{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:X5DMONB3AFCSZPWOF6ITIQNXDH","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"78e81509b9ee1590c2c0031bde8875d2da2835c499b4f497b04fcea4f1d84925","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-07-21T06:46:29Z","title_canon_sha256":"559da86eb7981f0dae14745c8e8a9151215452778881485a915772a1d2a2a607"},"schema_version":"1.0","source":{"id":"2007.10620","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2007.10620","created_at":"2026-07-05T02:05:41Z"},{"alias_kind":"arxiv_version","alias_value":"2007.10620v3","created_at":"2026-07-05T02:05:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2007.10620","created_at":"2026-07-05T02:05:41Z"},{"alias_kind":"pith_short_12","alias_value":"X5DMONB3AFCS","created_at":"2026-07-05T02:05:41Z"},{"alias_kind":"pith_short_16","alias_value":"X5DMONB3AFCSZPWO","created_at":"2026-07-05T02:05:41Z"},{"alias_kind":"pith_short_8","alias_value":"X5DMONB3","created_at":"2026-07-05T02:05:41Z"}],"graph_snapshots":[{"event_id":"sha256:2a0b2eb10f2038cb7537c889bdece69a1e91226c3e40c4dd9f4a6cc3a816d669","target":"graph","created_at":"2026-07-05T02:05:41Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2007.10620/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider a Mean Field Games model where the dynamics of the agents is given by a controlled Langevin equation and the cost is quadratic. A change of variables, introduced in [9], transforms the Mean Field Games system into a system of two coupled kinetic Fokker-Planck equations. We prove an existence result for the latter system, obtaining consequently existence of a solution for the Mean Field Games system.","authors_text":"Fabio Camilli","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-07-21T06:46:29Z","title":"A quadratic Mean Field Games model for the Langevin equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.10620","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:4ed6dcd07ddd263c5045c659b36dfa11958e86b17a0754ce6849adb41a682d12","target":"record","created_at":"2026-07-05T02:05:41Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"78e81509b9ee1590c2c0031bde8875d2da2835c499b4f497b04fcea4f1d84925","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-07-21T06:46:29Z","title_canon_sha256":"559da86eb7981f0dae14745c8e8a9151215452778881485a915772a1d2a2a607"},"schema_version":"1.0","source":{"id":"2007.10620","kind":"arxiv","version":3}},"canonical_sha256":"bf46c7343b01452cbece2f913441b719f52c432e811e622762624637b9d34284","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bf46c7343b01452cbece2f913441b719f52c432e811e622762624637b9d34284","first_computed_at":"2026-07-05T02:05:41.997849Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:05:41.997849Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iYPLi8fcJ/xpvXDALdDkaUcu8Psutjwl1v6XgHFftoM4DypASILvpxnuxdoFtkgBqb9bgDoW02O3kNx9oM6DDA==","signature_status":"signed_v1","signed_at":"2026-07-05T02:05:41.998300Z","signed_message":"canonical_sha256_bytes"},"source_id":"2007.10620","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4ed6dcd07ddd263c5045c659b36dfa11958e86b17a0754ce6849adb41a682d12","sha256:2a0b2eb10f2038cb7537c889bdece69a1e91226c3e40c4dd9f4a6cc3a816d669"],"state_sha256":"5a0374279c312957ea3a1fbca2b4adc001e07d6a361fd8bd7a39ce07badadbe6"}