{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:TSFJN6BWTNDDOM36OLXJWQMOKR","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":"faae810313be1d3b3661247ffe2f654a919c196978d5c81dc8a3407e81a984cd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-11-16T14:10:31Z","title_canon_sha256":"77d535715e81badd4189b5ad687d4c7629c0de5334fd1c9ca58b0fedddbcc0c9"},"schema_version":"1.0","source":{"id":"1711.06099","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.06099","created_at":"2026-05-18T00:30:23Z"},{"alias_kind":"arxiv_version","alias_value":"1711.06099v1","created_at":"2026-05-18T00:30:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.06099","created_at":"2026-05-18T00:30:23Z"},{"alias_kind":"pith_short_12","alias_value":"TSFJN6BWTNDD","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"TSFJN6BWTNDDOM36","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"TSFJN6BW","created_at":"2026-05-18T12:31:46Z"}],"graph_snapshots":[{"event_id":"sha256:52c4f7d3c826d3233ba50af9817a4274ad5acedff79cb82d163a92a92c0d3a04","target":"graph","created_at":"2026-05-18T00:30:23Z","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":"In this paper, it is shown that any well-posed 2nd order PDE can be reformulated as a well-posed first order least squares system. This system will be solved by an adaptive wavelet solver in optimal computational complexity. The applications that are considered are second order elliptic PDEs with general inhomogeneous boundary conditions, and the stationary Navier-Stokes equations.","authors_text":"Nikolaos Rekatsinas, Rob Stevenson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-11-16T14:10:31Z","title":"An optimal adaptive wavelet method for First Order System Least Squares"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.06099","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":"sha256:70cda946d7c41f96dd658664e8b89f5bd1bbf8cda48d72f84896f4fc079af9b5","target":"record","created_at":"2026-05-18T00:30:23Z","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":"faae810313be1d3b3661247ffe2f654a919c196978d5c81dc8a3407e81a984cd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-11-16T14:10:31Z","title_canon_sha256":"77d535715e81badd4189b5ad687d4c7629c0de5334fd1c9ca58b0fedddbcc0c9"},"schema_version":"1.0","source":{"id":"1711.06099","kind":"arxiv","version":1}},"canonical_sha256":"9c8a96f8369b4637337e72ee9b418e54766902d90b2113d448d9b56a8ae58382","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9c8a96f8369b4637337e72ee9b418e54766902d90b2113d448d9b56a8ae58382","first_computed_at":"2026-05-18T00:30:23.273488Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:30:23.273488Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jcF5NNiwGhDEpK1mAbmpei/jbhEzTN0VMBw4dxPhdDgOlYTdmWF4lLHogHZHff66z41tKWbYF2WS4RFT/hCFDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:30:23.274087Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.06099","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:70cda946d7c41f96dd658664e8b89f5bd1bbf8cda48d72f84896f4fc079af9b5","sha256:52c4f7d3c826d3233ba50af9817a4274ad5acedff79cb82d163a92a92c0d3a04"],"state_sha256":"3fe20ada724c78e759040663198e296a38c35da47b912549bc1a99efd2cefdd3"}