{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:EXSA3WQHVGATIHU33IFHEC4NBV","short_pith_number":"pith:EXSA3WQH","canonical_record":{"source":{"id":"2512.19201","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-12-22T09:39:43Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"586b5fc23df9369a28e2875384876da61e41ee4b2c22cc7d9b0c6dbc3c5fb52c","abstract_canon_sha256":"1f6d165b56441d72c9c39b4fdfc67a3cf77ad1056e7736fc9a77d09cfcd66144"},"schema_version":"1.0"},"canonical_sha256":"25e40dda07a981341e9bda0a720b8d0d40f6ab72608e60abd87c70de40663634","source":{"kind":"arxiv","id":"2512.19201","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:EXSA3WQHVGATIHU33IFHEC4NBV","target":"record","payload":{"canonical_record":{"source":{"id":"2512.19201","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-12-22T09:39:43Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"586b5fc23df9369a28e2875384876da61e41ee4b2c22cc7d9b0c6dbc3c5fb52c","abstract_canon_sha256":"1f6d165b56441d72c9c39b4fdfc67a3cf77ad1056e7736fc9a77d09cfcd66144"},"schema_version":"1.0"},"canonical_sha256":"25e40dda07a981341e9bda0a720b8d0d40f6ab72608e60abd87c70de40663634","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-15T01:21:48.731272Z","signature_b64":"LKv65y3/wYg+FOVM3yo/fMS0NYJRGQDVmTyfAiMFAKIUG1zm4aGLNVYKvg/GL15W6mjgqyiV59W3ecg7pGjwDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"25e40dda07a981341e9bda0a720b8d0d40f6ab72608e60abd87c70de40663634","last_reissued_at":"2026-07-15T01:21:48.730452Z","signature_status":"signed_v1","first_computed_at":"2026-07-15T01:21:48.730452Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2512.19201","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-15T01:21:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hhYAXUAwy9kW/tWVx+FK+eDt7xs8LiiUNNXpP+82sPlRXgHGjpQkQw3+kPP0En42rawhcyyOOK8mAAU6hG4TDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T18:17:53.670014Z"},"content_sha256":"a5c356e1e434d9f9ad6989c66a687101e478b825cedab80009dbbc562da5e0f7","schema_version":"1.0","event_id":"sha256:a5c356e1e434d9f9ad6989c66a687101e478b825cedab80009dbbc562da5e0f7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:EXSA3WQHVGATIHU33IFHEC4NBV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mean-field optimal control with stochastic leaders","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.OC","authors_text":"Ana Djurdjevac, Carsten Hartmann, Christof Sch\\\"utte, Nata\\v{s}a Djurdjevac Conrad, Sebastian Zimper","submitted_at":"2025-12-22T09:39:43Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.19201","kind":"arxiv","version":2},"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/2512.19201/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-15T01:21:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qknL6Yiu0ooRPNj2LRs2IBN3dkIo7pT88wQwUdmARMptYMOB1j77/8+80BHTTy3plTHk4xJ9dEJcK+AHaEAZBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T18:17:53.670621Z"},"content_sha256":"559b6fa38fb9c703ead0f55b0c0998fc231ce257e76d2cd6fb2dc65b73914b53","schema_version":"1.0","event_id":"sha256:559b6fa38fb9c703ead0f55b0c0998fc231ce257e76d2cd6fb2dc65b73914b53"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EXSA3WQHVGATIHU33IFHEC4NBV/bundle.json","state_url":"https://pith.science/pith/EXSA3WQHVGATIHU33IFHEC4NBV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EXSA3WQHVGATIHU33IFHEC4NBV/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-08T18:17:53Z","links":{"resolver":"https://pith.science/pith/EXSA3WQHVGATIHU33IFHEC4NBV","bundle":"https://pith.science/pith/EXSA3WQHVGATIHU33IFHEC4NBV/bundle.json","state":"https://pith.science/pith/EXSA3WQHVGATIHU33IFHEC4NBV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EXSA3WQHVGATIHU33IFHEC4NBV/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yCu0+0XaGgI7Tf+IBqw7gcagaQh9Q8hMprIF9yusUAIrKCoRILv+qd3ok/8NqSGpRXTw3YAyhfu6E6DGyGaaBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T18:17:53.674538Z","bundle_sha256":"11151981f6773c2823531ec089825df9d4ea61e7c18bb91cb6c84f488fb000e9"}}