{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:OD3FAXI6PGMYPL5YJ5LSOXMAZB","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":"23d2719466ff64c8bd7ebeb12344d6ef94c3cdf48c2cc28480bcf8508723a0b6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-06-19T20:11:21Z","title_canon_sha256":"4caae49d766eb0f7a92f13f27e83f88ec1d0c0bd8285b7c6f412957c72c69f5f"},"schema_version":"1.0","source":{"id":"1306.4690","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.4690","created_at":"2026-05-18T02:38:59Z"},{"alias_kind":"arxiv_version","alias_value":"1306.4690v2","created_at":"2026-05-18T02:38:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.4690","created_at":"2026-05-18T02:38:59Z"},{"alias_kind":"pith_short_12","alias_value":"OD3FAXI6PGMY","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"OD3FAXI6PGMYPL5Y","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"OD3FAXI6","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:d5a9dd6524042b5c29e37295b3fa1f08d4e24320b4b30fc1b60db67095e582b3","target":"graph","created_at":"2026-05-18T02:38:59Z","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 present a method for computing reduced-order models of parameterized partial differential equation solutions. The key analytical tool is the singular value expansion of the parameterized solution, which we approximate with a singular value decomposition of a parameter snapshot matrix. To evaluate the reduced-order model at a new parameter, we interpolate a subset of the right singular vectors to generate the reduced-order model's coefficients. We employ a novel method to select this subset that uses the parameter gradient of the right singular vectors to split the terms in the expansion yie","authors_text":"David F. Gleich, Jeremy Templeton, Paul G. Constantine, Yangyang Hou","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-06-19T20:11:21Z","title":"Model Reduction with MapReduce-enabled Tall-and-Skinny Singular Value Decomposition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.4690","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":"sha256:57bd8824b7d437ddbae8d769638856e97cd8d7ab5369797c97b8be68b10ec387","target":"record","created_at":"2026-05-18T02:38:59Z","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":"23d2719466ff64c8bd7ebeb12344d6ef94c3cdf48c2cc28480bcf8508723a0b6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-06-19T20:11:21Z","title_canon_sha256":"4caae49d766eb0f7a92f13f27e83f88ec1d0c0bd8285b7c6f412957c72c69f5f"},"schema_version":"1.0","source":{"id":"1306.4690","kind":"arxiv","version":2}},"canonical_sha256":"70f6505d1e799987afb84f57275d80c854785a90988bc3cc1a666dad8b6d0f2d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"70f6505d1e799987afb84f57275d80c854785a90988bc3cc1a666dad8b6d0f2d","first_computed_at":"2026-05-18T02:38:59.562737Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:38:59.562737Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8b9MbnkqTFf7WInCL4MB5GBNY7g702z609cOaKht9r5INLbikRV3Yhm2x/XPm0h+ZEOYnzvo9vvptXMljvoXDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:38:59.563125Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.4690","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:57bd8824b7d437ddbae8d769638856e97cd8d7ab5369797c97b8be68b10ec387","sha256:d5a9dd6524042b5c29e37295b3fa1f08d4e24320b4b30fc1b60db67095e582b3"],"state_sha256":"b16880bedecec8040b86e3ef5f07fb73857d177f7f9d82ba9c308e8859f1ac78"}