{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:U3R2FLEULFFKJNLHUOL44QQIKJ","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":"25baad79672d5371e01964a4274b0918a3ceb6dc2b1861c9365d5cd460a5a58a","cross_cats_sorted":["math.DS","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2015-11-17T02:24:53Z","title_canon_sha256":"073c070f0416c87da8d3fc8fbf6e61b1a712c95cd43bd0fa3283ae1966ecd863"},"schema_version":"1.0","source":{"id":"1511.05252","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.05252","created_at":"2026-05-18T01:26:49Z"},{"alias_kind":"arxiv_version","alias_value":"1511.05252v1","created_at":"2026-05-18T01:26:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.05252","created_at":"2026-05-18T01:26:49Z"},{"alias_kind":"pith_short_12","alias_value":"U3R2FLEULFFK","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"U3R2FLEULFFKJNLH","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"U3R2FLEU","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:d1cbe386e4abe0397b04d343fb71d4c005aec071026c223ffb768125ac3529c1","target":"graph","created_at":"2026-05-18T01:26:49Z","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 paper, the $\\mathcal{H}_{2}$ optimal approximation of a $n_{y}\\times{n_{u}}$ transfer function $\\mathbf{G}(s)$ by a finite dimensional system $\\hat{\\mathbf{H}}_{d}(s)$ including input/output delays, is addressed. The underlying $\\mathcal{H}_{2}$ optimality conditions of the approximation problem are firstly derived and established in the case of a poles/residues decomposition. These latter form an extension of the tangential interpolatory conditions, presented in~\\cite{gugercin2008h_2,dooren2007} for the delay-free case, which is the main contribution of this paper. Secondly, a two sta","authors_text":"C\\'edric Seren, Charles Poussot-Vassal, Igor Pontes Duff","cross_cats":["math.DS","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2015-11-17T02:24:53Z","title":"Optimal $\\mathcal{H}_{2}$ model approximation based on multiple input/output delays systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.05252","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:c02e7e75694dbc80f1bef50b1ed12da8a6f8dc23f83f3c3235ea3abe21c626ec","target":"record","created_at":"2026-05-18T01:26:49Z","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":"25baad79672d5371e01964a4274b0918a3ceb6dc2b1861c9365d5cd460a5a58a","cross_cats_sorted":["math.DS","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2015-11-17T02:24:53Z","title_canon_sha256":"073c070f0416c87da8d3fc8fbf6e61b1a712c95cd43bd0fa3283ae1966ecd863"},"schema_version":"1.0","source":{"id":"1511.05252","kind":"arxiv","version":1}},"canonical_sha256":"a6e3a2ac94594aa4b567a397ce4208526dd9ef216df5b12c33fd1da90330fc5b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a6e3a2ac94594aa4b567a397ce4208526dd9ef216df5b12c33fd1da90330fc5b","first_computed_at":"2026-05-18T01:26:49.625687Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:26:49.625687Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NPhExMzIvF90l6sMluduso/C3mnWP8FDGhcoyBkCKAVsQUefb8+vo4JyQoUxnf1LxAPaGqi4/8YXWFcC6mX/BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:26:49.626417Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.05252","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c02e7e75694dbc80f1bef50b1ed12da8a6f8dc23f83f3c3235ea3abe21c626ec","sha256:d1cbe386e4abe0397b04d343fb71d4c005aec071026c223ffb768125ac3529c1"],"state_sha256":"9c17ae8fee8fee552c83ee5ef37d202fc52ca340a1bb7799aa581675e050e34a"}