{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:ONSJ6IX4SFOCBQMPBFTK4PJRQZ","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":"da2f3c56fddb491f7f7e79b803766f25feb8bbe45f26bc32a42c1fe3058fc897","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-12-31T17:03:26Z","title_canon_sha256":"462c5db65f0a58cd8244c04b05083b562d6789f5bc9023bb09d694cc83cadb4a"},"schema_version":"1.0","source":{"id":"1401.0185","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.0185","created_at":"2026-05-18T03:03:30Z"},{"alias_kind":"arxiv_version","alias_value":"1401.0185v1","created_at":"2026-05-18T03:03:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.0185","created_at":"2026-05-18T03:03:30Z"},{"alias_kind":"pith_short_12","alias_value":"ONSJ6IX4SFOC","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"ONSJ6IX4SFOCBQMP","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"ONSJ6IX4","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:d2b308da226dc685f3d5af7a04d8bffff633454112e7e115e83b29626c09426c","target":"graph","created_at":"2026-05-18T03:03:30Z","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":"In this paper, we study numerical homogenization methods based on integral equations. Our work is motivated by materials such as concrete, modeled as composites structured as randomly distributed inclusions imbedded in a matrix. We investigate two integral reformulations of the corrector problem to be solved, namely the equivalent inclusion method based on the Lippmann-Schwinger equation, and a method based on boundary integral equations. The fully populated matrices obtained by the discretization of the integral operators are successfully dealt with using the H-matrix format.","authors_text":"MCSS), Olivier Zahm (GeM), Paul Cazeaux (LJLL","cross_cats":["math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-12-31T17:03:26Z","title":"Application of Hierarchical Matrix Techniques To The Homogenization of Composite Materials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0185","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:c338954c89679c7c177dcade35180ae1dd209351829b26b4a1989e45ebb788c6","target":"record","created_at":"2026-05-18T03:03:30Z","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":"da2f3c56fddb491f7f7e79b803766f25feb8bbe45f26bc32a42c1fe3058fc897","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-12-31T17:03:26Z","title_canon_sha256":"462c5db65f0a58cd8244c04b05083b562d6789f5bc9023bb09d694cc83cadb4a"},"schema_version":"1.0","source":{"id":"1401.0185","kind":"arxiv","version":1}},"canonical_sha256":"73649f22fc915c20c18f0966ae3d31865282a263a9f089efd5e50c0815151396","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"73649f22fc915c20c18f0966ae3d31865282a263a9f089efd5e50c0815151396","first_computed_at":"2026-05-18T03:03:30.807423Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:03:30.807423Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bYN3eHEQE4MdIEcQGuBCH0mRH4xW/qfcFs9BRMtfZ8vBZBC/YdiD4zOOp6vk+N/3IXbEBWIF6UL5SP6VSwGhAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:03:30.808111Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.0185","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c338954c89679c7c177dcade35180ae1dd209351829b26b4a1989e45ebb788c6","sha256:d2b308da226dc685f3d5af7a04d8bffff633454112e7e115e83b29626c09426c"],"state_sha256":"13dd92d4919166a9e28aee9dc475d2acd6c42cfe0037acf3017ec21882ae7154"}