{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:HZRFTGQHMSN62KGLAYTJXHAQUI","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":"c561b4293c0e560889fda111e39cbe921e22dd38e891426502c733a48eae9e7c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-11-14T11:28:46Z","title_canon_sha256":"693fde6f728e59a1d57e81088fd0642e565fa4ef66c16727f7d1f55ce4db348c"},"schema_version":"1.0","source":{"id":"1811.05731","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.05731","created_at":"2026-05-17T23:50:23Z"},{"alias_kind":"arxiv_version","alias_value":"1811.05731v2","created_at":"2026-05-17T23:50:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.05731","created_at":"2026-05-17T23:50:23Z"},{"alias_kind":"pith_short_12","alias_value":"HZRFTGQHMSN6","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"HZRFTGQHMSN62KGL","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"HZRFTGQH","created_at":"2026-05-18T12:32:28Z"}],"graph_snapshots":[{"event_id":"sha256:da98b0a8c0096d7d90bd9315d5c8eb2ae4e7d2e5a05cb2c53611e048cfc9e868","target":"graph","created_at":"2026-05-17T23:50:23Z","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":"Magnetostatic field calculations in micromagnetic simulations can be numerically expensive, particularly in the case of large-scale finite element simulations. The established finite element / boundary element method (FEM/BEM) by Fredkin & Koehler involves a densely populated matrix with unacceptable numerical costs for problems involving a large number of degrees of freedom $N$. By using hierarchical matrices of $\\mathcal{H}^2$ type, we show that the memory requirements for the FEM/BEM method can be reduced dramatically, effectively converting the quadratic complexity $\\mathcal{O}(N^2)$ of th","authors_text":"Riccardo Hertel, Steffen B\\\"orm, Sven Christophersen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-11-14T11:28:46Z","title":"Large-scale magnetostatic field calculation in finite element micromagnetics with H2-matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.05731","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":"sha256:1de28c975ee9fba37d6a2bb63901d1771f6e4e678c6bcbb916e7880b018fbfd0","target":"record","created_at":"2026-05-17T23:50:23Z","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":"c561b4293c0e560889fda111e39cbe921e22dd38e891426502c733a48eae9e7c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-11-14T11:28:46Z","title_canon_sha256":"693fde6f728e59a1d57e81088fd0642e565fa4ef66c16727f7d1f55ce4db348c"},"schema_version":"1.0","source":{"id":"1811.05731","kind":"arxiv","version":2}},"canonical_sha256":"3e62599a07649bed28cb06269b9c10a2362c4efc0ca0277fefe9bd749149b6a0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3e62599a07649bed28cb06269b9c10a2362c4efc0ca0277fefe9bd749149b6a0","first_computed_at":"2026-05-17T23:50:23.006421Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:23.006421Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QKlsV6gsj7zzi6/zo0SQSkyVUTSf5u9abFbUZHC7H3+nmwbelzB3oToXhmCkh1/Ahs2vkHTeUE0jBV/pYMB1Bw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:23.006954Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.05731","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1de28c975ee9fba37d6a2bb63901d1771f6e4e678c6bcbb916e7880b018fbfd0","sha256:da98b0a8c0096d7d90bd9315d5c8eb2ae4e7d2e5a05cb2c53611e048cfc9e868"],"state_sha256":"fd02d54ccccefa25a775a9440463e5c7418b95d693c85e52532f99c4aa7a1710"}