{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:WH4HV6VODWUOXMKT7FKOFK3MAN","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":"9507d83329a439dc894646f109d7c224139262972adba6da6ef4b63ab1a9c7ec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-01-27T18:24:28Z","title_canon_sha256":"bf3af700baadc09e30718aeef8e544b881ee16c7ae65ac456644fc71e0819fd0"},"schema_version":"1.0","source":{"id":"1601.07484","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.07484","created_at":"2026-05-18T01:21:45Z"},{"alias_kind":"arxiv_version","alias_value":"1601.07484v1","created_at":"2026-05-18T01:21:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.07484","created_at":"2026-05-18T01:21:45Z"},{"alias_kind":"pith_short_12","alias_value":"WH4HV6VODWUO","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"WH4HV6VODWUOXMKT","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"WH4HV6VO","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:22857faf29b18fe0a1d67efe0a18e9481259aac90a7ee73832470dedc67061c5","target":"graph","created_at":"2026-05-18T01:21:45Z","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 analyse the family of $C^1$-Virtual Elements introduced in \\cite{Brezzi:Marini:plates} for fourth-order problems and prove optimal estimates in $L^2$ and in $H^1$ via classical duality arguments.","authors_text":"Claudia Chinosi, L. Donatella Marini","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-01-27T18:24:28Z","title":"Virtual Element Method for fourth order problems: $L^2-$estimates"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.07484","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":"sha256:6e16a2a140efd87cb09bad08eb4c420e7d233fbf46df60a20e3ded7fb84dd594","target":"record","created_at":"2026-05-18T01:21:45Z","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":"9507d83329a439dc894646f109d7c224139262972adba6da6ef4b63ab1a9c7ec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-01-27T18:24:28Z","title_canon_sha256":"bf3af700baadc09e30718aeef8e544b881ee16c7ae65ac456644fc71e0819fd0"},"schema_version":"1.0","source":{"id":"1601.07484","kind":"arxiv","version":1}},"canonical_sha256":"b1f87afaae1da8ebb153f954e2ab6c0351865702dfe05b626e69e6d1b615e633","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b1f87afaae1da8ebb153f954e2ab6c0351865702dfe05b626e69e6d1b615e633","first_computed_at":"2026-05-18T01:21:45.783331Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:45.783331Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"C4Wf+zbDiB9kgAVhUkkI3jBr/RinGMBglqIARto5uFhoc3Je+a/lM4Bj2Tx2j200c91r394X9A42qxqox7NoCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:45.783794Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.07484","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6e16a2a140efd87cb09bad08eb4c420e7d233fbf46df60a20e3ded7fb84dd594","sha256:22857faf29b18fe0a1d67efe0a18e9481259aac90a7ee73832470dedc67061c5"],"state_sha256":"af3854706f2e3eb2cc25dc29074cbcd0e5f88dfcba122b28790906aadb6fbe31"}