{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:GKIGWT23BEQWQ23XND5MURDTRN","short_pith_number":"pith:GKIGWT23","canonical_record":{"source":{"id":"2109.12316","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.OC","submitted_at":"2021-09-25T08:43:22Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"b1cbffbe91cb67224acb837c65d631cfddd75c796fc97b424e163ecd10284116","abstract_canon_sha256":"a7051edfc90e04daf2efc1f7b7fd8af5f4417c54ffcd3be8d775470092307c6c"},"schema_version":"1.0"},"canonical_sha256":"32906b4f5b0921686b7768faca44738b57c56b4a448d962195b8e373597c8f34","source":{"kind":"arxiv","id":"2109.12316","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.12316","created_at":"2026-07-05T03:33:50Z"},{"alias_kind":"arxiv_version","alias_value":"2109.12316v3","created_at":"2026-07-05T03:33:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.12316","created_at":"2026-07-05T03:33:50Z"},{"alias_kind":"pith_short_12","alias_value":"GKIGWT23BEQW","created_at":"2026-07-05T03:33:50Z"},{"alias_kind":"pith_short_16","alias_value":"GKIGWT23BEQWQ23X","created_at":"2026-07-05T03:33:50Z"},{"alias_kind":"pith_short_8","alias_value":"GKIGWT23","created_at":"2026-07-05T03:33:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:GKIGWT23BEQWQ23XND5MURDTRN","target":"record","payload":{"canonical_record":{"source":{"id":"2109.12316","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.OC","submitted_at":"2021-09-25T08:43:22Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"b1cbffbe91cb67224acb837c65d631cfddd75c796fc97b424e163ecd10284116","abstract_canon_sha256":"a7051edfc90e04daf2efc1f7b7fd8af5f4417c54ffcd3be8d775470092307c6c"},"schema_version":"1.0"},"canonical_sha256":"32906b4f5b0921686b7768faca44738b57c56b4a448d962195b8e373597c8f34","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:33:50.052665Z","signature_b64":"ojANQ2FZsdarBH4FldoxfpklhDUV/rGNpt06NamDDh4Ytp6up6TbIUc1kxA1HG9y3uNTssNnHsUlFhQKaKV+CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"32906b4f5b0921686b7768faca44738b57c56b4a448d962195b8e373597c8f34","last_reissued_at":"2026-07-05T03:33:50.052187Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:33:50.052187Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2109.12316","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:33:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HDR8vgtt5L4/COCK9Tm7H1UHmFzvtMlfbVYqTIdWUAUK3aXXTj7cimyVHbYm+5NnyehMe20d9wOv4Qt2lCpOAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T19:40:13.352851Z"},"content_sha256":"05ecd48aae72074eca3a05b993cf33ce3c6480aa3c399c92007b59097b35b1a4","schema_version":"1.0","event_id":"sha256:05ecd48aae72074eca3a05b993cf33ce3c6480aa3c399c92007b59097b35b1a4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:GKIGWT23BEQWQ23XND5MURDTRN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A stochastic maximum principle for partially observed general mean-field control problems with only weak solution","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.OC","authors_text":"Chao Mi, Hao Liang, Juan Li","submitted_at":"2021-09-25T08:43:22Z","abstract_excerpt":"In this paper we focus on a general type of mean-field stochastic control problem with partial observation, in which the coefficients depend in a non-linear way not only on the state process $X_t$ and its control $u_t$ but also on the conditional law $E[X_t|\\mathcal{F}_t^Y]$ of the state process conditioned with respect to the past of observation process $Y$. We first deduce the well-posedness of the controlled system by showing weak existence and uniqueness in law. Neither supposing convexity of the control state space nor differentiability of the coefficients with respect to the control vari"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.12316","kind":"arxiv","version":3},"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/2109.12316/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":"2026-07-05T03:33:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Mw90nu/FVicNGQ17VSNrkCeyXG6I6DAK3QZpoMUzDavMgy7hiHKi1csyt3JHl6LVlaf6heEqD3HyHxGqvTC6Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T19:40:13.353353Z"},"content_sha256":"3aedb7311d92a6b137288725d4f12979b97016ded774a0d5d0aded616d5fbb06","schema_version":"1.0","event_id":"sha256:3aedb7311d92a6b137288725d4f12979b97016ded774a0d5d0aded616d5fbb06"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GKIGWT23BEQWQ23XND5MURDTRN/bundle.json","state_url":"https://pith.science/pith/GKIGWT23BEQWQ23XND5MURDTRN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GKIGWT23BEQWQ23XND5MURDTRN/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":"2026-08-16T19:40:13Z","links":{"resolver":"https://pith.science/pith/GKIGWT23BEQWQ23XND5MURDTRN","bundle":"https://pith.science/pith/GKIGWT23BEQWQ23XND5MURDTRN/bundle.json","state":"https://pith.science/pith/GKIGWT23BEQWQ23XND5MURDTRN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GKIGWT23BEQWQ23XND5MURDTRN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:GKIGWT23BEQWQ23XND5MURDTRN","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":"a7051edfc90e04daf2efc1f7b7fd8af5f4417c54ffcd3be8d775470092307c6c","cross_cats_sorted":["math.PR"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.OC","submitted_at":"2021-09-25T08:43:22Z","title_canon_sha256":"b1cbffbe91cb67224acb837c65d631cfddd75c796fc97b424e163ecd10284116"},"schema_version":"1.0","source":{"id":"2109.12316","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.12316","created_at":"2026-07-05T03:33:50Z"},{"alias_kind":"arxiv_version","alias_value":"2109.12316v3","created_at":"2026-07-05T03:33:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.12316","created_at":"2026-07-05T03:33:50Z"},{"alias_kind":"pith_short_12","alias_value":"GKIGWT23BEQW","created_at":"2026-07-05T03:33:50Z"},{"alias_kind":"pith_short_16","alias_value":"GKIGWT23BEQWQ23X","created_at":"2026-07-05T03:33:50Z"},{"alias_kind":"pith_short_8","alias_value":"GKIGWT23","created_at":"2026-07-05T03:33:50Z"}],"graph_snapshots":[{"event_id":"sha256:3aedb7311d92a6b137288725d4f12979b97016ded774a0d5d0aded616d5fbb06","target":"graph","created_at":"2026-07-05T03:33:50Z","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/2109.12316/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we focus on a general type of mean-field stochastic control problem with partial observation, in which the coefficients depend in a non-linear way not only on the state process $X_t$ and its control $u_t$ but also on the conditional law $E[X_t|\\mathcal{F}_t^Y]$ of the state process conditioned with respect to the past of observation process $Y$. We first deduce the well-posedness of the controlled system by showing weak existence and uniqueness in law. Neither supposing convexity of the control state space nor differentiability of the coefficients with respect to the control vari","authors_text":"Chao Mi, Hao Liang, Juan Li","cross_cats":["math.PR"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.OC","submitted_at":"2021-09-25T08:43:22Z","title":"A stochastic maximum principle for partially observed general mean-field control problems with only weak solution"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.12316","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":"sha256:05ecd48aae72074eca3a05b993cf33ce3c6480aa3c399c92007b59097b35b1a4","target":"record","created_at":"2026-07-05T03:33:50Z","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":"a7051edfc90e04daf2efc1f7b7fd8af5f4417c54ffcd3be8d775470092307c6c","cross_cats_sorted":["math.PR"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.OC","submitted_at":"2021-09-25T08:43:22Z","title_canon_sha256":"b1cbffbe91cb67224acb837c65d631cfddd75c796fc97b424e163ecd10284116"},"schema_version":"1.0","source":{"id":"2109.12316","kind":"arxiv","version":3}},"canonical_sha256":"32906b4f5b0921686b7768faca44738b57c56b4a448d962195b8e373597c8f34","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"32906b4f5b0921686b7768faca44738b57c56b4a448d962195b8e373597c8f34","first_computed_at":"2026-07-05T03:33:50.052187Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:33:50.052187Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ojANQ2FZsdarBH4FldoxfpklhDUV/rGNpt06NamDDh4Ytp6up6TbIUc1kxA1HG9y3uNTssNnHsUlFhQKaKV+CA==","signature_status":"signed_v1","signed_at":"2026-07-05T03:33:50.052665Z","signed_message":"canonical_sha256_bytes"},"source_id":"2109.12316","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:05ecd48aae72074eca3a05b993cf33ce3c6480aa3c399c92007b59097b35b1a4","sha256:3aedb7311d92a6b137288725d4f12979b97016ded774a0d5d0aded616d5fbb06"],"state_sha256":"a7cc8dd245551d76b284d60e959d0a484b5f3f1b9db0f1b90859f8219ee142d2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aCu63NAWoXEcy2VHJkDYIDQh8matwiOBMtOqS77/iMUtplVSXC5UZG/XKCEIup1rqTEn20LSGWgBpEv9qWWVAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T19:40:13.357490Z","bundle_sha256":"bf4b2a410f891ea133a562882efe150053d208a849fc1d9282dd2aac6c5f24b2"}}