{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:4VVIRIITUN4IQB66ZNTDDSQB5K","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":"5df785663c3bf40eb4ea95c6782224bd080583cb13b39fc02c1a2d28e7d98eba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-04-23T21:54:56Z","title_canon_sha256":"8877e72e312e84881e2edd6e1ebdc4c1c4c3b90cc2727aa4f228742a0c871396"},"schema_version":"1.0","source":{"id":"1804.08755","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.08755","created_at":"2026-05-18T00:17:37Z"},{"alias_kind":"arxiv_version","alias_value":"1804.08755v1","created_at":"2026-05-18T00:17:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.08755","created_at":"2026-05-18T00:17:37Z"},{"alias_kind":"pith_short_12","alias_value":"4VVIRIITUN4I","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"4VVIRIITUN4IQB66","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"4VVIRIIT","created_at":"2026-05-18T12:32:05Z"}],"graph_snapshots":[{"event_id":"sha256:49524dc92e7d24d2246599bdf0be695e7c78fba534619156d3b53e153b1ff6dc","target":"graph","created_at":"2026-05-18T00:17:37Z","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 contribution, we extend the concept of $\\mathcal{H}_2$ inner product and $\\mathcal{H}_2$ pseudo-optimality to dynamical systems modeled by differential-algebraic equations (DAEs). To this end, we derive projected Sylvester equations that characterize the $\\mathcal{H}_2$ inner product in terms of the matrices of the DAE realization. Using this result, we extend the $\\mathcal{H}_2$ pseudo-optimal rational Krylov algorithm for ordinary differential equations to the DAE case. This algorithm computes the globally optimal reduced-order model for a given subspace of $\\mathcal{H}_2$ defined by","authors_text":"Alessandro Castagnotto, Boris Lohmann, Philipp Seiwald, Tatjana Stykel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-04-23T21:54:56Z","title":"$\\mathcal{H}_2$ Pseudo-Optimal Reduction of Structured DAEs by Rational Interpolation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.08755","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":"sha256:4cc61647e3c33ae38af9663da155bc07baec72942ffd9e58fd0a7198b509f43b","target":"record","created_at":"2026-05-18T00:17:37Z","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":"5df785663c3bf40eb4ea95c6782224bd080583cb13b39fc02c1a2d28e7d98eba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-04-23T21:54:56Z","title_canon_sha256":"8877e72e312e84881e2edd6e1ebdc4c1c4c3b90cc2727aa4f228742a0c871396"},"schema_version":"1.0","source":{"id":"1804.08755","kind":"arxiv","version":1}},"canonical_sha256":"e56a88a113a3788807decb6631ca01eab26243995d6b45c9002ef606ad56886e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e56a88a113a3788807decb6631ca01eab26243995d6b45c9002ef606ad56886e","first_computed_at":"2026-05-18T00:17:37.454521Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:17:37.454521Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bDHh+rvdNyfI1VmFa410eBwp3scYtpqUKWKZK237cK7clONIBXc7QLaLOn7j5f4rp489arHnboxv3xm/+wkeBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:17:37.455310Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.08755","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4cc61647e3c33ae38af9663da155bc07baec72942ffd9e58fd0a7198b509f43b","sha256:49524dc92e7d24d2246599bdf0be695e7c78fba534619156d3b53e153b1ff6dc"],"state_sha256":"b05593eff1b55ba9640d19a7eb814339a5a308d378ca46799d879676f384aed0"}