{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:KMVQWJVCKZIJZLSTEX3IQGCEFD","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":"27c25140dcbe1790358acbd38ab9786078f2e495dfd0cd02e21361202870e826","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-12-28T15:40:02Z","title_canon_sha256":"538309634dabe8715311a805a36e7da4828218554e257bc900f7e8c248c71613"},"schema_version":"1.0","source":{"id":"1812.11051","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.11051","created_at":"2026-05-17T23:47:43Z"},{"alias_kind":"arxiv_version","alias_value":"1812.11051v2","created_at":"2026-05-17T23:47:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.11051","created_at":"2026-05-17T23:47:43Z"},{"alias_kind":"pith_short_12","alias_value":"KMVQWJVCKZIJ","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"KMVQWJVCKZIJZLST","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"KMVQWJVC","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:e923e715496e2ff13b3cb21850ae6f8830adf0ea6f92d381bedbcc1937475bcb","target":"graph","created_at":"2026-05-17T23:47:43Z","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 the Navier-Stokes equations in a channel with a narrowing of varying height. The model is discretized with high-order spectral element ansatz functions, resulting in 6372 degrees of freedom. The steady-state snapshot solutions define a reduced order space through a standard POD procedure. The reduced order space allows to accurately and efficiently evaluate the steady-state solutions for different geometries. In particular, we detail different aspects of implementing the reduced order model in combination with a spectral element discretization. It is shown that an expansion in elem","authors_text":"Annalisa Quaini, Gianluigi Rozza, Martin W. Hess","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-12-28T15:40:02Z","title":"A Spectral Element Reduced Basis Method for Navier-Stokes Equations with Geometric Variations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.11051","kind":"arxiv","version":2},"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":"sha256:4e161a26855e8029c0b36644684542cca8f63b64e653484948eb59445cfe2fe1","target":"record","created_at":"2026-05-17T23:47:43Z","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":"27c25140dcbe1790358acbd38ab9786078f2e495dfd0cd02e21361202870e826","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-12-28T15:40:02Z","title_canon_sha256":"538309634dabe8715311a805a36e7da4828218554e257bc900f7e8c248c71613"},"schema_version":"1.0","source":{"id":"1812.11051","kind":"arxiv","version":2}},"canonical_sha256":"532b0b26a256509cae5325f688184428d45ffb655fcf0a340958e01b6507f982","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"532b0b26a256509cae5325f688184428d45ffb655fcf0a340958e01b6507f982","first_computed_at":"2026-05-17T23:47:43.942298Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:43.942298Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YI8WQPlf4Wx0GIyqD0HjW9oMf5QZpORZxmvSWGx0Ru+ireln0YgdYgruCaUk5n0QvwsWJcs0H/xzQI8nZlXgAA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:43.942908Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.11051","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4e161a26855e8029c0b36644684542cca8f63b64e653484948eb59445cfe2fe1","sha256:e923e715496e2ff13b3cb21850ae6f8830adf0ea6f92d381bedbcc1937475bcb"],"state_sha256":"b4cb874ebdfb9420d2280968f3cce501763db188a37dde34e379a089c25a2857"}