{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:D4D75ISVM5L26OPVBBMRSUUTOS","short_pith_number":"pith:D4D75ISV","canonical_record":{"source":{"id":"1702.00201","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-02-01T10:47:36Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"bb9dd7b7a248f6f480aab7f612282da29d97b5b97205e4c4cf1baad56583e65b","abstract_canon_sha256":"b904583a3a2db475c23de256340ad0fbc5b5094b33994c6ddc4fcf51c199881b"},"schema_version":"1.0"},"canonical_sha256":"1f07fea2556757af39f50859195293748570cb707328244cea05587519467772","source":{"kind":"arxiv","id":"1702.00201","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.00201","created_at":"2026-05-18T00:51:34Z"},{"alias_kind":"arxiv_version","alias_value":"1702.00201v1","created_at":"2026-05-18T00:51:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.00201","created_at":"2026-05-18T00:51:34Z"},{"alias_kind":"pith_short_12","alias_value":"D4D75ISVM5L2","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"D4D75ISVM5L26OPV","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"D4D75ISV","created_at":"2026-05-18T12:31:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:D4D75ISVM5L26OPVBBMRSUUTOS","target":"record","payload":{"canonical_record":{"source":{"id":"1702.00201","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-02-01T10:47:36Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"bb9dd7b7a248f6f480aab7f612282da29d97b5b97205e4c4cf1baad56583e65b","abstract_canon_sha256":"b904583a3a2db475c23de256340ad0fbc5b5094b33994c6ddc4fcf51c199881b"},"schema_version":"1.0"},"canonical_sha256":"1f07fea2556757af39f50859195293748570cb707328244cea05587519467772","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:34.966204Z","signature_b64":"p50DtfGvoSWWb3P/+Na7mE8+FW9SOVIzRc9cgcnp3EJY32799OySZAvpbAqrDUuld16R8Cki4me1hDfm3Y2AAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1f07fea2556757af39f50859195293748570cb707328244cea05587519467772","last_reissued_at":"2026-05-18T00:51:34.965701Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:34.965701Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1702.00201","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:51:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ATV7wL1LCleJza4EC3eKJRNX5XzTOuOcp29BasHYZc/dHBi9C6NVdNPa3eHS9jZi43J4ZZDZEQPOdNZtTJe0Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T11:16:01.637966Z"},"content_sha256":"1d56150710bcc76b3bae470a642dd30e4bb6d05b365f57aa1e8fe3a41d5357e8","schema_version":"1.0","event_id":"sha256:1d56150710bcc76b3bae470a642dd30e4bb6d05b365f57aa1e8fe3a41d5357e8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:D4D75ISVM5L26OPVBBMRSUUTOS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Existence and optimality conditions for relaxed mean-field stochastic control problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.OC","authors_text":"Brahim Mezerdi, Khaled Bahlali, Meriem Mezerdi","submitted_at":"2017-02-01T10:47:36Z","abstract_excerpt":"We consider optimal control problems for systems governed by mean-field stochastic differential equations, where the control enters both the drift and the diffusion coefficient. We study the relaxed model, in which admissible controls are measure-valued processes and the relaxed state process is driven by an orthogonal martingale measure, whose covariance measure is the relaxed control. This is a natural extension of the original strict control problem, for which we prove the existence of an optimal control. Then, we derive optimality necessary conditions for this problem, in terms of two adjo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.00201","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T00:51:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SZD0+R64+8H4ypT5P11PZy+Xzf/kbPVjiyXreqllWboQZ4y6lMjKWhR5IsG9SDwEv3zBuurRMykwwoRWv3eeAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T11:16:01.638338Z"},"content_sha256":"73d0c45b8aaef067b2a07b3c134f4d667829ae8ab5666e34de1ed771e7bc975b","schema_version":"1.0","event_id":"sha256:73d0c45b8aaef067b2a07b3c134f4d667829ae8ab5666e34de1ed771e7bc975b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D4D75ISVM5L26OPVBBMRSUUTOS/bundle.json","state_url":"https://pith.science/pith/D4D75ISVM5L26OPVBBMRSUUTOS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D4D75ISVM5L26OPVBBMRSUUTOS/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":"2026-06-03T11:16:01Z","links":{"resolver":"https://pith.science/pith/D4D75ISVM5L26OPVBBMRSUUTOS","bundle":"https://pith.science/pith/D4D75ISVM5L26OPVBBMRSUUTOS/bundle.json","state":"https://pith.science/pith/D4D75ISVM5L26OPVBBMRSUUTOS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D4D75ISVM5L26OPVBBMRSUUTOS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:D4D75ISVM5L26OPVBBMRSUUTOS","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":"b904583a3a2db475c23de256340ad0fbc5b5094b33994c6ddc4fcf51c199881b","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-02-01T10:47:36Z","title_canon_sha256":"bb9dd7b7a248f6f480aab7f612282da29d97b5b97205e4c4cf1baad56583e65b"},"schema_version":"1.0","source":{"id":"1702.00201","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.00201","created_at":"2026-05-18T00:51:34Z"},{"alias_kind":"arxiv_version","alias_value":"1702.00201v1","created_at":"2026-05-18T00:51:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.00201","created_at":"2026-05-18T00:51:34Z"},{"alias_kind":"pith_short_12","alias_value":"D4D75ISVM5L2","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"D4D75ISVM5L26OPV","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"D4D75ISV","created_at":"2026-05-18T12:31:10Z"}],"graph_snapshots":[{"event_id":"sha256:73d0c45b8aaef067b2a07b3c134f4d667829ae8ab5666e34de1ed771e7bc975b","target":"graph","created_at":"2026-05-18T00:51:34Z","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"},"paper":{"abstract_excerpt":"We consider optimal control problems for systems governed by mean-field stochastic differential equations, where the control enters both the drift and the diffusion coefficient. We study the relaxed model, in which admissible controls are measure-valued processes and the relaxed state process is driven by an orthogonal martingale measure, whose covariance measure is the relaxed control. This is a natural extension of the original strict control problem, for which we prove the existence of an optimal control. Then, we derive optimality necessary conditions for this problem, in terms of two adjo","authors_text":"Brahim Mezerdi, Khaled Bahlali, Meriem Mezerdi","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-02-01T10:47:36Z","title":"Existence and optimality conditions for relaxed mean-field stochastic control problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.00201","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":"sha256:1d56150710bcc76b3bae470a642dd30e4bb6d05b365f57aa1e8fe3a41d5357e8","target":"record","created_at":"2026-05-18T00:51:34Z","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":"b904583a3a2db475c23de256340ad0fbc5b5094b33994c6ddc4fcf51c199881b","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-02-01T10:47:36Z","title_canon_sha256":"bb9dd7b7a248f6f480aab7f612282da29d97b5b97205e4c4cf1baad56583e65b"},"schema_version":"1.0","source":{"id":"1702.00201","kind":"arxiv","version":1}},"canonical_sha256":"1f07fea2556757af39f50859195293748570cb707328244cea05587519467772","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1f07fea2556757af39f50859195293748570cb707328244cea05587519467772","first_computed_at":"2026-05-18T00:51:34.965701Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:51:34.965701Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"p50DtfGvoSWWb3P/+Na7mE8+FW9SOVIzRc9cgcnp3EJY32799OySZAvpbAqrDUuld16R8Cki4me1hDfm3Y2AAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:51:34.966204Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.00201","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1d56150710bcc76b3bae470a642dd30e4bb6d05b365f57aa1e8fe3a41d5357e8","sha256:73d0c45b8aaef067b2a07b3c134f4d667829ae8ab5666e34de1ed771e7bc975b"],"state_sha256":"2f414db1f339c5954c852d60cc21a1fd6faf78f15174e1c8f44717a2a0a4e898"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E3u7Q5M7AHAjT8qiG23ovhDsmGoQia4OmtBNsce9T5jOP4qrSuc8TKXAwAf9Mp787IKnUFmcDZSTrFmDlwq+AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T11:16:01.640268Z","bundle_sha256":"a5d7927e3246b5f542bb792d022441355b1753c1d873f39f4e543de772179a32"}}