{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:EWEHIRUBZ3B4LUPLIH2BPJGCGL","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":"de5d7e49df05909a914f0379b832ceff2ff2f8f0686797c07db8d3505cea3e33","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-09-03T16:40:08Z","title_canon_sha256":"38e14060a53838be796ae1938e836685a1e433cb4b6ea07e596cf7d579b67e10"},"schema_version":"1.0","source":{"id":"1409.1155","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.1155","created_at":"2026-05-18T02:43:37Z"},{"alias_kind":"arxiv_version","alias_value":"1409.1155v1","created_at":"2026-05-18T02:43:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.1155","created_at":"2026-05-18T02:43:37Z"},{"alias_kind":"pith_short_12","alias_value":"EWEHIRUBZ3B4","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"EWEHIRUBZ3B4LUPL","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"EWEHIRUB","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:9fab45b1388b7429070003150df1909a2ca5cac80040818f0673220a53fcab36","target":"graph","created_at":"2026-05-18T02:43:37Z","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":"This paper is the companion article of [Gloria, M3AS, 21 (2011), No. 3, pp 1601-1630]. One common drawback among numerical homogenization methods is the presence of the so-called resonance error, which roughly speaking is a function of the ratio $\\frac{\\varepsilon}{\\rho}$, where $\\rho$ is a typical macroscopic lengthscale and $\\varepsilon$ is the typical size of the heterogeneities. In the present work, we make a systematic use of regularization and extrapolation to reduce this resonance error at the level of the approximation of homogenized coefficients and correctors for general non-necessar","authors_text":"Antoine Gloria (ULB, INRIA Lille - Nord Europe), Zakaria Habibi (INRIA Lille - Nord Europe)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-09-03T16:40:08Z","title":"Reduction of the resonance error in numerical homogenisation II: correctors and extrapolation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.1155","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:e873c5cd583fce0eadd05550c3f8527f8aea78b0e9b1f010480741d87d9cfc6f","target":"record","created_at":"2026-05-18T02:43:37Z","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":"de5d7e49df05909a914f0379b832ceff2ff2f8f0686797c07db8d3505cea3e33","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-09-03T16:40:08Z","title_canon_sha256":"38e14060a53838be796ae1938e836685a1e433cb4b6ea07e596cf7d579b67e10"},"schema_version":"1.0","source":{"id":"1409.1155","kind":"arxiv","version":1}},"canonical_sha256":"2588744681cec3c5d1eb41f417a4c232d0dbc9869db925152676139ae292c674","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2588744681cec3c5d1eb41f417a4c232d0dbc9869db925152676139ae292c674","first_computed_at":"2026-05-18T02:43:37.588401Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:43:37.588401Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"40f+XsLA+6XHxiGVzoarfemRLTbOEJFMQXjKPIp1gTkiqilMU+StL+4MZJW5JZqzZ/f4fzA0d+UwxHAt2q7bDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:43:37.589034Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.1155","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e873c5cd583fce0eadd05550c3f8527f8aea78b0e9b1f010480741d87d9cfc6f","sha256:9fab45b1388b7429070003150df1909a2ca5cac80040818f0673220a53fcab36"],"state_sha256":"e01afe704dbef3b31588009772037cff4217740cef0b0d286c1cca32dd79cd02"}