{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:FMVX52XEV6BCFI7UGTFOHX5XUX","short_pith_number":"pith:FMVX52XE","schema_version":"1.0","canonical_sha256":"2b2b7eeae4af8222a3f434cae3dfb7a5edb1cfdbc90f72dcefdbd116dd704f18","source":{"kind":"arxiv","id":"2403.01012","version":5},"attestation_state":"computed","paper":{"title":"Hilbert Space-Valued LQ Mean Field Games: An Infinite-Dimensional Analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.PR","q-fin.MF","q-fin.RM"],"primary_cat":"math.OC","authors_text":"Dena Firoozi, Hanchao Liu","submitted_at":"2024-03-01T22:21:43Z","abstract_excerpt":"This paper presents a comprehensive study of linear-quadratic (LQ) mean field games (MFGs) in Hilbert spaces, generalizing the classic LQ MFG theory to scenarios involving $N$ agents with dynamics governed by infinite-dimensional stochastic equations. In this framework, both state and control processes of each agent take values in separable Hilbert spaces. All agents are coupled through the average state of the population which appears in their linear dynamics and quadratic cost functional. Specifically, the dynamics of each agent incorporates an infinite-dimensional noise, namely a $Q$-Wiener"},"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":"2403.01012","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-03-01T22:21:43Z","cross_cats_sorted":["math.FA","math.PR","q-fin.MF","q-fin.RM"],"title_canon_sha256":"036e87c91b9292441bbc4014ce042051073b4759b310fcac10977ed432ce2a1d","abstract_canon_sha256":"f97aaaf1729de1cc122f4f7e1fba90544dbbc5b458454b9e906d7234ebd10770"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:50:57.772555Z","signature_b64":"TgSQlu1aQHGtj4zReEJ/ew3BLMdAP2O6v4KJ1NbluA8kMu3sgYv4G3g8SRWoq9LR6J+HMLkkF4ptH/gGa92fCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2b2b7eeae4af8222a3f434cae3dfb7a5edb1cfdbc90f72dcefdbd116dd704f18","last_reissued_at":"2026-07-05T11:50:57.772036Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:50:57.772036Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hilbert Space-Valued LQ Mean Field Games: An Infinite-Dimensional Analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.PR","q-fin.MF","q-fin.RM"],"primary_cat":"math.OC","authors_text":"Dena Firoozi, Hanchao Liu","submitted_at":"2024-03-01T22:21:43Z","abstract_excerpt":"This paper presents a comprehensive study of linear-quadratic (LQ) mean field games (MFGs) in Hilbert spaces, generalizing the classic LQ MFG theory to scenarios involving $N$ agents with dynamics governed by infinite-dimensional stochastic equations. In this framework, both state and control processes of each agent take values in separable Hilbert spaces. All agents are coupled through the average state of the population which appears in their linear dynamics and quadratic cost functional. Specifically, the dynamics of each agent incorporates an infinite-dimensional noise, namely a $Q$-Wiener"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.01012","kind":"arxiv","version":5},"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/2403.01012/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":"2403.01012","created_at":"2026-07-05T11:50:57.772096+00:00"},{"alias_kind":"arxiv_version","alias_value":"2403.01012v5","created_at":"2026-07-05T11:50:57.772096+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.01012","created_at":"2026-07-05T11:50:57.772096+00:00"},{"alias_kind":"pith_short_12","alias_value":"FMVX52XEV6BC","created_at":"2026-07-05T11:50:57.772096+00:00"},{"alias_kind":"pith_short_16","alias_value":"FMVX52XEV6BCFI7U","created_at":"2026-07-05T11:50:57.772096+00:00"},{"alias_kind":"pith_short_8","alias_value":"FMVX52XE","created_at":"2026-07-05T11:50:57.772096+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2506.11468","citing_title":"Linear-quadratic stochastic nonzero-sum differential games between graphon teams","ref_index":10,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FMVX52XEV6BCFI7UGTFOHX5XUX","json":"https://pith.science/pith/FMVX52XEV6BCFI7UGTFOHX5XUX.json","graph_json":"https://pith.science/api/pith-number/FMVX52XEV6BCFI7UGTFOHX5XUX/graph.json","events_json":"https://pith.science/api/pith-number/FMVX52XEV6BCFI7UGTFOHX5XUX/events.json","paper":"https://pith.science/paper/FMVX52XE"},"agent_actions":{"view_html":"https://pith.science/pith/FMVX52XEV6BCFI7UGTFOHX5XUX","download_json":"https://pith.science/pith/FMVX52XEV6BCFI7UGTFOHX5XUX.json","view_paper":"https://pith.science/paper/FMVX52XE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2403.01012&json=true","fetch_graph":"https://pith.science/api/pith-number/FMVX52XEV6BCFI7UGTFOHX5XUX/graph.json","fetch_events":"https://pith.science/api/pith-number/FMVX52XEV6BCFI7UGTFOHX5XUX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FMVX52XEV6BCFI7UGTFOHX5XUX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FMVX52XEV6BCFI7UGTFOHX5XUX/action/storage_attestation","attest_author":"https://pith.science/pith/FMVX52XEV6BCFI7UGTFOHX5XUX/action/author_attestation","sign_citation":"https://pith.science/pith/FMVX52XEV6BCFI7UGTFOHX5XUX/action/citation_signature","submit_replication":"https://pith.science/pith/FMVX52XEV6BCFI7UGTFOHX5XUX/action/replication_record"}},"created_at":"2026-07-05T11:50:57.772096+00:00","updated_at":"2026-07-05T11:50:57.772096+00:00"}