{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:HKK3VRGSVCXHCVY3FAI5RTLFEU","short_pith_number":"pith:HKK3VRGS","schema_version":"1.0","canonical_sha256":"3a95bac4d2a8ae71571b2811d8cd65250be6172e7be641b5ce937df450b7f698","source":{"kind":"arxiv","id":"1509.02100","version":2},"attestation_state":"computed","paper":{"title":"Mean-Field Stochastic Linear Quadratic Optimal Control Problems: Open-Loop Solvabilities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Jingrui Sun","submitted_at":"2015-09-07T15:58:44Z","abstract_excerpt":"This paper is concerned with a mean-field linear quadratic (LQ, for short) optimal control problem with deterministic coefficients. It is shown that convexity of the cost functional is necessary for the finiteness of the mean-field LQ problem, whereas uniform convexity of the cost functional is sufficient for the open-loop solvability of the problem. By considering a family of uniformly convex cost functionals, a characterization of the finiteness of the problem is derived and a minimizing sequence, whose convergence is equivalent to the open-loop solvability of the problem, is constructed. Th"},"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":"1509.02100","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-09-07T15:58:44Z","cross_cats_sorted":[],"title_canon_sha256":"ba565c21c770a8d01c44887a3db82536337333bc8755a9fa16d8ce20537a6bc4","abstract_canon_sha256":"5ad962ab0f5ee654afb1607459bcf8fdbf2227e10fe850d4e07475e93b25161f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:32:59.052794Z","signature_b64":"xeek3SoLD969wXIhcw1A7+M9vGReYNhIIPNHY80Bh3w6PO/e776hS2VZ283H565sOOd5uOk5dMndtiVhBuAWAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3a95bac4d2a8ae71571b2811d8cd65250be6172e7be641b5ce937df450b7f698","last_reissued_at":"2026-05-18T01:32:59.052383Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:32:59.052383Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Mean-Field Stochastic Linear Quadratic Optimal Control Problems: Open-Loop Solvabilities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Jingrui Sun","submitted_at":"2015-09-07T15:58:44Z","abstract_excerpt":"This paper is concerned with a mean-field linear quadratic (LQ, for short) optimal control problem with deterministic coefficients. It is shown that convexity of the cost functional is necessary for the finiteness of the mean-field LQ problem, whereas uniform convexity of the cost functional is sufficient for the open-loop solvability of the problem. By considering a family of uniformly convex cost functionals, a characterization of the finiteness of the problem is derived and a minimizing sequence, whose convergence is equivalent to the open-loop solvability of the problem, is constructed. Th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.02100","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":"1509.02100","created_at":"2026-05-18T01:32:59.052437+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.02100v2","created_at":"2026-05-18T01:32:59.052437+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.02100","created_at":"2026-05-18T01:32:59.052437+00:00"},{"alias_kind":"pith_short_12","alias_value":"HKK3VRGSVCXH","created_at":"2026-05-18T12:29:25.134429+00:00"},{"alias_kind":"pith_short_16","alias_value":"HKK3VRGSVCXHCVY3","created_at":"2026-05-18T12:29:25.134429+00:00"},{"alias_kind":"pith_short_8","alias_value":"HKK3VRGS","created_at":"2026-05-18T12:29:25.134429+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/HKK3VRGSVCXHCVY3FAI5RTLFEU","json":"https://pith.science/pith/HKK3VRGSVCXHCVY3FAI5RTLFEU.json","graph_json":"https://pith.science/api/pith-number/HKK3VRGSVCXHCVY3FAI5RTLFEU/graph.json","events_json":"https://pith.science/api/pith-number/HKK3VRGSVCXHCVY3FAI5RTLFEU/events.json","paper":"https://pith.science/paper/HKK3VRGS"},"agent_actions":{"view_html":"https://pith.science/pith/HKK3VRGSVCXHCVY3FAI5RTLFEU","download_json":"https://pith.science/pith/HKK3VRGSVCXHCVY3FAI5RTLFEU.json","view_paper":"https://pith.science/paper/HKK3VRGS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.02100&json=true","fetch_graph":"https://pith.science/api/pith-number/HKK3VRGSVCXHCVY3FAI5RTLFEU/graph.json","fetch_events":"https://pith.science/api/pith-number/HKK3VRGSVCXHCVY3FAI5RTLFEU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HKK3VRGSVCXHCVY3FAI5RTLFEU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HKK3VRGSVCXHCVY3FAI5RTLFEU/action/storage_attestation","attest_author":"https://pith.science/pith/HKK3VRGSVCXHCVY3FAI5RTLFEU/action/author_attestation","sign_citation":"https://pith.science/pith/HKK3VRGSVCXHCVY3FAI5RTLFEU/action/citation_signature","submit_replication":"https://pith.science/pith/HKK3VRGSVCXHCVY3FAI5RTLFEU/action/replication_record"}},"created_at":"2026-05-18T01:32:59.052437+00:00","updated_at":"2026-05-18T01:32:59.052437+00:00"}