{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:NX6BNMULLBLRR6TVYNR3CEB6C4","short_pith_number":"pith:NX6BNMUL","schema_version":"1.0","canonical_sha256":"6dfc16b28b585718fa75c363b1103e170a2c2d1a940d25c6e2837e2bb9a2be3f","source":{"kind":"arxiv","id":"1602.04402","version":1},"attestation_state":"computed","paper":{"title":"Balanced Truncation of Linear Time-Invariant Systems over Finite-frequency Ranges","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.OC"],"primary_cat":"cs.SY","authors_text":"Peter Benner, Xin Du","submitted_at":"2016-02-13T23:29:09Z","abstract_excerpt":"This paper discusses model order reduction of LTI systems over limited frequency intervals within the framework of balanced truncation. Two new \\emph{frequency-dependent balanced truncation} methods were developed, one is \\emph{SF-type frequency-dependent balanced truncation} to copy with the cases that only a single dominating point of the operating frequency interval is pre-known, the other is \\emph{interval-type frequency-dependent balanced truncation} to deal with the cases that both of the upper and lower bound of frequency interval are known \\emph{a priori}. SF-type error bound and inter"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1602.04402","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2016-02-13T23:29:09Z","cross_cats_sorted":["math.DS","math.OC"],"title_canon_sha256":"7e03dfe637f1d9a9020786eccd650813364177d7d78c95cb627b5e93ab418060","abstract_canon_sha256":"49c913cb240452a271a4a67ba6c563dd9b328797496b49708aff4393cabee678"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:50.985868Z","signature_b64":"LZgY1GGozg2+04wlUadPYK2jSMHlOuMxEG6RlTek35C7TVwKmHfiBVMiLKnEWKF+H3ayNvAvBZauD0k1gSElDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6dfc16b28b585718fa75c363b1103e170a2c2d1a940d25c6e2837e2bb9a2be3f","last_reissued_at":"2026-05-18T01:20:50.985411Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:50.985411Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Balanced Truncation of Linear Time-Invariant Systems over Finite-frequency Ranges","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.OC"],"primary_cat":"cs.SY","authors_text":"Peter Benner, Xin Du","submitted_at":"2016-02-13T23:29:09Z","abstract_excerpt":"This paper discusses model order reduction of LTI systems over limited frequency intervals within the framework of balanced truncation. Two new \\emph{frequency-dependent balanced truncation} methods were developed, one is \\emph{SF-type frequency-dependent balanced truncation} to copy with the cases that only a single dominating point of the operating frequency interval is pre-known, the other is \\emph{interval-type frequency-dependent balanced truncation} to deal with the cases that both of the upper and lower bound of frequency interval are known \\emph{a priori}. SF-type error bound and inter"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.04402","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1602.04402","created_at":"2026-05-18T01:20:50.985490+00:00"},{"alias_kind":"arxiv_version","alias_value":"1602.04402v1","created_at":"2026-05-18T01:20:50.985490+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.04402","created_at":"2026-05-18T01:20:50.985490+00:00"},{"alias_kind":"pith_short_12","alias_value":"NX6BNMULLBLR","created_at":"2026-05-18T12:30:36.002864+00:00"},{"alias_kind":"pith_short_16","alias_value":"NX6BNMULLBLRR6TV","created_at":"2026-05-18T12:30:36.002864+00:00"},{"alias_kind":"pith_short_8","alias_value":"NX6BNMUL","created_at":"2026-05-18T12:30:36.002864+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/NX6BNMULLBLRR6TVYNR3CEB6C4","json":"https://pith.science/pith/NX6BNMULLBLRR6TVYNR3CEB6C4.json","graph_json":"https://pith.science/api/pith-number/NX6BNMULLBLRR6TVYNR3CEB6C4/graph.json","events_json":"https://pith.science/api/pith-number/NX6BNMULLBLRR6TVYNR3CEB6C4/events.json","paper":"https://pith.science/paper/NX6BNMUL"},"agent_actions":{"view_html":"https://pith.science/pith/NX6BNMULLBLRR6TVYNR3CEB6C4","download_json":"https://pith.science/pith/NX6BNMULLBLRR6TVYNR3CEB6C4.json","view_paper":"https://pith.science/paper/NX6BNMUL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1602.04402&json=true","fetch_graph":"https://pith.science/api/pith-number/NX6BNMULLBLRR6TVYNR3CEB6C4/graph.json","fetch_events":"https://pith.science/api/pith-number/NX6BNMULLBLRR6TVYNR3CEB6C4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NX6BNMULLBLRR6TVYNR3CEB6C4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NX6BNMULLBLRR6TVYNR3CEB6C4/action/storage_attestation","attest_author":"https://pith.science/pith/NX6BNMULLBLRR6TVYNR3CEB6C4/action/author_attestation","sign_citation":"https://pith.science/pith/NX6BNMULLBLRR6TVYNR3CEB6C4/action/citation_signature","submit_replication":"https://pith.science/pith/NX6BNMULLBLRR6TVYNR3CEB6C4/action/replication_record"}},"created_at":"2026-05-18T01:20:50.985490+00:00","updated_at":"2026-05-18T01:20:50.985490+00:00"}