{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:4P322LSQIUSNLNBJGFKDZMMWCR","short_pith_number":"pith:4P322LSQ","schema_version":"1.0","canonical_sha256":"e3f7ad2e504524d5b42931543cb1961444381a92657e652505ae7b18cabc6a03","source":{"kind":"arxiv","id":"2506.05595","version":1},"attestation_state":"computed","paper":{"title":"Stochastic maximum principle for optimal control problem of non exchangeable mean field systems","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.OC","authors_text":"Huy\\^en Pham, Idris Kharroubi, Samy Mekkaoui","submitted_at":"2025-06-05T21:13:06Z","abstract_excerpt":"We study the Pontryagin maximum principle by deriving necessary and sufficient conditions for a class of optimal control problems arising in non exchangeable mean field systems, where agents interact through heterogeneous and asymmetric couplings. Our analysis leads to a collection of forward-backward stochastic differential equations (FBSDE) of non exchangeable mean field type. Under suitable assumptions, we establish the solvability of this system. As an illustration, we consider the linear-quadratic case, where the optimal control is characterized by an infinite dimensional system of Riccat"},"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":"2506.05595","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.OC","submitted_at":"2025-06-05T21:13:06Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"aea7cf38d3a85ae7341bb3965bf523361c8990a452ede24c04a99b8ceeaeed6d","abstract_canon_sha256":"8c51c47a588f5e87816453d9aa411699d2949f5d93523e25fe5e7a8d79dad4fc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:17:06.515096Z","signature_b64":"aOoKbQYuJps4bTuzvYhOJPBdx9jhATxf5rlAORv4LTyM1VCUpISJFAMIFADsIU8xoJNG3tqb3NAMgLXa/nWwDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e3f7ad2e504524d5b42931543cb1961444381a92657e652505ae7b18cabc6a03","last_reissued_at":"2026-07-05T11:17:06.514611Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:17:06.514611Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stochastic maximum principle for optimal control problem of non exchangeable mean field systems","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.OC","authors_text":"Huy\\^en Pham, Idris Kharroubi, Samy Mekkaoui","submitted_at":"2025-06-05T21:13:06Z","abstract_excerpt":"We study the Pontryagin maximum principle by deriving necessary and sufficient conditions for a class of optimal control problems arising in non exchangeable mean field systems, where agents interact through heterogeneous and asymmetric couplings. Our analysis leads to a collection of forward-backward stochastic differential equations (FBSDE) of non exchangeable mean field type. Under suitable assumptions, we establish the solvability of this system. As an illustration, we consider the linear-quadratic case, where the optimal control is characterized by an infinite dimensional system of Riccat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.05595","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.05595/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":"2506.05595","created_at":"2026-07-05T11:17:06.514665+00:00"},{"alias_kind":"arxiv_version","alias_value":"2506.05595v1","created_at":"2026-07-05T11:17:06.514665+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.05595","created_at":"2026-07-05T11:17:06.514665+00:00"},{"alias_kind":"pith_short_12","alias_value":"4P322LSQIUSN","created_at":"2026-07-05T11:17:06.514665+00:00"},{"alias_kind":"pith_short_16","alias_value":"4P322LSQIUSNLNBJ","created_at":"2026-07-05T11:17:06.514665+00:00"},{"alias_kind":"pith_short_8","alias_value":"4P322LSQ","created_at":"2026-07-05T11:17:06.514665+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.14901","citing_title":"Non--exchangeable mean field games with moderate interactions and common noise","ref_index":30,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4P322LSQIUSNLNBJGFKDZMMWCR","json":"https://pith.science/pith/4P322LSQIUSNLNBJGFKDZMMWCR.json","graph_json":"https://pith.science/api/pith-number/4P322LSQIUSNLNBJGFKDZMMWCR/graph.json","events_json":"https://pith.science/api/pith-number/4P322LSQIUSNLNBJGFKDZMMWCR/events.json","paper":"https://pith.science/paper/4P322LSQ"},"agent_actions":{"view_html":"https://pith.science/pith/4P322LSQIUSNLNBJGFKDZMMWCR","download_json":"https://pith.science/pith/4P322LSQIUSNLNBJGFKDZMMWCR.json","view_paper":"https://pith.science/paper/4P322LSQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2506.05595&json=true","fetch_graph":"https://pith.science/api/pith-number/4P322LSQIUSNLNBJGFKDZMMWCR/graph.json","fetch_events":"https://pith.science/api/pith-number/4P322LSQIUSNLNBJGFKDZMMWCR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4P322LSQIUSNLNBJGFKDZMMWCR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4P322LSQIUSNLNBJGFKDZMMWCR/action/storage_attestation","attest_author":"https://pith.science/pith/4P322LSQIUSNLNBJGFKDZMMWCR/action/author_attestation","sign_citation":"https://pith.science/pith/4P322LSQIUSNLNBJGFKDZMMWCR/action/citation_signature","submit_replication":"https://pith.science/pith/4P322LSQIUSNLNBJGFKDZMMWCR/action/replication_record"}},"created_at":"2026-07-05T11:17:06.514665+00:00","updated_at":"2026-07-05T11:17:06.514665+00:00"}