{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:SROAMLJT4SXOM2VPR7XZXAMNGK","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":"ae2083bae2eeaf4d3a1988203330e25d0c887fecfdcc147dc67f32e755e13b66","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-05-08T12:01:58Z","title_canon_sha256":"53dff9951b660d7d7ac0dcb958cd851e4d5e7faa0947f1a5507c8ff5f0ac87a9"},"schema_version":"1.0","source":{"id":"1805.02962","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.02962","created_at":"2026-05-18T00:16:35Z"},{"alias_kind":"arxiv_version","alias_value":"1805.02962v1","created_at":"2026-05-18T00:16:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.02962","created_at":"2026-05-18T00:16:35Z"},{"alias_kind":"pith_short_12","alias_value":"SROAMLJT4SXO","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"SROAMLJT4SXOM2VP","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"SROAMLJT","created_at":"2026-05-18T12:32:53Z"}],"graph_snapshots":[{"event_id":"sha256:44b3b171973bdf82aca145ea90260c975d9ad404693715cb9ee8b38a100cb204","target":"graph","created_at":"2026-05-18T00:16:35Z","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 first construct the $H^2$(curl)-conforming finite elements both on a rectangle and a triangle. They possess some fascinating properties which have been proven by a rigorous theoretical analysis. Then we apply the elements to construct a finite element space for discretizing quad-curl problems. Convergence orders $O(h^k)$ in the $H$(curl) norm and $O(h^{k-1})$ in the $H^2$(curl) norm are established. Numerical experiments are provided to confirm our theoretical results.","authors_text":"Lixiu Wang, Qian Zhang, Zhimin Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-05-08T12:01:58Z","title":"An $H^2$(curl)-conforming finite element in 2D and its applications to the quad-curl problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.02962","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":"sha256:88dda9b5134b4322ab21417f47f1e62106a16b7f1190886fe1402376fb027c93","target":"record","created_at":"2026-05-18T00:16:35Z","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":"ae2083bae2eeaf4d3a1988203330e25d0c887fecfdcc147dc67f32e755e13b66","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-05-08T12:01:58Z","title_canon_sha256":"53dff9951b660d7d7ac0dcb958cd851e4d5e7faa0947f1a5507c8ff5f0ac87a9"},"schema_version":"1.0","source":{"id":"1805.02962","kind":"arxiv","version":1}},"canonical_sha256":"945c062d33e4aee66aaf8fef9b818d32a6f13c75555deca6f5eed48719ea875b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"945c062d33e4aee66aaf8fef9b818d32a6f13c75555deca6f5eed48719ea875b","first_computed_at":"2026-05-18T00:16:35.110012Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:16:35.110012Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TeNaah3vg30D020118S//my8PZYVWZgENpQS1tqOMcXqfj04AMJ4b1HnTqKRCcBsx98Ta42LD59B4WY/Qvd0Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:16:35.110690Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.02962","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:88dda9b5134b4322ab21417f47f1e62106a16b7f1190886fe1402376fb027c93","sha256:44b3b171973bdf82aca145ea90260c975d9ad404693715cb9ee8b38a100cb204"],"state_sha256":"997f8df18e7766767d080282af3beced9d92a5f4766698ae0dc174071a89eb86"}