{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:T7Q6Q4GFBAD27CTFA2T4LTZMMW","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"5502378692271e921bb8391ff90a633cf73d879896259a83d30ede7a67a6dcc6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-21T22:35:25Z","title_canon_sha256":"dd19a12b39fe9b0f8fd82d16173000459a635af994c6d5cb07382a65b142f55d"},"schema_version":"1.0","source":{"id":"1709.07533","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.07533","created_at":"2026-05-18T00:11:40Z"},{"alias_kind":"arxiv_version","alias_value":"1709.07533v1","created_at":"2026-05-18T00:11:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.07533","created_at":"2026-05-18T00:11:40Z"},{"alias_kind":"pith_short_12","alias_value":"T7Q6Q4GFBAD2","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"T7Q6Q4GFBAD27CTF","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"T7Q6Q4GF","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:eaf44af2f82c3eb13f70b85bc2dafd51e9226692e6cd29b305ffbfc8b1dfa8a8","target":"graph","created_at":"2026-05-18T00:11:40Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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","authors_text":"Bojan Guzina, Shixu Meng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-21T22:35:25Z","title":"On the dynamic homogenization of periodic media: Willis' approach versus two-scale paradigm"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.07533","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:6160effd308a9355b3d47f1361ead4884fc9a7659d997ed08a7ea49ed1831009","target":"record","created_at":"2026-05-18T00:11:40Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"5502378692271e921bb8391ff90a633cf73d879896259a83d30ede7a67a6dcc6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-21T22:35:25Z","title_canon_sha256":"dd19a12b39fe9b0f8fd82d16173000459a635af994c6d5cb07382a65b142f55d"},"schema_version":"1.0","source":{"id":"1709.07533","kind":"arxiv","version":1}},"canonical_sha256":"9fe1e870c50807af8a6506a7c5cf2c65ae48ed844705582e71d1e0fb8268db90","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9fe1e870c50807af8a6506a7c5cf2c65ae48ed844705582e71d1e0fb8268db90","first_computed_at":"2026-05-18T00:11:40.793595Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:11:40.793595Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"x0XNaDfvKRF/DaVnNWJ0Hgdk7oWoCt40SkfVxznSd9AYEeipK+7C3G7bprwAQqrcKdqaDXkP5Piu5SAJdELPDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:11:40.794375Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.07533","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6160effd308a9355b3d47f1361ead4884fc9a7659d997ed08a7ea49ed1831009","sha256:eaf44af2f82c3eb13f70b85bc2dafd51e9226692e6cd29b305ffbfc8b1dfa8a8"],"state_sha256":"186f1d264357253425ac19006f9da8593ee647587f1a0593f4509d34194ca100"}