLS36RR","download_json":"https://pith.science/pith/CNQQIM7GV565DIFQINSXLS36RR.json","view_paper":"https://pith.science/paper/CNQQIM7G","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1506.06583&json=true","fetch_graph":"https://pith.science/api/pith-number/CNQQIM7GV565DIFQINSXLS36RR/graph.json","fetch_events":"https://pith.science/api/pith-number/CNQQIM7GV565DIFQINSXLS36RR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CNQQIM7GV565DIFQINSXLS36RR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CNQQIM7GV565DIFQINSXLS36RR/action/storage_attestation","attest_author":"https://pith.science/pith/CNQQIM7GV565DIFQINSXLS36RR/action/author_attestation","sign_citation":"https://pith.science/pith/CNQQIM7GV565DIFQINSXLS36RR/action/citation_signature","submit_replication":"https://pith.science/pith/CNQQIM7GV565DIFQINSXLS36RR/action/replication_record"}},"created_at":"2026-05-18T01:19:16.065663+00:00","updated_at":"2026-05-18T01:19:16.065663+00:00"}