{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:TMJN65UJPRXRGCPX3PKLLGKXQL","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":"3c6247e1c0be1efc76a187da64ec4a31cba527e8fffd67385d1b8dc7ab997198","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-09-17T12:54:32Z","title_canon_sha256":"ebdcd22e41940185abb8adfa6c3d305bcab7c000ebc154ab16a5276eb493bd2b"},"schema_version":"1.0","source":{"id":"1709.05655","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.05655","created_at":"2026-05-18T00:34:59Z"},{"alias_kind":"arxiv_version","alias_value":"1709.05655v1","created_at":"2026-05-18T00:34:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.05655","created_at":"2026-05-18T00:34:59Z"},{"alias_kind":"pith_short_12","alias_value":"TMJN65UJPRXR","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"TMJN65UJPRXRGCPX","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"TMJN65UJ","created_at":"2026-05-18T12:31:46Z"}],"graph_snapshots":[{"event_id":"sha256:68a3e37dab81877197fb6d27a681724e379a8562d136a95a89728ed2a6f2816a","target":"graph","created_at":"2026-05-18T00:34:59Z","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":"When solving partial differential equations numerically, usually a high order spatial discretisation is needed. Model order reduction (MOR) techniques are often used to reduce the order of spatially-discretised systems and hence reduce computational complexity. A particular MOR technique to obtain a reduced order model (ROM) is balanced truncation (BT), a method which has been extensively studied for deterministic linear systems. As so-called type I BT it has already been extended to bilinear equations, an important subclass of nonlinear systems. We provide an alternative generalisation of the","authors_text":"Martin Redmann","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-09-17T12:54:32Z","title":"Type II balanced truncation for deterministic bilinear control systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.05655","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":"sha256:54b0d18d6b1d5fd5301eced4c2291c43231a350df75d75dce30918bf453bb820","target":"record","created_at":"2026-05-18T00:34:59Z","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":"3c6247e1c0be1efc76a187da64ec4a31cba527e8fffd67385d1b8dc7ab997198","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-09-17T12:54:32Z","title_canon_sha256":"ebdcd22e41940185abb8adfa6c3d305bcab7c000ebc154ab16a5276eb493bd2b"},"schema_version":"1.0","source":{"id":"1709.05655","kind":"arxiv","version":1}},"canonical_sha256":"9b12df76897c6f1309f7dbd4b5995782c31fee2645f365d93da8a247f52e005c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9b12df76897c6f1309f7dbd4b5995782c31fee2645f365d93da8a247f52e005c","first_computed_at":"2026-05-18T00:34:59.959338Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:34:59.959338Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"l0OvPR0S6TRIuYOYzOVvGAn0wovkLrgfZppd4AUt8rtLMI5UMp8GhBF4OgA0UeOK6ml2lOVvraLWVI22zp63AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:34:59.960138Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.05655","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:54b0d18d6b1d5fd5301eced4c2291c43231a350df75d75dce30918bf453bb820","sha256:68a3e37dab81877197fb6d27a681724e379a8562d136a95a89728ed2a6f2816a"],"state_sha256":"fc78dcbd0adc5900e6c8afd7eddbdd1727e53505f6baf40341535c6cf7030df6"}