{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:T7Q6Q4GFBAD27CTFA2T4LTZMMW","short_pith_number":"pith:T7Q6Q4GF","schema_version":"1.0","canonical_sha256":"9fe1e870c50807af8a6506a7c5cf2c65ae48ed844705582e71d1e0fb8268db90","source":{"kind":"arxiv","id":"1709.07533","version":1},"attestation_state":"computed","paper":{"title":"On the dynamic homogenization of periodic media: Willis' approach versus two-scale paradigm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Bojan Guzina, Shixu Meng","submitted_at":"2017-09-21T22:35:25Z","abstract_excerpt":"When considering an effective i.e. homogenized description of waves in periodic media that transcends the usual quasi-static approximation, there are generally two schools of thought: (i) the two-scale approach that is prevalent in mathematics, and (ii) the Willis' homogenization framework that has been gaining popularity in engineering and physical sciences. Notwithstanding a mounting body of literature on the two competing paradigms, a clear understanding of their relationship is still lacking. In this study we deploy an effective impedance of the scalar wave equation as a lens for compariso"},"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":"1709.07533","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-21T22:35:25Z","cross_cats_sorted":[],"title_canon_sha256":"dd19a12b39fe9b0f8fd82d16173000459a635af994c6d5cb07382a65b142f55d","abstract_canon_sha256":"5502378692271e921bb8391ff90a633cf73d879896259a83d30ede7a67a6dcc6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:11:40.794375Z","signature_b64":"x0XNaDfvKRF/DaVnNWJ0Hgdk7oWoCt40SkfVxznSd9AYEeipK+7C3G7bprwAQqrcKdqaDXkP5Piu5SAJdELPDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9fe1e870c50807af8a6506a7c5cf2c65ae48ed844705582e71d1e0fb8268db90","last_reissued_at":"2026-05-18T00:11:40.793595Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:11:40.793595Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the dynamic homogenization of periodic media: Willis' approach versus two-scale paradigm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Bojan Guzina, Shixu Meng","submitted_at":"2017-09-21T22:35:25Z","abstract_excerpt":"When considering an effective i.e. homogenized description of waves in periodic media that transcends the usual quasi-static approximation, there are generally two schools of thought: (i) the two-scale approach that is prevalent in mathematics, and (ii) the Willis' homogenization framework that has been gaining popularity in engineering and physical sciences. Notwithstanding a mounting body of literature on the two competing paradigms, a clear understanding of their relationship is still lacking. In this study we deploy an effective impedance of the scalar wave equation as a lens for compariso"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.07533","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":"1709.07533","created_at":"2026-05-18T00:11:40.793726+00:00"},{"alias_kind":"arxiv_version","alias_value":"1709.07533v1","created_at":"2026-05-18T00:11:40.793726+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.07533","created_at":"2026-05-18T00:11:40.793726+00:00"},{"alias_kind":"pith_short_12","alias_value":"T7Q6Q4GFBAD2","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_16","alias_value":"T7Q6Q4GFBAD27CTF","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_8","alias_value":"T7Q6Q4GF","created_at":"2026-05-18T12:31:43.269735+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/T7Q6Q4GFBAD27CTFA2T4LTZMMW","json":"https://pith.science/pith/T7Q6Q4GFBAD27CTFA2T4LTZMMW.json","graph_json":"https://pith.science/api/pith-number/T7Q6Q4GFBAD27CTFA2T4LTZMMW/graph.json","events_json":"https://pith.science/api/pith-number/T7Q6Q4GFBAD27CTFA2T4LTZMMW/events.json","paper":"https://pith.science/paper/T7Q6Q4GF"},"agent_actions":{"view_html":"https://pith.science/pith/T7Q6Q4GFBAD27CTFA2T4LTZMMW","download_json":"https://pith.science/pith/T7Q6Q4GFBAD27CTFA2T4LTZMMW.json","view_paper":"https://pith.science/paper/T7Q6Q4GF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1709.07533&json=true","fetch_graph":"https://pith.science/api/pith-number/T7Q6Q4GFBAD27CTFA2T4LTZMMW/graph.json","fetch_events":"https://pith.science/api/pith-number/T7Q6Q4GFBAD27CTFA2T4LTZMMW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/T7Q6Q4GFBAD27CTFA2T4LTZMMW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/T7Q6Q4GFBAD27CTFA2T4LTZMMW/action/storage_attestation","attest_author":"https://pith.science/pith/T7Q6Q4GFBAD27CTFA2T4LTZMMW/action/author_attestation","sign_citation":"https://pith.science/pith/T7Q6Q4GFBAD27CTFA2T4LTZMMW/action/citation_signature","submit_replication":"https://pith.science/pith/T7Q6Q4GFBAD27CTFA2T4LTZMMW/action/replication_record"}},"created_at":"2026-05-18T00:11:40.793726+00:00","updated_at":"2026-05-18T00:11:40.793726+00:00"}