{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:6I3YUWGG5XLQLMX2KJEJVDFHKF","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":"56a630c95e19567e28b973c6e10eceeed6c5be154bd955fff9d3257217b054fc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-04-22T02:05:29Z","title_canon_sha256":"ccbb9eea145befaca40736adfc1ead2e9d5e8ec8f3013637d6f446e899db31b2"},"schema_version":"1.0","source":{"id":"2504.15526","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.15526","created_at":"2026-07-05T10:52:26Z"},{"alias_kind":"arxiv_version","alias_value":"2504.15526v1","created_at":"2026-07-05T10:52:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.15526","created_at":"2026-07-05T10:52:26Z"},{"alias_kind":"pith_short_12","alias_value":"6I3YUWGG5XLQ","created_at":"2026-07-05T10:52:26Z"},{"alias_kind":"pith_short_16","alias_value":"6I3YUWGG5XLQLMX2","created_at":"2026-07-05T10:52:26Z"},{"alias_kind":"pith_short_8","alias_value":"6I3YUWGG","created_at":"2026-07-05T10:52:26Z"}],"graph_snapshots":[{"event_id":"sha256:fa3fb865adc16cf41b6502560ceb04530ba5e8434abb37f56db6652e35002a09","target":"graph","created_at":"2026-07-05T10:52:26Z","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/2504.15526/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper studies Mean Field Games (MFGs) in which agent dynamics are given by jump processes of controlled intensity, with mean-field interaction via the controls and affecting the jump intensities. We establish the existence of MFG equilibria in a general discrete-time setting, and prove a limit theorem as the time discretization goes to zero, establishing equilibria in the continuous-time setting for a class of MFGs of intensity control. This motivates numerical schemes that involve directly solving discrete-time games as opposed to coupled Hamilton-Jacobi-Bellman and Kolmogorov equations.","authors_text":"H. Mete Soner, Nicolas Garcia, Ronnie Sircar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-04-22T02:05:29Z","title":"Mean Field Games of Control and Cryptocurrency Mining"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.15526","kind":"arxiv","version":1},"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":"sha256:85bd990bd2bfe748fdf71cac3e369b4427d140b88aaa7487a6b4ed4658f43948","target":"record","created_at":"2026-07-05T10:52:26Z","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":"56a630c95e19567e28b973c6e10eceeed6c5be154bd955fff9d3257217b054fc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-04-22T02:05:29Z","title_canon_sha256":"ccbb9eea145befaca40736adfc1ead2e9d5e8ec8f3013637d6f446e899db31b2"},"schema_version":"1.0","source":{"id":"2504.15526","kind":"arxiv","version":1}},"canonical_sha256":"f2378a58c6edd705b2fa52489a8ca7515237f63a0873a303093f0587f8aa3d0f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f2378a58c6edd705b2fa52489a8ca7515237f63a0873a303093f0587f8aa3d0f","first_computed_at":"2026-07-05T10:52:26.019671Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:52:26.019671Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"io5KyjAvI/IdL54a4X/B7ogJxgwVJjfZlX9iW+5BA19DTmzZZEetKva4/hwGZMHMVbtR2nolSq3ppYO0RzRZBg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:52:26.020138Z","signed_message":"canonical_sha256_bytes"},"source_id":"2504.15526","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:85bd990bd2bfe748fdf71cac3e369b4427d140b88aaa7487a6b4ed4658f43948","sha256:fa3fb865adc16cf41b6502560ceb04530ba5e8434abb37f56db6652e35002a09"],"state_sha256":"a46d32f4546c00d15bc2ed359b110a676639634ace3cbe3484b23d018e475d56"}