{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:DR4FSNA4JXYKFRYSL6W2T35UWH","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":"972c092a4faf7dcd7f5924684b6ee446bdc4179bad5f87ed8620d5912020a7b5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-01-28T18:58:10Z","title_canon_sha256":"78b5bd4d42315909791050eada3877a1cd67e0023ef931836fc7007c5b8d006e"},"schema_version":"1.0","source":{"id":"1701.08313","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.08313","created_at":"2026-05-18T00:30:05Z"},{"alias_kind":"arxiv_version","alias_value":"1701.08313v2","created_at":"2026-05-18T00:30:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.08313","created_at":"2026-05-18T00:30:05Z"},{"alias_kind":"pith_short_12","alias_value":"DR4FSNA4JXYK","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"DR4FSNA4JXYKFRYS","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"DR4FSNA4","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:17e93ebf1be6f51482cdeb638b1cd57bcf5023d7031c2df6c836cbca6b1d72e2","target":"graph","created_at":"2026-05-18T00:30:05Z","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":"The Heterogeneous Multiscale Finite Element Method (FE-HMM) is a two-scale FEM based on asymptotic homogenization for solving multiscale partial differential equations. It was introduced in [W. E and B. Engquist, \\emph{Commun. Math. Sci.}, 1 (2003), 87--132]. The objective of the present work is an FE-HMM formulation for the homogenization of linear elastic solids in a geometrical linear frame, and doing so, for the first time, of a vector-valued field problem. A key ingredient of FE-HMM is that macrostiffness is estimated by stiffness sampling on heterogeneous microdomains in terms a of modif","authors_text":"Andreas Fischer, Bernhard Eidel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-01-28T18:58:10Z","title":"The Heterogeneous Multiscale Finite Element Method for the Homogenization of Linear Elastic Solids and a Comparison with the FE$^2$ Method"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.08313","kind":"arxiv","version":2},"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":"sha256:27bb4c67c1f5389e7e33c9ea6125811e6d63f950419631c227fe567769ea9b0a","target":"record","created_at":"2026-05-18T00:30:05Z","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":"972c092a4faf7dcd7f5924684b6ee446bdc4179bad5f87ed8620d5912020a7b5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-01-28T18:58:10Z","title_canon_sha256":"78b5bd4d42315909791050eada3877a1cd67e0023ef931836fc7007c5b8d006e"},"schema_version":"1.0","source":{"id":"1701.08313","kind":"arxiv","version":2}},"canonical_sha256":"1c7859341c4df0a2c7125fada9efb4b1e8a35b0f656960f2e2f5e784b9e8a644","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1c7859341c4df0a2c7125fada9efb4b1e8a35b0f656960f2e2f5e784b9e8a644","first_computed_at":"2026-05-18T00:30:05.787849Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:30:05.787849Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"a5sa+hCO0na8tf5/RzzbAM9EUrrsOavnO9DWlhc7uHlHYZLBk25eXrQhc6UbT5TylZM0lRp6+7y1xEEB4TNCAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:30:05.788259Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.08313","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:27bb4c67c1f5389e7e33c9ea6125811e6d63f950419631c227fe567769ea9b0a","sha256:17e93ebf1be6f51482cdeb638b1cd57bcf5023d7031c2df6c836cbca6b1d72e2"],"state_sha256":"8eb524661f66f8b838a6e60970069d6e48d6cb88b618be4a408eeaecc250089e"}