{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:APW6V33FJKD3VKOH42KLH5CCEU","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":"673ce84aff5008e0f0f67592622aebd35fc7b81aeca37e14af6261b6b31f4cc8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-04-27T13:37:48Z","title_canon_sha256":"9610df6d4d2e934572b1f7f6f2db29aa7326a6b27cefd60404de19fd928865ed"},"schema_version":"1.0","source":{"id":"1804.10497","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.10497","created_at":"2026-05-18T00:17:20Z"},{"alias_kind":"arxiv_version","alias_value":"1804.10497v1","created_at":"2026-05-18T00:17:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.10497","created_at":"2026-05-18T00:17:20Z"},{"alias_kind":"pith_short_12","alias_value":"APW6V33FJKD3","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"APW6V33FJKD3VKOH","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"APW6V33F","created_at":"2026-05-18T12:32:13Z"}],"graph_snapshots":[{"event_id":"sha256:840d01a04221b8c93ae94711c87216dc02da851c67b240cc17fc7b8168af78ed","target":"graph","created_at":"2026-05-18T00:17:20Z","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":"We consider, as a simple model problem, the application of Virtual Element Methods (VEM) to the linear Magnetostatic three-dimensional problem in the formulation of F. Kikuchi. In doing so, we also introduce new serendipity VEM spaces, where the serendipity reduction is made only on the faces of a general polyhedral decomposition (assuming that internal degrees of freedom could be more easily eliminated by static condensation). These new spaces are meant, more generally, for the combined approximation of $H^1$-conforming ($0$-forms), $H({\\rm {\\bf curl}})$-conforming ($1$-forms), and $H({\\rm di","authors_text":"A. Russo, F. Brezzi, F. Dassi, L. Beir\\~ao da Veiga, L.D. Marini","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-04-27T13:37:48Z","title":"A family of three-dimensional virtual elements with applications to magnetostatic"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.10497","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":"sha256:793145c3b4e443c49b9aa888faaa25631cdab71ed52f6d8e8335629ba744b7df","target":"record","created_at":"2026-05-18T00:17:20Z","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":"673ce84aff5008e0f0f67592622aebd35fc7b81aeca37e14af6261b6b31f4cc8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-04-27T13:37:48Z","title_canon_sha256":"9610df6d4d2e934572b1f7f6f2db29aa7326a6b27cefd60404de19fd928865ed"},"schema_version":"1.0","source":{"id":"1804.10497","kind":"arxiv","version":1}},"canonical_sha256":"03edeaef654a87baa9c7e694b3f44225290a98b859a35a197943af07a0d57fcc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"03edeaef654a87baa9c7e694b3f44225290a98b859a35a197943af07a0d57fcc","first_computed_at":"2026-05-18T00:17:20.593242Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:17:20.593242Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FTd7fCIM0TUulM8ux3ayiaOAjgHiZSqe0V9HWSPCe7n/hN2CznjaBJHUVnRvnIdudQLXSknvi1nA3pMSMIg2AA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:17:20.593859Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.10497","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:793145c3b4e443c49b9aa888faaa25631cdab71ed52f6d8e8335629ba744b7df","sha256:840d01a04221b8c93ae94711c87216dc02da851c67b240cc17fc7b8168af78ed"],"state_sha256":"50344109b31254fa5fc53aee5a6e8caa7c6afcca527b436df3ab57b9e9e08eaf"}