{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:WIGZEMEZ7BVXCCO2UWWEQB7CG2","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":"3f5ca6a9db8d04a3e02fc02e31d23bf61bccf3580236f1f8711cf5de3fcc61f5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2024-09-29T15:11:28Z","title_canon_sha256":"16ec804736ae7a3f763e4050512567c7d029bb6a52b62d6307ad8d718ecf16af"},"schema_version":"1.0","source":{"id":"2409.19730","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.19730","created_at":"2026-07-05T10:11:24Z"},{"alias_kind":"arxiv_version","alias_value":"2409.19730v2","created_at":"2026-07-05T10:11:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.19730","created_at":"2026-07-05T10:11:24Z"},{"alias_kind":"pith_short_12","alias_value":"WIGZEMEZ7BVX","created_at":"2026-07-05T10:11:24Z"},{"alias_kind":"pith_short_16","alias_value":"WIGZEMEZ7BVXCCO2","created_at":"2026-07-05T10:11:24Z"},{"alias_kind":"pith_short_8","alias_value":"WIGZEMEZ","created_at":"2026-07-05T10:11:24Z"}],"graph_snapshots":[{"event_id":"sha256:177620ce42af8b87b0e586c0b6fe7241c207841b9aa624f53b7ba9fb55726de2","target":"graph","created_at":"2026-07-05T10:11:24Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2409.19730/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Controllability and observability energy functions play a fundamental role in model order reduction and are inherently connected to optimal control problems. For linear dynamical systems the energy functions are known to be quadratic polynomials and various low-rank approximation techniques allow for computing them in a large-scale setting. For nonlinear problems computing the energy functions is significantly more challenging. In this paper, we investigate a special class of nonlinear systems that have a linear state and a polynomial output equation. We show that the energy functions of these","authors_text":"Linus Balicki, Serkan Gugercin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2024-09-29T15:11:28Z","title":"Energy-Based Approximation of Linear Systems with Polynomial Outputs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.19730","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":"sha256:92732b152dd31f417454564a831b6231b4fa88f306a595c891f3c1a9d794ec6d","target":"record","created_at":"2026-07-05T10:11:24Z","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":"3f5ca6a9db8d04a3e02fc02e31d23bf61bccf3580236f1f8711cf5de3fcc61f5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2024-09-29T15:11:28Z","title_canon_sha256":"16ec804736ae7a3f763e4050512567c7d029bb6a52b62d6307ad8d718ecf16af"},"schema_version":"1.0","source":{"id":"2409.19730","kind":"arxiv","version":2}},"canonical_sha256":"b20d923099f86b7109daa5ac4807e2369afdbc5682b902ff3232a393d06df488","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b20d923099f86b7109daa5ac4807e2369afdbc5682b902ff3232a393d06df488","first_computed_at":"2026-07-05T10:11:24.862105Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:11:24.862105Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O6IX4NDgxjBSjlTKBmCk1l9dHwtxupOrauMeapPTlXEKkwu0Ue126P+ZYD7KC9ILNNxb5g0RBzF/63SitKfIBA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:11:24.862641Z","signed_message":"canonical_sha256_bytes"},"source_id":"2409.19730","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:92732b152dd31f417454564a831b6231b4fa88f306a595c891f3c1a9d794ec6d","sha256:177620ce42af8b87b0e586c0b6fe7241c207841b9aa624f53b7ba9fb55726de2"],"state_sha256":"e9054bca37349c38a8427008b89211eaa0ff92b6212d94c9fb5432c3b2aaa13a"}