{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:5WFWW7UBUKD7XWPWSFDOGFDCOA","short_pith_number":"pith:5WFWW7UB","schema_version":"1.0","canonical_sha256":"ed8b6b7e81a287fbd9f69146e314627024a09d3a4c5a4e56394bd38c9a668280","source":{"kind":"arxiv","id":"1607.06716","version":2},"attestation_state":"computed","paper":{"title":"Quantitative analysis of boundary layers in periodic homogenization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Christophe Prange, Jean-Christophe Mourrat, Scott Armstrong, Tuomo Kuusi","submitted_at":"2016-07-22T15:52:49Z","abstract_excerpt":"We prove quantitative estimates on the rate of convergence for the oscillating Dirichlet problem in periodic homogenization of divergence-form uniformly elliptic systems. The estimates are optimal in dimensions larger than three and new in every dimension. We also prove a regularity estimate on the homogenized boundary condition."},"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":"1607.06716","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-07-22T15:52:49Z","cross_cats_sorted":[],"title_canon_sha256":"baf3f6e12b8994df4f3a6f6c08fc9cade0695224f43b056d1dc546c41f7116ac","abstract_canon_sha256":"687fc620ca92efa6d381e1789b37ace9525aa921cdd7268709741741c6bfb9cb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:02.489984Z","signature_b64":"hLYF7ySDzGpWdOcuop7agggk3JMBQzG6E8RRFxAwPOTo6DWttB0Pc5ooTR/Q4uCdTMoBJwbGlmToyAJYuKBlBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ed8b6b7e81a287fbd9f69146e314627024a09d3a4c5a4e56394bd38c9a668280","last_reissued_at":"2026-05-18T00:39:02.489375Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:02.489375Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quantitative analysis of boundary layers in periodic homogenization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Christophe Prange, Jean-Christophe Mourrat, Scott Armstrong, Tuomo Kuusi","submitted_at":"2016-07-22T15:52:49Z","abstract_excerpt":"We prove quantitative estimates on the rate of convergence for the oscillating Dirichlet problem in periodic homogenization of divergence-form uniformly elliptic systems. The estimates are optimal in dimensions larger than three and new in every dimension. We also prove a regularity estimate on the homogenized boundary condition."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.06716","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":"1607.06716","created_at":"2026-05-18T00:39:02.489460+00:00"},{"alias_kind":"arxiv_version","alias_value":"1607.06716v2","created_at":"2026-05-18T00:39:02.489460+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.06716","created_at":"2026-05-18T00:39:02.489460+00:00"},{"alias_kind":"pith_short_12","alias_value":"5WFWW7UBUKD7","created_at":"2026-05-18T12:30:01.593930+00:00"},{"alias_kind":"pith_short_16","alias_value":"5WFWW7UBUKD7XWPW","created_at":"2026-05-18T12:30:01.593930+00:00"},{"alias_kind":"pith_short_8","alias_value":"5WFWW7UB","created_at":"2026-05-18T12:30:01.593930+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/5WFWW7UBUKD7XWPWSFDOGFDCOA","json":"https://pith.science/pith/5WFWW7UBUKD7XWPWSFDOGFDCOA.json","graph_json":"https://pith.science/api/pith-number/5WFWW7UBUKD7XWPWSFDOGFDCOA/graph.json","events_json":"https://pith.science/api/pith-number/5WFWW7UBUKD7XWPWSFDOGFDCOA/events.json","paper":"https://pith.science/paper/5WFWW7UB"},"agent_actions":{"view_html":"https://pith.science/pith/5WFWW7UBUKD7XWPWSFDOGFDCOA","download_json":"https://pith.science/pith/5WFWW7UBUKD7XWPWSFDOGFDCOA.json","view_paper":"https://pith.science/paper/5WFWW7UB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1607.06716&json=true","fetch_graph":"https://pith.science/api/pith-number/5WFWW7UBUKD7XWPWSFDOGFDCOA/graph.json","fetch_events":"https://pith.science/api/pith-number/5WFWW7UBUKD7XWPWSFDOGFDCOA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5WFWW7UBUKD7XWPWSFDOGFDCOA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5WFWW7UBUKD7XWPWSFDOGFDCOA/action/storage_attestation","attest_author":"https://pith.science/pith/5WFWW7UBUKD7XWPWSFDOGFDCOA/action/author_attestation","sign_citation":"https://pith.science/pith/5WFWW7UBUKD7XWPWSFDOGFDCOA/action/citation_signature","submit_replication":"https://pith.science/pith/5WFWW7UBUKD7XWPWSFDOGFDCOA/action/replication_record"}},"created_at":"2026-05-18T00:39:02.489460+00:00","updated_at":"2026-05-18T00:39:02.489460+00:00"}