{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:FZ5UO6LWK2NENA26KXVEL462SB","short_pith_number":"pith:FZ5UO6LW","schema_version":"1.0","canonical_sha256":"2e7b477976569a46835e55ea45f3da906ff34763e4ff0bae0baf00f35600985d","source":{"kind":"arxiv","id":"1107.5340","version":1},"attestation_state":"computed","paper":{"title":"Properties of sub-matrices of Sylvester matrices and triangular toeplitz matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"robin hill, Uwe Schwerdtfeger, Yousong Luo","submitted_at":"2011-07-12T11:58:38Z","abstract_excerpt":"In this note we discover and prove some interesting and important relations among sub-matrices of Sylvester matrices and triangular toeplitz matrices. The main result is Hill's identity discovered by R. D. Hill which has an important application in optimal control problems."},"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":"1107.5340","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-07-12T11:58:38Z","cross_cats_sorted":[],"title_canon_sha256":"4c7942c27a4e691449a7ee2e7a2bbc80cd4390310451c720b5636abe23a1c424","abstract_canon_sha256":"8d7fa5d8b6e842e58c1bcff82e9433f3aac682637fb0bc7e57c9b9dd389317da"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:16:52.246393Z","signature_b64":"9F3FuWD4y3WIMcfgwsB9ZBrC6Kp3Lq49lQIdpQckmJkTLTptgDj0kodaaa0kXW3ErsCpRlThzx3LTJCUJircAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2e7b477976569a46835e55ea45f3da906ff34763e4ff0bae0baf00f35600985d","last_reissued_at":"2026-05-18T04:16:52.245863Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:16:52.245863Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Properties of sub-matrices of Sylvester matrices and triangular toeplitz matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"robin hill, Uwe Schwerdtfeger, Yousong Luo","submitted_at":"2011-07-12T11:58:38Z","abstract_excerpt":"In this note we discover and prove some interesting and important relations among sub-matrices of Sylvester matrices and triangular toeplitz matrices. The main result is Hill's identity discovered by R. D. Hill which has an important application in optimal control problems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.5340","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":"1107.5340","created_at":"2026-05-18T04:16:52.245937+00:00"},{"alias_kind":"arxiv_version","alias_value":"1107.5340v1","created_at":"2026-05-18T04:16:52.245937+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.5340","created_at":"2026-05-18T04:16:52.245937+00:00"},{"alias_kind":"pith_short_12","alias_value":"FZ5UO6LWK2NE","created_at":"2026-05-18T12:26:28.662955+00:00"},{"alias_kind":"pith_short_16","alias_value":"FZ5UO6LWK2NENA26","created_at":"2026-05-18T12:26:28.662955+00:00"},{"alias_kind":"pith_short_8","alias_value":"FZ5UO6LW","created_at":"2026-05-18T12:26:28.662955+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/FZ5UO6LWK2NENA26KXVEL462SB","json":"https://pith.science/pith/FZ5UO6LWK2NENA26KXVEL462SB.json","graph_json":"https://pith.science/api/pith-number/FZ5UO6LWK2NENA26KXVEL462SB/graph.json","events_json":"https://pith.science/api/pith-number/FZ5UO6LWK2NENA26KXVEL462SB/events.json","paper":"https://pith.science/paper/FZ5UO6LW"},"agent_actions":{"view_html":"https://pith.science/pith/FZ5UO6LWK2NENA26KXVEL462SB","download_json":"https://pith.science/pith/FZ5UO6LWK2NENA26KXVEL462SB.json","view_paper":"https://pith.science/paper/FZ5UO6LW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1107.5340&json=true","fetch_graph":"https://pith.science/api/pith-number/FZ5UO6LWK2NENA26KXVEL462SB/graph.json","fetch_events":"https://pith.science/api/pith-number/FZ5UO6LWK2NENA26KXVEL462SB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FZ5UO6LWK2NENA26KXVEL462SB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FZ5UO6LWK2NENA26KXVEL462SB/action/storage_attestation","attest_author":"https://pith.science/pith/FZ5UO6LWK2NENA26KXVEL462SB/action/author_attestation","sign_citation":"https://pith.science/pith/FZ5UO6LWK2NENA26KXVEL462SB/action/citation_signature","submit_replication":"https://pith.science/pith/FZ5UO6LWK2NENA26KXVEL462SB/action/replication_record"}},"created_at":"2026-05-18T04:16:52.245937+00:00","updated_at":"2026-05-18T04:16:52.245937+00:00"}