{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:TSFJN6BWTNDDOM36OLXJWQMOKR","short_pith_number":"pith:TSFJN6BW","canonical_record":{"source":{"id":"1711.06099","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-11-16T14:10:31Z","cross_cats_sorted":[],"title_canon_sha256":"77d535715e81badd4189b5ad687d4c7629c0de5334fd1c9ca58b0fedddbcc0c9","abstract_canon_sha256":"faae810313be1d3b3661247ffe2f654a919c196978d5c81dc8a3407e81a984cd"},"schema_version":"1.0"},"canonical_sha256":"9c8a96f8369b4637337e72ee9b418e54766902d90b2113d448d9b56a8ae58382","source":{"kind":"arxiv","id":"1711.06099","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:TSFJN6BWTNDDOM36OLXJWQMOKR","target":"record","payload":{"canonical_record":{"source":{"id":"1711.06099","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-11-16T14:10:31Z","cross_cats_sorted":[],"title_canon_sha256":"77d535715e81badd4189b5ad687d4c7629c0de5334fd1c9ca58b0fedddbcc0c9","abstract_canon_sha256":"faae810313be1d3b3661247ffe2f654a919c196978d5c81dc8a3407e81a984cd"},"schema_version":"1.0"},"canonical_sha256":"9c8a96f8369b4637337e72ee9b418e54766902d90b2113d448d9b56a8ae58382","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:30:23.274087Z","signature_b64":"jcF5NNiwGhDEpK1mAbmpei/jbhEzTN0VMBw4dxPhdDgOlYTdmWF4lLHogHZHff66z41tKWbYF2WS4RFT/hCFDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9c8a96f8369b4637337e72ee9b418e54766902d90b2113d448d9b56a8ae58382","last_reissued_at":"2026-05-18T00:30:23.273488Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:30:23.273488Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1711.06099","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:30:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9ED4K83x9djWyHW63QCDhz9uXf7X0neeOTbjMuHbEJ6iI1fPfRFbBDEMghYb8JBKNgs2RmeAzbnYz0HJmup0AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T22:33:18.281561Z"},"content_sha256":"70cda946d7c41f96dd658664e8b89f5bd1bbf8cda48d72f84896f4fc079af9b5","schema_version":"1.0","event_id":"sha256:70cda946d7c41f96dd658664e8b89f5bd1bbf8cda48d72f84896f4fc079af9b5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:TSFJN6BWTNDDOM36OLXJWQMOKR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An optimal adaptive wavelet method for First Order System Least Squares","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Nikolaos Rekatsinas, Rob Stevenson","submitted_at":"2017-11-16T14:10:31Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.06099","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:30:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g+h0D/HbmNGTchrEPjsyMJ4oTVf3W8/FUisTJsxOeuAe0VQBHVFaQPcqPoOgGYvFXQ1+L+1w+qLss9YeO7TqAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T22:33:18.281911Z"},"content_sha256":"52c4f7d3c826d3233ba50af9817a4274ad5acedff79cb82d163a92a92c0d3a04","schema_version":"1.0","event_id":"sha256:52c4f7d3c826d3233ba50af9817a4274ad5acedff79cb82d163a92a92c0d3a04"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TSFJN6BWTNDDOM36OLXJWQMOKR/bundle.json","state_url":"https://pith.science/pith/TSFJN6BWTNDDOM36OLXJWQMOKR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TSFJN6BWTNDDOM36OLXJWQMOKR/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-28T22:33:18Z","links":{"resolver":"https://pith.science/pith/TSFJN6BWTNDDOM36OLXJWQMOKR","bundle":"https://pith.science/pith/TSFJN6BWTNDDOM36OLXJWQMOKR/bundle.json","state":"https://pith.science/pith/TSFJN6BWTNDDOM36OLXJWQMOKR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TSFJN6BWTNDDOM36OLXJWQMOKR/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T4u+G1HqJJdPnO8RrIlqWXhDLxUMy0NYB9OSK1FEVj4+a0EHxlJjygOw19Y2S1HlG/RDs2o8HAaA9pcc7qEeDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T22:33:18.284073Z","bundle_sha256":"2fe681e58bb46897578deabd434f87936226c0fe061ee096895103f09a83ec36"}}