{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:3VE6KBMAFVYFNRT7XGPUKQDWH2","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":"0f7c1571257d3aba509e74685cf37a2d920680e748bfab828c89a637b6f53d35","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2022-05-18T07:22:07Z","title_canon_sha256":"5c5ac05bd9f0763b7421f35bf9a6d563de5245f5b7fffad1356ee5fbf9ccc947"},"schema_version":"1.0","source":{"id":"2205.08764","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2205.08764","created_at":"2026-07-05T04:24:28Z"},{"alias_kind":"arxiv_version","alias_value":"2205.08764v1","created_at":"2026-07-05T04:24:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2205.08764","created_at":"2026-07-05T04:24:28Z"},{"alias_kind":"pith_short_12","alias_value":"3VE6KBMAFVYF","created_at":"2026-07-05T04:24:28Z"},{"alias_kind":"pith_short_16","alias_value":"3VE6KBMAFVYFNRT7","created_at":"2026-07-05T04:24:28Z"},{"alias_kind":"pith_short_8","alias_value":"3VE6KBMA","created_at":"2026-07-05T04:24:28Z"}],"graph_snapshots":[{"event_id":"sha256:0615573e8a16752691c58f8df09105f158771aec6701efb69a0b40ac269b3986","target":"graph","created_at":"2026-07-05T04:24:28Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2205.08764/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The lowest-order nonconforming virtual element extends the Morley triangular element to polygons for the approximation of the weak solution $u\\in V:=H^2_0(\\Omega)$ to the biharmonic equation. The abstract framework allows (even a mixture of) two examples of the local discrete spaces $V_h(P)$ and a smoother allows rough source terms $F\\in V^*=H^{-2}(\\Omega)$. The a priori and a posteriori error analysis in this paper circumvents any trace of second derivatives by some computable conforming companion operator $J:V_h\\to V$ from the nonconforming virtual element space $V_h$. The operator $J$ is a ","authors_text":"Amiya K. Pani, Carsten Carstensen, Rekha Khot","cross_cats":["cs.NA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2022-05-18T07:22:07Z","title":"Nonconforming virtual elements for the biharmonic equation with Morley degrees of freedom on polygonal meshes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2205.08764","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":"sha256:816e1ba1fd071b103039f25e6c0df81a4e28e4e912566555ab45a6f89636ec93","target":"record","created_at":"2026-07-05T04:24:28Z","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":"0f7c1571257d3aba509e74685cf37a2d920680e748bfab828c89a637b6f53d35","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2022-05-18T07:22:07Z","title_canon_sha256":"5c5ac05bd9f0763b7421f35bf9a6d563de5245f5b7fffad1356ee5fbf9ccc947"},"schema_version":"1.0","source":{"id":"2205.08764","kind":"arxiv","version":1}},"canonical_sha256":"dd49e505802d7056c67fb99f4540763e82fed992dfe45a11a5efc0b7f6c6b396","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dd49e505802d7056c67fb99f4540763e82fed992dfe45a11a5efc0b7f6c6b396","first_computed_at":"2026-07-05T04:24:28.984041Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:24:28.984041Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"U29s7fPWbLtqY6rawVLK8YlFpLDMUT00YGy65RMXKQCdlChOD1qauL0csvt4s3g9GaV019Kk1WDrINIcxAt5Dg==","signature_status":"signed_v1","signed_at":"2026-07-05T04:24:28.984494Z","signed_message":"canonical_sha256_bytes"},"source_id":"2205.08764","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:816e1ba1fd071b103039f25e6c0df81a4e28e4e912566555ab45a6f89636ec93","sha256:0615573e8a16752691c58f8df09105f158771aec6701efb69a0b40ac269b3986"],"state_sha256":"74a3dd83604eb704c24bdcff7da67d4d1995d3fbedaa2fb8962b05e20f32eca8"}