{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:URFL4JKD76644EOHI4KZRC4KLS","short_pith_number":"pith:URFL4JKD","schema_version":"1.0","canonical_sha256":"a44abe2543ffbdce11c74715988b8a5c999b3265cdcaeecb922e2c2de9feb36e","source":{"kind":"arxiv","id":"1512.06891","version":1},"attestation_state":"computed","paper":{"title":"Embedded eigenvalues of the Neumann problem in a strip with a box-shaped perturbation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"math.SP","authors_text":"G. Cardone, S.A. Nazarov, T. Durante","submitted_at":"2015-12-21T22:15:05Z","abstract_excerpt":"We consider the spectral Neumann problem for the Laplace operator in an acoustic waveguide $\\Pi_{l}^{\\varepsilon}$ obtained from a straight unit strip by a low box-shaped perturbation of size $2l\\times\\varepsilon,$ where $\\varepsilon>0$ is a small parameter. We prove the existence of the length parameter $l_{k}^{\\varepsilon}=\\pi k+O\\left( \\varepsilon\\right) $ with any $k=1,2,3,...$ such that the waveguide $\\Pi_{l_{k}^{\\varepsilon}}^{\\varepsilon }$ supports a trapped mode with an eigenvalue $\\lambda_{k}^{\\varepsilon}% =\\pi^{2}-4\\pi^{4}l^{2}\\varepsilon^{2}+O\\left( \\varepsilon^{3}\\right) $ embedd"},"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":"1512.06891","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-12-21T22:15:05Z","cross_cats_sorted":["math-ph","math.AP","math.MP"],"title_canon_sha256":"2ac225ed04be61409b39a534896379e38fede59e7e8a6b7fba2364829c151125","abstract_canon_sha256":"c97fd580ebfcdc74626db0d320c0adadc716856cca47d2589fb9147dff0aecb0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:45.962517Z","signature_b64":"YReFv8Tr+KRWw1BnchJIvdPf6tWSET46eIrVxK+DXdk7U2H9nhjG59OsIBBj+3TBGRYyPLtJIw9C2jUbyxJVBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a44abe2543ffbdce11c74715988b8a5c999b3265cdcaeecb922e2c2de9feb36e","last_reissued_at":"2026-05-18T00:16:45.961993Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:45.961993Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Embedded eigenvalues of the Neumann problem in a strip with a box-shaped perturbation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"math.SP","authors_text":"G. Cardone, S.A. Nazarov, T. Durante","submitted_at":"2015-12-21T22:15:05Z","abstract_excerpt":"We consider the spectral Neumann problem for the Laplace operator in an acoustic waveguide $\\Pi_{l}^{\\varepsilon}$ obtained from a straight unit strip by a low box-shaped perturbation of size $2l\\times\\varepsilon,$ where $\\varepsilon>0$ is a small parameter. We prove the existence of the length parameter $l_{k}^{\\varepsilon}=\\pi k+O\\left( \\varepsilon\\right) $ with any $k=1,2,3,...$ such that the waveguide $\\Pi_{l_{k}^{\\varepsilon}}^{\\varepsilon }$ supports a trapped mode with an eigenvalue $\\lambda_{k}^{\\varepsilon}% =\\pi^{2}-4\\pi^{4}l^{2}\\varepsilon^{2}+O\\left( \\varepsilon^{3}\\right) $ embedd"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.06891","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":"1512.06891","created_at":"2026-05-18T00:16:45.962081+00:00"},{"alias_kind":"arxiv_version","alias_value":"1512.06891v1","created_at":"2026-05-18T00:16:45.962081+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.06891","created_at":"2026-05-18T00:16:45.962081+00:00"},{"alias_kind":"pith_short_12","alias_value":"URFL4JKD7664","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_16","alias_value":"URFL4JKD76644EOH","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_8","alias_value":"URFL4JKD","created_at":"2026-05-18T12:29:44.643036+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/URFL4JKD76644EOHI4KZRC4KLS","json":"https://pith.science/pith/URFL4JKD76644EOHI4KZRC4KLS.json","graph_json":"https://pith.science/api/pith-number/URFL4JKD76644EOHI4KZRC4KLS/graph.json","events_json":"https://pith.science/api/pith-number/URFL4JKD76644EOHI4KZRC4KLS/events.json","paper":"https://pith.science/paper/URFL4JKD"},"agent_actions":{"view_html":"https://pith.science/pith/URFL4JKD76644EOHI4KZRC4KLS","download_json":"https://pith.science/pith/URFL4JKD76644EOHI4KZRC4KLS.json","view_paper":"https://pith.science/paper/URFL4JKD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1512.06891&json=true","fetch_graph":"https://pith.science/api/pith-number/URFL4JKD76644EOHI4KZRC4KLS/graph.json","fetch_events":"https://pith.science/api/pith-number/URFL4JKD76644EOHI4KZRC4KLS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/URFL4JKD76644EOHI4KZRC4KLS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/URFL4JKD76644EOHI4KZRC4KLS/action/storage_attestation","attest_author":"https://pith.science/pith/URFL4JKD76644EOHI4KZRC4KLS/action/author_attestation","sign_citation":"https://pith.science/pith/URFL4JKD76644EOHI4KZRC4KLS/action/citation_signature","submit_replication":"https://pith.science/pith/URFL4JKD76644EOHI4KZRC4KLS/action/replication_record"}},"created_at":"2026-05-18T00:16:45.962081+00:00","updated_at":"2026-05-18T00:16:45.962081+00:00"}