{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:WH4HV6VODWUOXMKT7FKOFK3MAN","short_pith_number":"pith:WH4HV6VO","canonical_record":{"source":{"id":"1601.07484","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-01-27T18:24:28Z","cross_cats_sorted":[],"title_canon_sha256":"bf3af700baadc09e30718aeef8e544b881ee16c7ae65ac456644fc71e0819fd0","abstract_canon_sha256":"9507d83329a439dc894646f109d7c224139262972adba6da6ef4b63ab1a9c7ec"},"schema_version":"1.0"},"canonical_sha256":"b1f87afaae1da8ebb153f954e2ab6c0351865702dfe05b626e69e6d1b615e633","source":{"kind":"arxiv","id":"1601.07484","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:WH4HV6VODWUOXMKT7FKOFK3MAN","target":"record","payload":{"canonical_record":{"source":{"id":"1601.07484","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-01-27T18:24:28Z","cross_cats_sorted":[],"title_canon_sha256":"bf3af700baadc09e30718aeef8e544b881ee16c7ae65ac456644fc71e0819fd0","abstract_canon_sha256":"9507d83329a439dc894646f109d7c224139262972adba6da6ef4b63ab1a9c7ec"},"schema_version":"1.0"},"canonical_sha256":"b1f87afaae1da8ebb153f954e2ab6c0351865702dfe05b626e69e6d1b615e633","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:45.783794Z","signature_b64":"C4Wf+zbDiB9kgAVhUkkI3jBr/RinGMBglqIARto5uFhoc3Je+a/lM4Bj2Tx2j200c91r394X9A42qxqox7NoCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b1f87afaae1da8ebb153f954e2ab6c0351865702dfe05b626e69e6d1b615e633","last_reissued_at":"2026-05-18T01:21:45.783331Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:45.783331Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.07484","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:21:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"npXBqmyQsan8L7h4CftJZpPZiTWIE0T8zAzQ/FJ377yNEU34AXTfEcCnhPhlslSk5ShlaEtmFRFmwYQkzdo3BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T16:26:26.965211Z"},"content_sha256":"6e16a2a140efd87cb09bad08eb4c420e7d233fbf46df60a20e3ded7fb84dd594","schema_version":"1.0","event_id":"sha256:6e16a2a140efd87cb09bad08eb4c420e7d233fbf46df60a20e3ded7fb84dd594"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:WH4HV6VODWUOXMKT7FKOFK3MAN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Virtual Element Method for fourth order problems: $L^2-$estimates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Claudia Chinosi, L. Donatella Marini","submitted_at":"2016-01-27T18:24:28Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.07484","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:21:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BzFobG9mRF5ewGMrQiFSUFWfWj2YnLf7wCVBjaL5C4co+HpaERFE4Dvb2CNNRMVbJe6+YNDxVS8wrnR+uuc0Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T16:26:26.965859Z"},"content_sha256":"22857faf29b18fe0a1d67efe0a18e9481259aac90a7ee73832470dedc67061c5","schema_version":"1.0","event_id":"sha256:22857faf29b18fe0a1d67efe0a18e9481259aac90a7ee73832470dedc67061c5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WH4HV6VODWUOXMKT7FKOFK3MAN/bundle.json","state_url":"https://pith.science/pith/WH4HV6VODWUOXMKT7FKOFK3MAN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WH4HV6VODWUOXMKT7FKOFK3MAN/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-06T16:26:26Z","links":{"resolver":"https://pith.science/pith/WH4HV6VODWUOXMKT7FKOFK3MAN","bundle":"https://pith.science/pith/WH4HV6VODWUOXMKT7FKOFK3MAN/bundle.json","state":"https://pith.science/pith/WH4HV6VODWUOXMKT7FKOFK3MAN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WH4HV6VODWUOXMKT7FKOFK3MAN/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DmeLDYHZQw3CFkLMwZCkmKlr6vc/HFUm/4RlByAEaCiD2Ksxv36qVUhGJRS70J+JxjJYjDwpS0p0m4+S9E5WCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T16:26:26.968947Z","bundle_sha256":"a1bc210f1b06970bd25dc7592454d27253aca546237bdeda273874f5f561cd84"}}