{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:BPIA3JKXIHTXUJ4V4XJJKH4TGR","short_pith_number":"pith:BPIA3JKX","schema_version":"1.0","canonical_sha256":"0bd00da55741e77a2795e5d2951f9334572ed80d88be3e793e4c53fb1ee9cb8d","source":{"kind":"arxiv","id":"1608.06475","version":2},"attestation_state":"computed","paper":{"title":"Stabilization Control for Linear Continuous-time Mean-field Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Huanshui Zhang, Qingyuan Qi","submitted_at":"2016-08-23T11:57:05Z","abstract_excerpt":"This paper investigates the stabilization and control problems for linear continuous-time mean-field systems (MFS). Under standard assumptions, necessary and sufficient conditions to stabilize the mean-field systems in the mean square sense are explored for the first time. It is shown that, under the assumption of exact detectability (exact observability), the mean-field system is stabilizable if and only if a coupled algebraic Riccati equation (ARE) admits a unique positive semi-definite solution (positive definite solution), which coincides with the classical stabilization results for standa"},"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":"1608.06475","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-08-23T11:57:05Z","cross_cats_sorted":[],"title_canon_sha256":"e9c67d997d0656467db765eedb12ea4e24fbf1767ea63d5584e5614abea0bd31","abstract_canon_sha256":"77cffd6ea98262a92a96678793e2a4de2052d0f27fd2edb842f789197d54db72"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:43.529119Z","signature_b64":"Op0/JHfAC0i6ZEFbAKCpK+7u1DEr8uBQxUWKtWyYWaqggDnLSKHD39691goEZqlHDE3DYNvYpJPd5L1xEtWSAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0bd00da55741e77a2795e5d2951f9334572ed80d88be3e793e4c53fb1ee9cb8d","last_reissued_at":"2026-05-18T00:43:43.528616Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:43.528616Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stabilization Control for Linear Continuous-time Mean-field Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Huanshui Zhang, Qingyuan Qi","submitted_at":"2016-08-23T11:57:05Z","abstract_excerpt":"This paper investigates the stabilization and control problems for linear continuous-time mean-field systems (MFS). Under standard assumptions, necessary and sufficient conditions to stabilize the mean-field systems in the mean square sense are explored for the first time. It is shown that, under the assumption of exact detectability (exact observability), the mean-field system is stabilizable if and only if a coupled algebraic Riccati equation (ARE) admits a unique positive semi-definite solution (positive definite solution), which coincides with the classical stabilization results for standa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.06475","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":"1608.06475","created_at":"2026-05-18T00:43:43.528704+00:00"},{"alias_kind":"arxiv_version","alias_value":"1608.06475v2","created_at":"2026-05-18T00:43:43.528704+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.06475","created_at":"2026-05-18T00:43:43.528704+00:00"},{"alias_kind":"pith_short_12","alias_value":"BPIA3JKXIHTX","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_16","alias_value":"BPIA3JKXIHTXUJ4V","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_8","alias_value":"BPIA3JKX","created_at":"2026-05-18T12:30:07.202191+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/BPIA3JKXIHTXUJ4V4XJJKH4TGR","json":"https://pith.science/pith/BPIA3JKXIHTXUJ4V4XJJKH4TGR.json","graph_json":"https://pith.science/api/pith-number/BPIA3JKXIHTXUJ4V4XJJKH4TGR/graph.json","events_json":"https://pith.science/api/pith-number/BPIA3JKXIHTXUJ4V4XJJKH4TGR/events.json","paper":"https://pith.science/paper/BPIA3JKX"},"agent_actions":{"view_html":"https://pith.science/pith/BPIA3JKXIHTXUJ4V4XJJKH4TGR","download_json":"https://pith.science/pith/BPIA3JKXIHTXUJ4V4XJJKH4TGR.json","view_paper":"https://pith.science/paper/BPIA3JKX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1608.06475&json=true","fetch_graph":"https://pith.science/api/pith-number/BPIA3JKXIHTXUJ4V4XJJKH4TGR/graph.json","fetch_events":"https://pith.science/api/pith-number/BPIA3JKXIHTXUJ4V4XJJKH4TGR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BPIA3JKXIHTXUJ4V4XJJKH4TGR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BPIA3JKXIHTXUJ4V4XJJKH4TGR/action/storage_attestation","attest_author":"https://pith.science/pith/BPIA3JKXIHTXUJ4V4XJJKH4TGR/action/author_attestation","sign_citation":"https://pith.science/pith/BPIA3JKXIHTXUJ4V4XJJKH4TGR/action/citation_signature","submit_replication":"https://pith.science/pith/BPIA3JKXIHTXUJ4V4XJJKH4TGR/action/replication_record"}},"created_at":"2026-05-18T00:43:43.528704+00:00","updated_at":"2026-05-18T00:43:43.528704+00:00"}