{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:6SQBVEUNTVAKBE7B2MMWI74JJJ","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":"5bb9cf7e6fe9a1ba6ed7a161c86294078b3c05792c6722e75c6d9a976084785f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2023-02-21T04:47:50Z","title_canon_sha256":"56162c3ac985687cef255a342345ba5bf6b5646a9ccf87cf4e0d13abc0df756b"},"schema_version":"1.0","source":{"id":"2302.10440","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2302.10440","created_at":"2026-07-05T08:10:54Z"},{"alias_kind":"arxiv_version","alias_value":"2302.10440v2","created_at":"2026-07-05T08:10:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2302.10440","created_at":"2026-07-05T08:10:54Z"},{"alias_kind":"pith_short_12","alias_value":"6SQBVEUNTVAK","created_at":"2026-07-05T08:10:54Z"},{"alias_kind":"pith_short_16","alias_value":"6SQBVEUNTVAKBE7B","created_at":"2026-07-05T08:10:54Z"},{"alias_kind":"pith_short_8","alias_value":"6SQBVEUN","created_at":"2026-07-05T08:10:54Z"}],"graph_snapshots":[{"event_id":"sha256:8840c7fd8beb32147ed316195352662710765617ca221e4e07ec98184a7cba51","target":"graph","created_at":"2026-07-05T08:10:54Z","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/2302.10440/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We propose a single-level numerical approach to solve Stackelberg mean field game (MFG) problems. In Stackelberg MFG, an infinite population of agents play a non-cooperative game and choose their controls to optimize their individual objectives while interacting with the principal and other agents through the population distribution. The principal can influence the mean field Nash equilibrium at the population level through policies, and she optimizes her own objective, which depends on the population distribution. This leads to a bi-level problem between the principal and mean field of agents","authors_text":"Gokce Dayanikli, Mathieu Lauriere","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2023-02-21T04:47:50Z","title":"A Machine Learning Method for Stackelberg Mean Field Games"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.10440","kind":"arxiv","version":2},"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:f40dfdb100be6ae5b2f51cfde6c37047feab14cc4bda14c85923cf7fa7d15da4","target":"record","created_at":"2026-07-05T08:10:54Z","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":"5bb9cf7e6fe9a1ba6ed7a161c86294078b3c05792c6722e75c6d9a976084785f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2023-02-21T04:47:50Z","title_canon_sha256":"56162c3ac985687cef255a342345ba5bf6b5646a9ccf87cf4e0d13abc0df756b"},"schema_version":"1.0","source":{"id":"2302.10440","kind":"arxiv","version":2}},"canonical_sha256":"f4a01a928d9d40a093e1d319647f894a497dad39f981d45ed7e37bf93f6dfdf1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f4a01a928d9d40a093e1d319647f894a497dad39f981d45ed7e37bf93f6dfdf1","first_computed_at":"2026-07-05T08:10:54.514016Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:10:54.514016Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ldbjPKY9L6wSeqkrd2oLMEuGRsNo6dcyDo7Ogum+IAYxxmuiPnRf1WeqYhJ3d0YTaa/ch9AxoBnFTJGX8rdaAw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:10:54.514554Z","signed_message":"canonical_sha256_bytes"},"source_id":"2302.10440","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f40dfdb100be6ae5b2f51cfde6c37047feab14cc4bda14c85923cf7fa7d15da4","sha256:8840c7fd8beb32147ed316195352662710765617ca221e4e07ec98184a7cba51"],"state_sha256":"f8bbd32eee0ab0c615fa4d6823bfb31cdc887489528853de14352ad5b8da8544"}