{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:7IAIOP2ZGN6AOZA4HO2HI625A3","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":"6527d5fb0257583095e2a1eb061834dec1666c4c3aa822bb335d502bbae99eb7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-05-25T09:39:43Z","title_canon_sha256":"eb139980c974f5d37d924b36082d0b62a328eaca0d9cdd9c74ed1500d26defb6"},"schema_version":"1.0","source":{"id":"1805.10058","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.10058","created_at":"2026-05-17T23:57:41Z"},{"alias_kind":"arxiv_version","alias_value":"1805.10058v1","created_at":"2026-05-17T23:57:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.10058","created_at":"2026-05-17T23:57:41Z"},{"alias_kind":"pith_short_12","alias_value":"7IAIOP2ZGN6A","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"7IAIOP2ZGN6AOZA4","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"7IAIOP2Z","created_at":"2026-05-18T12:32:11Z"}],"graph_snapshots":[{"event_id":"sha256:f89e08933285810edef47118120bb8772d531daf7f5e7b9564fbbc12f8440b13","target":"graph","created_at":"2026-05-17T23:57:41Z","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":"Alfv\\'en-like operators are of interest in magnetohydrodynamics, which is used in plasma physics to study the macroscopic behavior of plasma. Motivated by this important and complex application, we focus on a parameter-dependent curl-div problem that can be seen as a prototype of an Alfv\\'en-like operator, and we discretize it using isogeometric analysis based on tensor-product B-splines. The involved coefficient matrices can be very ill-conditioned, so that standard numerical solution methods perform quite poorly here. In order to overcome the difficulties caused by such ill-conditioning, a t","authors_text":"Ahmed Ratnani, Carla Manni, Hendrik Speleers, Mariarosa Mazza, Stefano Serra-Capizzano","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-05-25T09:39:43Z","title":"Isogeometric analysis for 2D and 3D curl-div problems: Spectral symbols and fast iterative solvers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.10058","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":"sha256:709fb5223843cbc950efdf8a307d38ac64776cba3430d8c6febad1f6f2353bd9","target":"record","created_at":"2026-05-17T23:57:41Z","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":"6527d5fb0257583095e2a1eb061834dec1666c4c3aa822bb335d502bbae99eb7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-05-25T09:39:43Z","title_canon_sha256":"eb139980c974f5d37d924b36082d0b62a328eaca0d9cdd9c74ed1500d26defb6"},"schema_version":"1.0","source":{"id":"1805.10058","kind":"arxiv","version":1}},"canonical_sha256":"fa00873f59337c07641c3bb4747b5d06d9a05345eccae8f0f6358337bd64ae2a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fa00873f59337c07641c3bb4747b5d06d9a05345eccae8f0f6358337bd64ae2a","first_computed_at":"2026-05-17T23:57:41.301629Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:41.301629Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uOYvlW6dF31Z21jx16rgbuXaW2De74Ir5LoM1+eNyl2xV3ariVEYRXkHajOVholBM8XC0xE/xZpPlLQC/ZvFAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:41.302069Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.10058","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:709fb5223843cbc950efdf8a307d38ac64776cba3430d8c6febad1f6f2353bd9","sha256:f89e08933285810edef47118120bb8772d531daf7f5e7b9564fbbc12f8440b13"],"state_sha256":"562355f0d12b2354c449193190d6487d443cb6f29cd59117ae328cbc3ceeb4a8"}