{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:ISCAJ34LELNNYGETFTMV2T45Y6","short_pith_number":"pith:ISCAJ34L","schema_version":"1.0","canonical_sha256":"448404ef8b22dadc18932cd95d4f9dc782c49085b610edd59ad65cf00a1bbf38","source":{"kind":"arxiv","id":"1908.04183","version":6},"attestation_state":"computed","paper":{"title":"Intrinsic Lipschitz Regularity of Mean-Field Optimal Controls","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Beno\\^it Bonnet, Francesco Rossi","submitted_at":"2019-08-12T14:51:12Z","abstract_excerpt":"In this article, we provide sufficient conditions under which the controlled vector fields solution of optimal control problems formulated on continuity equations are Lipschitz regular in space. Our approach involves a novel combination of mean-field approximations for infinite-dimensional multi-agent optimal control problems, along with a careful extension of an existence result of locally optimal Lipschitz feedbacks. The latter is based on the reformulation of a coercivity estimate in the language of Wasserstein calculus, which is used to obtain uniform Lipschitz bounds along sequences of ap"},"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":"1908.04183","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-08-12T14:51:12Z","cross_cats_sorted":[],"title_canon_sha256":"87ea31c6402eefca6be59c52939faa4c0a8e2c9875a15be86ba7322b48859f17","abstract_canon_sha256":"470ca82b53864678c14ea12746b8829e498235087efda56a26cb51cb66f1e307"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:13:11.126117Z","signature_b64":"eZtd03g35mHV0qdfQn3ONfktzQznvCzfnGJFfEYqWoI1GSOujxd8TK7vqCM1AgczSG0Bdl3kiS2P5iUPV3WICQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"448404ef8b22dadc18932cd95d4f9dc782c49085b610edd59ad65cf00a1bbf38","last_reissued_at":"2026-07-05T02:13:11.125747Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:13:11.125747Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Intrinsic Lipschitz Regularity of Mean-Field Optimal Controls","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Beno\\^it Bonnet, Francesco Rossi","submitted_at":"2019-08-12T14:51:12Z","abstract_excerpt":"In this article, we provide sufficient conditions under which the controlled vector fields solution of optimal control problems formulated on continuity equations are Lipschitz regular in space. Our approach involves a novel combination of mean-field approximations for infinite-dimensional multi-agent optimal control problems, along with a careful extension of an existence result of locally optimal Lipschitz feedbacks. The latter is based on the reformulation of a coercivity estimate in the language of Wasserstein calculus, which is used to obtain uniform Lipschitz bounds along sequences of ap"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.04183","kind":"arxiv","version":6},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.04183/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1908.04183","created_at":"2026-07-05T02:13:11.125818+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.04183v6","created_at":"2026-07-05T02:13:11.125818+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.04183","created_at":"2026-07-05T02:13:11.125818+00:00"},{"alias_kind":"pith_short_12","alias_value":"ISCAJ34LELNN","created_at":"2026-07-05T02:13:11.125818+00:00"},{"alias_kind":"pith_short_16","alias_value":"ISCAJ34LELNNYGET","created_at":"2026-07-05T02:13:11.125818+00:00"},{"alias_kind":"pith_short_8","alias_value":"ISCAJ34L","created_at":"2026-07-05T02:13:11.125818+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/ISCAJ34LELNNYGETFTMV2T45Y6","json":"https://pith.science/pith/ISCAJ34LELNNYGETFTMV2T45Y6.json","graph_json":"https://pith.science/api/pith-number/ISCAJ34LELNNYGETFTMV2T45Y6/graph.json","events_json":"https://pith.science/api/pith-number/ISCAJ34LELNNYGETFTMV2T45Y6/events.json","paper":"https://pith.science/paper/ISCAJ34L"},"agent_actions":{"view_html":"https://pith.science/pith/ISCAJ34LELNNYGETFTMV2T45Y6","download_json":"https://pith.science/pith/ISCAJ34LELNNYGETFTMV2T45Y6.json","view_paper":"https://pith.science/paper/ISCAJ34L","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.04183&json=true","fetch_graph":"https://pith.science/api/pith-number/ISCAJ34LELNNYGETFTMV2T45Y6/graph.json","fetch_events":"https://pith.science/api/pith-number/ISCAJ34LELNNYGETFTMV2T45Y6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ISCAJ34LELNNYGETFTMV2T45Y6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ISCAJ34LELNNYGETFTMV2T45Y6/action/storage_attestation","attest_author":"https://pith.science/pith/ISCAJ34LELNNYGETFTMV2T45Y6/action/author_attestation","sign_citation":"https://pith.science/pith/ISCAJ34LELNNYGETFTMV2T45Y6/action/citation_signature","submit_replication":"https://pith.science/pith/ISCAJ34LELNNYGETFTMV2T45Y6/action/replication_record"}},"created_at":"2026-07-05T02:13:11.125818+00:00","updated_at":"2026-07-05T02:13:11.125818+00:00"}