{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:JOYSZS5GHOYJLGYFNY423F4MQI","short_pith_number":"pith:JOYSZS5G","schema_version":"1.0","canonical_sha256":"4bb12ccba63bb0959b056e39ad978c8239cf01669788a243b74c57579747fa16","source":{"kind":"arxiv","id":"1404.2555","version":2},"attestation_state":"computed","paper":{"title":"Spectral properties of elliptic operator with double-contrast coefficients near a hyperplane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.SP","authors_text":"Andrii Khrabustovskyi, Michael Plum","submitted_at":"2014-04-09T17:22:34Z","abstract_excerpt":"In this paper we study the asymptotic behaviour as $\\varepsilon\\to 0$ of the spectrum of the elliptic operator $\\mathcal{A}^\\varepsilon=-{1\\over b^\\varepsilon}\\mathrm{div}(a^\\varepsilon\\nabla)$ posed in a bounded domain $\\Omega\\subset\\mathbb{R}^n$ $(n \\geq 2)$ subject to Dirichlet boundary conditions on $\\partial\\Omega$. When $\\varepsilon\\to 0$ both coefficients $a^\\varepsilon$ and $b^\\varepsilon$ become high contrast in a small neighborhood of a hyperplane $\\Gamma$ intersecting $\\Omega$. We prove that the spectrum of $\\mathcal{A}^\\varepsilon$ converges to the spectrum of an operator acting in"},"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":"1404.2555","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2014-04-09T17:22:34Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"578ec74b6a966d6b472f15f0ce1d1f90b018c669a601a4030abbf1d4b0389f03","abstract_canon_sha256":"cd70da74edf48c57370895c76677abf3dddcf479bbe0f8e4be7a8d5ef046a5a5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:29:47.086547Z","signature_b64":"/juYjJTzeFEvyvXL6XnBg32q7FwXBaQbSZTjSz/L3cVo6fPyTHGj3G0qbveqExcoBUkA+IPa7fxQbpXWeQPNCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4bb12ccba63bb0959b056e39ad978c8239cf01669788a243b74c57579747fa16","last_reissued_at":"2026-05-18T01:29:47.086099Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:29:47.086099Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spectral properties of elliptic operator with double-contrast coefficients near a hyperplane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.SP","authors_text":"Andrii Khrabustovskyi, Michael Plum","submitted_at":"2014-04-09T17:22:34Z","abstract_excerpt":"In this paper we study the asymptotic behaviour as $\\varepsilon\\to 0$ of the spectrum of the elliptic operator $\\mathcal{A}^\\varepsilon=-{1\\over b^\\varepsilon}\\mathrm{div}(a^\\varepsilon\\nabla)$ posed in a bounded domain $\\Omega\\subset\\mathbb{R}^n$ $(n \\geq 2)$ subject to Dirichlet boundary conditions on $\\partial\\Omega$. When $\\varepsilon\\to 0$ both coefficients $a^\\varepsilon$ and $b^\\varepsilon$ become high contrast in a small neighborhood of a hyperplane $\\Gamma$ intersecting $\\Omega$. We prove that the spectrum of $\\mathcal{A}^\\varepsilon$ converges to the spectrum of an operator acting in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.2555","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":"1404.2555","created_at":"2026-05-18T01:29:47.086160+00:00"},{"alias_kind":"arxiv_version","alias_value":"1404.2555v2","created_at":"2026-05-18T01:29:47.086160+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.2555","created_at":"2026-05-18T01:29:47.086160+00:00"},{"alias_kind":"pith_short_12","alias_value":"JOYSZS5GHOYJ","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_16","alias_value":"JOYSZS5GHOYJLGYF","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_8","alias_value":"JOYSZS5G","created_at":"2026-05-18T12:28:35.611951+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/JOYSZS5GHOYJLGYFNY423F4MQI","json":"https://pith.science/pith/JOYSZS5GHOYJLGYFNY423F4MQI.json","graph_json":"https://pith.science/api/pith-number/JOYSZS5GHOYJLGYFNY423F4MQI/graph.json","events_json":"https://pith.science/api/pith-number/JOYSZS5GHOYJLGYFNY423F4MQI/events.json","paper":"https://pith.science/paper/JOYSZS5G"},"agent_actions":{"view_html":"https://pith.science/pith/JOYSZS5GHOYJLGYFNY423F4MQI","download_json":"https://pith.science/pith/JOYSZS5GHOYJLGYFNY423F4MQI.json","view_paper":"https://pith.science/paper/JOYSZS5G","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1404.2555&json=true","fetch_graph":"https://pith.science/api/pith-number/JOYSZS5GHOYJLGYFNY423F4MQI/graph.json","fetch_events":"https://pith.science/api/pith-number/JOYSZS5GHOYJLGYFNY423F4MQI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JOYSZS5GHOYJLGYFNY423F4MQI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JOYSZS5GHOYJLGYFNY423F4MQI/action/storage_attestation","attest_author":"https://pith.science/pith/JOYSZS5GHOYJLGYFNY423F4MQI/action/author_attestation","sign_citation":"https://pith.science/pith/JOYSZS5GHOYJLGYFNY423F4MQI/action/citation_signature","submit_replication":"https://pith.science/pith/JOYSZS5GHOYJLGYFNY423F4MQI/action/replication_record"}},"created_at":"2026-05-18T01:29:47.086160+00:00","updated_at":"2026-05-18T01:29:47.086160+00:00"}