{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:F5IKAYHNUAGBL346OWGE5KJBVP","short_pith_number":"pith:F5IKAYHN","schema_version":"1.0","canonical_sha256":"2f50a060eda00c15ef9e758c4ea921abdd1edd10d3684dbc9394cd19253e3d39","source":{"kind":"arxiv","id":"1710.09609","version":1},"attestation_state":"computed","paper":{"title":"Heterogeneous Multiscale Method for the Maxwell equations with high contrast","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Barbara Verf\\\"urth","submitted_at":"2017-10-26T09:34:34Z","abstract_excerpt":"In this paper, we suggest a new Heterogeneous Multiscale Method (HMM) for the (time-harmonic) Maxwell scattering problem with high contrast. The method is constructed for a setting as in Bouchitt\\'e, Bourel and Felbacq (C.R. Math. Acad. Sci. Paris 347(9-10):571--576, 2009), where the high contrast in the parameter leads to unusual effective parameters in the homogenized equation. We present a new homogenization result for this special setting, compare it to existing homogenization approaches and analyze the stability of the two-scale solution with respect to the wavenumber and the data. This i"},"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":"1710.09609","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-10-26T09:34:34Z","cross_cats_sorted":[],"title_canon_sha256":"27a4d4a861fe45de55064e04d7ae982447f815445e9b55e05880909a3e8bbd6e","abstract_canon_sha256":"b1798bd7ef2248b77abbfa7c38b3e8ab7195113be809aae8a7caba38b9128382"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:56.800774Z","signature_b64":"I7FCWP9I5RNunMcXO6uqf7vxdgA4cz/5sO1yORG3WOGjBxr7THm8XkkxXsif3vDLJWhoSMk6aUaXeUPRzPVzDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2f50a060eda00c15ef9e758c4ea921abdd1edd10d3684dbc9394cd19253e3d39","last_reissued_at":"2026-05-18T00:31:56.800220Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:56.800220Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Heterogeneous Multiscale Method for the Maxwell equations with high contrast","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Barbara Verf\\\"urth","submitted_at":"2017-10-26T09:34:34Z","abstract_excerpt":"In this paper, we suggest a new Heterogeneous Multiscale Method (HMM) for the (time-harmonic) Maxwell scattering problem with high contrast. The method is constructed for a setting as in Bouchitt\\'e, Bourel and Felbacq (C.R. Math. Acad. Sci. Paris 347(9-10):571--576, 2009), where the high contrast in the parameter leads to unusual effective parameters in the homogenized equation. We present a new homogenization result for this special setting, compare it to existing homogenization approaches and analyze the stability of the two-scale solution with respect to the wavenumber and the data. This i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.09609","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":"1710.09609","created_at":"2026-05-18T00:31:56.800303+00:00"},{"alias_kind":"arxiv_version","alias_value":"1710.09609v1","created_at":"2026-05-18T00:31:56.800303+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.09609","created_at":"2026-05-18T00:31:56.800303+00:00"},{"alias_kind":"pith_short_12","alias_value":"F5IKAYHNUAGB","created_at":"2026-05-18T12:31:15.632608+00:00"},{"alias_kind":"pith_short_16","alias_value":"F5IKAYHNUAGBL346","created_at":"2026-05-18T12:31:15.632608+00:00"},{"alias_kind":"pith_short_8","alias_value":"F5IKAYHN","created_at":"2026-05-18T12:31:15.632608+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/F5IKAYHNUAGBL346OWGE5KJBVP","json":"https://pith.science/pith/F5IKAYHNUAGBL346OWGE5KJBVP.json","graph_json":"https://pith.science/api/pith-number/F5IKAYHNUAGBL346OWGE5KJBVP/graph.json","events_json":"https://pith.science/api/pith-number/F5IKAYHNUAGBL346OWGE5KJBVP/events.json","paper":"https://pith.science/paper/F5IKAYHN"},"agent_actions":{"view_html":"https://pith.science/pith/F5IKAYHNUAGBL346OWGE5KJBVP","download_json":"https://pith.science/pith/F5IKAYHNUAGBL346OWGE5KJBVP.json","view_paper":"https://pith.science/paper/F5IKAYHN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1710.09609&json=true","fetch_graph":"https://pith.science/api/pith-number/F5IKAYHNUAGBL346OWGE5KJBVP/graph.json","fetch_events":"https://pith.science/api/pith-number/F5IKAYHNUAGBL346OWGE5KJBVP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/F5IKAYHNUAGBL346OWGE5KJBVP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/F5IKAYHNUAGBL346OWGE5KJBVP/action/storage_attestation","attest_author":"https://pith.science/pith/F5IKAYHNUAGBL346OWGE5KJBVP/action/author_attestation","sign_citation":"https://pith.science/pith/F5IKAYHNUAGBL346OWGE5KJBVP/action/citation_signature","submit_replication":"https://pith.science/pith/F5IKAYHNUAGBL346OWGE5KJBVP/action/replication_record"}},"created_at":"2026-05-18T00:31:56.800303+00:00","updated_at":"2026-05-18T00:31:56.800303+00:00"}