{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:S3NU4SKIWD5SXUJWY4JBR7PIQY","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":"10e5e382709f78fa15b1870022f2c1f1925ea3e68519e2893ba2b6cde964adf8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-04-21T15:38:25Z","title_canon_sha256":"dff31c17f6b29eb29c44effc4f31f3f9cc02334c0c286a1ecd46441462dda36e"},"schema_version":"1.0","source":{"id":"1704.06606","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.06606","created_at":"2026-05-18T00:23:45Z"},{"alias_kind":"arxiv_version","alias_value":"1704.06606v4","created_at":"2026-05-18T00:23:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.06606","created_at":"2026-05-18T00:23:45Z"},{"alias_kind":"pith_short_12","alias_value":"S3NU4SKIWD5S","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"S3NU4SKIWD5SXUJW","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"S3NU4SKI","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:459cde52179310bf068a93542e99f7e9af47176a442e3f24978d9a777780f128","target":"graph","created_at":"2026-05-18T00:23:45Z","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":"New contributions are offered to the theory and practice of the Discrete Empirical Interpolation Method (DEIM). These include a detailed characterization of the canonical structure; a substantial tightening of the error bound for the DEIM oblique projection, based on index selection via a strong rank revealing QR factorization; and an extension of the DEIM approximation to weighted inner products defined by a real symmetric positive-definite matrix $W$. The weighted DEIM ($W$-DEIM) can be deployed in the more general framework where the POD Galerkin projection is formulated in a discretization","authors_text":"Arvind K. Saibaba, Zlatko Drma\\v{c}","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-04-21T15:38:25Z","title":"The Discrete Empirical Interpolation Method: Canonical Structure and Formulation in Weighted Inner Product Spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.06606","kind":"arxiv","version":4},"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":"sha256:648f05958765e80a5d3c576cd0d1c39e1fe2f2d1d9de9ac069e8d7a20e27fc08","target":"record","created_at":"2026-05-18T00:23:45Z","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":"10e5e382709f78fa15b1870022f2c1f1925ea3e68519e2893ba2b6cde964adf8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-04-21T15:38:25Z","title_canon_sha256":"dff31c17f6b29eb29c44effc4f31f3f9cc02334c0c286a1ecd46441462dda36e"},"schema_version":"1.0","source":{"id":"1704.06606","kind":"arxiv","version":4}},"canonical_sha256":"96db4e4948b0fb2bd136c71218fde8861eb2d6c7cbb27a3953c237df100f8f75","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"96db4e4948b0fb2bd136c71218fde8861eb2d6c7cbb27a3953c237df100f8f75","first_computed_at":"2026-05-18T00:23:45.737646Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:45.737646Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RkirpgmjM6nRfiAJzj1OLUTrvjMqPT4ZqLa7ydydVxBrQNxm0sd+7qwIdpFNWfTjmgXK4xPLR81kzHCqh/LPCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:45.738126Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.06606","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:648f05958765e80a5d3c576cd0d1c39e1fe2f2d1d9de9ac069e8d7a20e27fc08","sha256:459cde52179310bf068a93542e99f7e9af47176a442e3f24978d9a777780f128"],"state_sha256":"21cf43ff343522aea6a73e2466782c6d67da2db84b2d2d9bb734de5da8a6c697"}