{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:EXSA3WQHVGATIHU33IFHEC4NBV","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":"1f6d165b56441d72c9c39b4fdfc67a3cf77ad1056e7736fc9a77d09cfcd66144","cross_cats_sorted":["math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-12-22T09:39:43Z","title_canon_sha256":"586b5fc23df9369a28e2875384876da61e41ee4b2c22cc7d9b0c6dbc3c5fb52c"},"schema_version":"1.0","source":{"id":"2512.19201","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2512.19201","created_at":"2026-07-15T01:21:48Z"},{"alias_kind":"arxiv_version","alias_value":"2512.19201v2","created_at":"2026-07-15T01:21:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2512.19201","created_at":"2026-07-15T01:21:48Z"},{"alias_kind":"pith_short_12","alias_value":"EXSA3WQHVGAT","created_at":"2026-07-15T01:21:48Z"},{"alias_kind":"pith_short_16","alias_value":"EXSA3WQHVGATIHU3","created_at":"2026-07-15T01:21:48Z"},{"alias_kind":"pith_short_8","alias_value":"EXSA3WQH","created_at":"2026-07-15T01:21:48Z"}],"graph_snapshots":[{"event_id":"sha256:559b6fa38fb9c703ead0f55b0c0998fc231ce257e76d2cd6fb2dc65b73914b53","target":"graph","created_at":"2026-07-15T01:21:48Z","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/2512.19201/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider interacting agent systems with a large number of stochastic agents influenced by a fixed number of external stochastic lead agents. Such settings arise, for example in models of opinion dynamics, where a small number of leaders can steer the behaviour of a large population of followers. In this context, we study a partial mean-field limit where the number of followers tends to infinity, while the number of leaders stays constant. The partial mean-field limit dynamics is then given by a McKean-Vlasov stochastic differential equation (SDE) for the followers, coupled to a controlled I","authors_text":"Ana Djurdjevac, Carsten Hartmann, Christof Sch\\\"utte, Nata\\v{s}a Djurdjevac Conrad, Sebastian Zimper","cross_cats":["math.PR"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-12-22T09:39:43Z","title":"Mean-field optimal control with stochastic leaders"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.19201","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:a5c356e1e434d9f9ad6989c66a687101e478b825cedab80009dbbc562da5e0f7","target":"record","created_at":"2026-07-15T01:21:48Z","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":"1f6d165b56441d72c9c39b4fdfc67a3cf77ad1056e7736fc9a77d09cfcd66144","cross_cats_sorted":["math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-12-22T09:39:43Z","title_canon_sha256":"586b5fc23df9369a28e2875384876da61e41ee4b2c22cc7d9b0c6dbc3c5fb52c"},"schema_version":"1.0","source":{"id":"2512.19201","kind":"arxiv","version":2}},"canonical_sha256":"25e40dda07a981341e9bda0a720b8d0d40f6ab72608e60abd87c70de40663634","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"25e40dda07a981341e9bda0a720b8d0d40f6ab72608e60abd87c70de40663634","first_computed_at":"2026-07-15T01:21:48.730452Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-15T01:21:48.730452Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LKv65y3/wYg+FOVM3yo/fMS0NYJRGQDVmTyfAiMFAKIUG1zm4aGLNVYKvg/GL15W6mjgqyiV59W3ecg7pGjwDQ==","signature_status":"signed_v1","signed_at":"2026-07-15T01:21:48.731272Z","signed_message":"canonical_sha256_bytes"},"source_id":"2512.19201","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a5c356e1e434d9f9ad6989c66a687101e478b825cedab80009dbbc562da5e0f7","sha256:559b6fa38fb9c703ead0f55b0c0998fc231ce257e76d2cd6fb2dc65b73914b53"],"state_sha256":"0b37137a727b7788ace3b2fe44dc241a50e5107ddb5e6e8127f31fffadc0a3b3"}