{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:RUQWNR3NEK5VLGLDGESXKE5O7E","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":"ab92e9e0514dcd491e1ecf8f9d08b5c32cb5372948b679cfcc7b6f8b220c5636","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-04-24T08:13:57Z","title_canon_sha256":"b45a5f9d9ae725bf8f7928de8032092a09ae19e88a930be0c8e5b2d15c27567f"},"schema_version":"1.0","source":{"id":"1504.06418","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.06418","created_at":"2026-05-18T02:17:53Z"},{"alias_kind":"arxiv_version","alias_value":"1504.06418v1","created_at":"2026-05-18T02:17:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.06418","created_at":"2026-05-18T02:17:53Z"},{"alias_kind":"pith_short_12","alias_value":"RUQWNR3NEK5V","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"RUQWNR3NEK5VLGLD","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"RUQWNR3N","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:1245b99673113a94ebbad7cb4c93a2a6ce9163ee4b7d27ef7b3a742ab9619c34","target":"graph","created_at":"2026-05-18T02:17:53Z","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":"It is shown that the h-adaptive mixed finite element method for the discretization of eigenvalue clusters of the Laplace operator produces optimal convergence rates in terms of nonlinear approximation classes. The results are valid for the typical mixed spaces of Raviart-Thomas or Brezzi-Douglas-Marini type with arbitrary fixed polynomial degree in two and three space dimensions.","authors_text":"Daniele Boffi, Dietmar Gallistl, Francesca Gardini, Lucia Gastaldi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-04-24T08:13:57Z","title":"Optimal convergence of adaptive FEM for eigenvalue clusters in mixed form"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.06418","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":"sha256:930768e96d4b6a8f3d4e7235f324adf0656211dd30780d0599a35ac850bb96fe","target":"record","created_at":"2026-05-18T02:17:53Z","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":"ab92e9e0514dcd491e1ecf8f9d08b5c32cb5372948b679cfcc7b6f8b220c5636","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-04-24T08:13:57Z","title_canon_sha256":"b45a5f9d9ae725bf8f7928de8032092a09ae19e88a930be0c8e5b2d15c27567f"},"schema_version":"1.0","source":{"id":"1504.06418","kind":"arxiv","version":1}},"canonical_sha256":"8d2166c76d22bb55996331257513aef90eb6bca663220479c7e0f74d972b8628","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8d2166c76d22bb55996331257513aef90eb6bca663220479c7e0f74d972b8628","first_computed_at":"2026-05-18T02:17:53.703491Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:17:53.703491Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"y6+YjXMSlsmk19Uh7NERPSWqIa+zq6B7XxE+AHy9J5LgAFujtJmqxfUjJhcvARTASTh99XYMTgY2or8eSaORBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:17:53.704047Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.06418","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:930768e96d4b6a8f3d4e7235f324adf0656211dd30780d0599a35ac850bb96fe","sha256:1245b99673113a94ebbad7cb4c93a2a6ce9163ee4b7d27ef7b3a742ab9619c34"],"state_sha256":"7c49c690fcafe47f6da187852f7b6ff4084c98911487438454bfe7cc5cd05d9d"}