{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:RELKE5HLYFKGW2ORFD2WX33SEB","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":"7e921e008fd4512682c297210b2b61b5b2fb35df34c617d94b4a514473fbb5b8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-01-17T22:06:41Z","title_canon_sha256":"77fa0aa3a7e24a291b436a1bff97864e64e0477737ab85bbf5a663a0159efe1a"},"schema_version":"1.0","source":{"id":"1201.3651","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.3651","created_at":"2026-05-18T02:49:20Z"},{"alias_kind":"arxiv_version","alias_value":"1201.3651v3","created_at":"2026-05-18T02:49:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.3651","created_at":"2026-05-18T02:49:20Z"},{"alias_kind":"pith_short_12","alias_value":"RELKE5HLYFKG","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"RELKE5HLYFKGW2OR","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"RELKE5HL","created_at":"2026-05-18T12:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:e11c00737c20cf07d38ad97ee26fb56458abac9624c7fbbade53ccd881bab33d","target":"graph","created_at":"2026-05-18T02:49:20Z","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":"Bounds are developed for the condition number of the linear finite element equations of an anisotropic diffusion problem with arbitrary meshes. They depend on three factors. The first, factor proportional to a power of the number of mesh elements, represents the condition number of the linear finite element equations for the Laplacian operator on a uniform mesh. The other two factors arise from the mesh nonuniformity viewed in the Euclidean metric and in the metric defined by the diffusion matrix. The new bounds reveal that the conditioning of the finite element equations with adaptive anisotr","authors_text":"Hongguo Xu, Lennard Kamenski, Weizhang Huang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-01-17T22:06:41Z","title":"Conditioning of Finite Element Equations with Arbitrary Anisotropic Meshes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.3651","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":"sha256:1da3428d01d0f85308b0e15d28e0c4fe72845f9f5376e1df1770c9d9e636fbb8","target":"record","created_at":"2026-05-18T02:49:20Z","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":"7e921e008fd4512682c297210b2b61b5b2fb35df34c617d94b4a514473fbb5b8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-01-17T22:06:41Z","title_canon_sha256":"77fa0aa3a7e24a291b436a1bff97864e64e0477737ab85bbf5a663a0159efe1a"},"schema_version":"1.0","source":{"id":"1201.3651","kind":"arxiv","version":3}},"canonical_sha256":"8916a274ebc1546b69d128f56bef72206a87f8d616abc096b6b60aa10cd00e1e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8916a274ebc1546b69d128f56bef72206a87f8d616abc096b6b60aa10cd00e1e","first_computed_at":"2026-05-18T02:49:20.608532Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:49:20.608532Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Z/03HIg6oRAnrqkVreyZupUZQ6bQjnjOSbz6VL3abtPOQJQDhmKAtcYgyAKSf/G6pCUVLSgkCu+Uddc+rAOpDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:49:20.609160Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.3651","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1da3428d01d0f85308b0e15d28e0c4fe72845f9f5376e1df1770c9d9e636fbb8","sha256:e11c00737c20cf07d38ad97ee26fb56458abac9624c7fbbade53ccd881bab33d"],"state_sha256":"409f36109014a4f882ffbec5771c597d436c99156f9aa1bec4187454e62ac9e7"}