{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:L7H3JCAYIE6HXK4NIQS33KDXJ4","short_pith_number":"pith:L7H3JCAY","schema_version":"1.0","canonical_sha256":"5fcfb48818413c7bab8d4425bda8774f13c6bf513afb6a2cce051ede3b19eae9","source":{"kind":"arxiv","id":"1806.03475","version":2},"attestation_state":"computed","paper":{"title":"Input Matrix Construction and Approximation Using a Graphic Approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Tong Zhou, Yuan Zhang","submitted_at":"2018-06-09T13:28:50Z","abstract_excerpt":"Given a state transition matrix (STM), we reinvestigate the problem of constructing the sparest input matrix with a fixed number of inputs to guarantee controllability. We give a new and simple graph theoretic characterization for the sparsity pattern of input matrices to guarantee controllability for a general STM admitting multiple eigenvalues, and provide a deterministic procedure with polynomial time complexity to construct real valued input matrices with arbi- trarily prescribed sparsity pattern satisfying controllability. Based on this criterion, some novel results on sparsely controllin"},"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":"1806.03475","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-06-09T13:28:50Z","cross_cats_sorted":[],"title_canon_sha256":"bbdb9cb4bf1e14d23e75204e92b02b4d16d1704698a8943694ce74b60856c1c2","abstract_canon_sha256":"b09f3cc4074c8978fa91b53bb0dfa79f932fea3b47525a2eadd645b3053929b5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:45.390100Z","signature_b64":"V/QD42qUgv1TmEPghiLRDQJD0MxgZpqCltnUUIdx54FaSo3mVdBdmWW8juq829IS6W8yGLtTCFdXRSO4yT9LBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5fcfb48818413c7bab8d4425bda8774f13c6bf513afb6a2cce051ede3b19eae9","last_reissued_at":"2026-05-18T00:05:45.389432Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:45.389432Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Input Matrix Construction and Approximation Using a Graphic Approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Tong Zhou, Yuan Zhang","submitted_at":"2018-06-09T13:28:50Z","abstract_excerpt":"Given a state transition matrix (STM), we reinvestigate the problem of constructing the sparest input matrix with a fixed number of inputs to guarantee controllability. We give a new and simple graph theoretic characterization for the sparsity pattern of input matrices to guarantee controllability for a general STM admitting multiple eigenvalues, and provide a deterministic procedure with polynomial time complexity to construct real valued input matrices with arbi- trarily prescribed sparsity pattern satisfying controllability. Based on this criterion, some novel results on sparsely controllin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.03475","kind":"arxiv","version":2},"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":"1806.03475","created_at":"2026-05-18T00:05:45.389534+00:00"},{"alias_kind":"arxiv_version","alias_value":"1806.03475v2","created_at":"2026-05-18T00:05:45.389534+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.03475","created_at":"2026-05-18T00:05:45.389534+00:00"},{"alias_kind":"pith_short_12","alias_value":"L7H3JCAYIE6H","created_at":"2026-05-18T12:32:33.847187+00:00"},{"alias_kind":"pith_short_16","alias_value":"L7H3JCAYIE6HXK4N","created_at":"2026-05-18T12:32:33.847187+00:00"},{"alias_kind":"pith_short_8","alias_value":"L7H3JCAY","created_at":"2026-05-18T12:32:33.847187+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/L7H3JCAYIE6HXK4NIQS33KDXJ4","json":"https://pith.science/pith/L7H3JCAYIE6HXK4NIQS33KDXJ4.json","graph_json":"https://pith.science/api/pith-number/L7H3JCAYIE6HXK4NIQS33KDXJ4/graph.json","events_json":"https://pith.science/api/pith-number/L7H3JCAYIE6HXK4NIQS33KDXJ4/events.json","paper":"https://pith.science/paper/L7H3JCAY"},"agent_actions":{"view_html":"https://pith.science/pith/L7H3JCAYIE6HXK4NIQS33KDXJ4","download_json":"https://pith.science/pith/L7H3JCAYIE6HXK4NIQS33KDXJ4.json","view_paper":"https://pith.science/paper/L7H3JCAY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1806.03475&json=true","fetch_graph":"https://pith.science/api/pith-number/L7H3JCAYIE6HXK4NIQS33KDXJ4/graph.json","fetch_events":"https://pith.science/api/pith-number/L7H3JCAYIE6HXK4NIQS33KDXJ4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/L7H3JCAYIE6HXK4NIQS33KDXJ4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/L7H3JCAYIE6HXK4NIQS33KDXJ4/action/storage_attestation","attest_author":"https://pith.science/pith/L7H3JCAYIE6HXK4NIQS33KDXJ4/action/author_attestation","sign_citation":"https://pith.science/pith/L7H3JCAYIE6HXK4NIQS33KDXJ4/action/citation_signature","submit_replication":"https://pith.science/pith/L7H3JCAYIE6HXK4NIQS33KDXJ4/action/replication_record"}},"created_at":"2026-05-18T00:05:45.389534+00:00","updated_at":"2026-05-18T00:05:45.389534+00:00"}