{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:365QGGVE6V7CPUA7E4IWWZSVK6","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":"e943ad16257bf35b0405f728c868f2afcb6d7dcff639eb7a595b4ff557272c6a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-11-09T10:44:02Z","title_canon_sha256":"3957e34684e335c1af15c5db565934df9b97f76bc74fde81cd83a9c43890a89f"},"schema_version":"1.0","source":{"id":"1511.02626","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.02626","created_at":"2026-05-18T00:48:28Z"},{"alias_kind":"arxiv_version","alias_value":"1511.02626v3","created_at":"2026-05-18T00:48:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.02626","created_at":"2026-05-18T00:48:28Z"},{"alias_kind":"pith_short_12","alias_value":"365QGGVE6V7C","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"365QGGVE6V7CPUA7","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"365QGGVE","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:2cbfe761a37802cbf4e6937187cfa7150f1f4041d57bee1b96a989e11006c737","target":"graph","created_at":"2026-05-18T00:48:28Z","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":"We consider the efficient solution of strongly elliptic partial differential equations with random load based on the finite element method. The solution's two-point correlation can efficiently be approximated by means of an $\\mathcal{H}$-matrix, in particular if the correlation length is rather short or the correlation kernel is non-smooth. Since the inverses of the finite element matrices which correspond to the differential operator under consideration can likewise efficiently be approximated in the $\\mathcal{H}$-matrix format, we can solve the correspondent $\\mathcal{H}$-matrix equation in ","authors_text":"Helmut Harbrecht, J\\\"urgen D\\\"olz, Michael D. Peters","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-11-09T10:44:02Z","title":"$\\mathcal{H}$-matrix based second moment analysis for rough random fields and finite element discretizations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.02626","kind":"arxiv","version":3},"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":"sha256:68ac58d14497e1d34764b6e942ba5c8e2e5ff6bd062a8a1384955a98855f3d9c","target":"record","created_at":"2026-05-18T00:48:28Z","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":"e943ad16257bf35b0405f728c868f2afcb6d7dcff639eb7a595b4ff557272c6a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-11-09T10:44:02Z","title_canon_sha256":"3957e34684e335c1af15c5db565934df9b97f76bc74fde81cd83a9c43890a89f"},"schema_version":"1.0","source":{"id":"1511.02626","kind":"arxiv","version":3}},"canonical_sha256":"dfbb031aa4f57e27d01f27116b665557a13938bb13a1dbbf12ed7a4a135b928d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dfbb031aa4f57e27d01f27116b665557a13938bb13a1dbbf12ed7a4a135b928d","first_computed_at":"2026-05-18T00:48:28.584065Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:28.584065Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fgQBpCx+IHry8MhBxkblG7p/18VwGMLMoE+yUNOoKUcrOl3ykmdOEsLTDqhZpFFcc7lwku8kaCzvzaUznpZiAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:28.584605Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.02626","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:68ac58d14497e1d34764b6e942ba5c8e2e5ff6bd062a8a1384955a98855f3d9c","sha256:2cbfe761a37802cbf4e6937187cfa7150f1f4041d57bee1b96a989e11006c737"],"state_sha256":"433f83b77da9932dfe0846ecf5578e45c253da91aa440206313972642ee59992"}