{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:OTMTMJYRITYADLMS4VHTRTQRUA","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":"d269127e60a452160ec9e93707cd6cbbc830ce046376c0b3f4964dbea2c6a5bb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-02-02T08:35:47Z","title_canon_sha256":"b91931b026bfe9a33e3af619c7385d93b70aed439b00db86ea6551d1a779f7a4"},"schema_version":"1.0","source":{"id":"1802.00597","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.00597","created_at":"2026-05-18T00:24:32Z"},{"alias_kind":"arxiv_version","alias_value":"1802.00597v1","created_at":"2026-05-18T00:24:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.00597","created_at":"2026-05-18T00:24:32Z"},{"alias_kind":"pith_short_12","alias_value":"OTMTMJYRITYA","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"OTMTMJYRITYADLMS","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"OTMTMJYR","created_at":"2026-05-18T12:32:43Z"}],"graph_snapshots":[{"event_id":"sha256:f5dc9f21990ad5685602ace2effe8aa5691c6aabbb5bb16bcfe51560727fe82a","target":"graph","created_at":"2026-05-18T00:24:32Z","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 study the spectral approximation of a second-order elliptic differential eigenvalue problem that arises from structural vibration problems using isogeometric analysis. In this paper, we generalize recent work in this direction. We present optimally blended quadrature rules for the isogeometric spectral approximation of a diffusion-reaction operator with both Dirichlet and Neumann boundary conditions. The blended rules improve the accuracy and the robustness of the isogeometric approximation. In particular, the optimal blending rules minimize the dispersion error and lead to two extra orders","authors_text":"Quanling Deng, Victor Calo, Vladimir Puzyrev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-02-02T08:35:47Z","title":"Isogeometric spectral approximation for elliptic differential operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.00597","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:d9f6e376b1f9652bf0697d31a808b209d11b2069e3e2d1b607a2c9e8bbf6df3d","target":"record","created_at":"2026-05-18T00:24:32Z","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":"d269127e60a452160ec9e93707cd6cbbc830ce046376c0b3f4964dbea2c6a5bb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-02-02T08:35:47Z","title_canon_sha256":"b91931b026bfe9a33e3af619c7385d93b70aed439b00db86ea6551d1a779f7a4"},"schema_version":"1.0","source":{"id":"1802.00597","kind":"arxiv","version":1}},"canonical_sha256":"74d936271144f001ad92e54f38ce11a037a8a7bb43f04cd27220df7244d2205a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"74d936271144f001ad92e54f38ce11a037a8a7bb43f04cd27220df7244d2205a","first_computed_at":"2026-05-18T00:24:32.795970Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:24:32.795970Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qgKZ71TRQytDz6S7a6enQbz7EHTElho8T+eIKs/HgQaNFtwr9yc/KYFANedu00Axe4j0ZYTvOeYs8FI/RxRkAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:24:32.796528Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.00597","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d9f6e376b1f9652bf0697d31a808b209d11b2069e3e2d1b607a2c9e8bbf6df3d","sha256:f5dc9f21990ad5685602ace2effe8aa5691c6aabbb5bb16bcfe51560727fe82a"],"state_sha256":"a64b38b39a5d527d8c65fc8ec470579836f3c7a4f52c8d580689101195fcb145"}