{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:MSN5M7KN5BXSQ4IC5UMCCXS23E","short_pith_number":"pith:MSN5M7KN","canonical_record":{"source":{"id":"1603.06071","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-03-19T09:52:43Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"bcee541fff9a3ff670b1f009087a515af1ddd0c135f1fe30792ddcd7db6c5f6f","abstract_canon_sha256":"1a39ad9acdcc4c5ffc53e4c3da8c21e4cb1a37d93ffd8323a6f4118ffa38e0cd"},"schema_version":"1.0"},"canonical_sha256":"649bd67d4de86f287102ed18215e5ad92549303fb62872174247370779a0cce6","source":{"kind":"arxiv","id":"1603.06071","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.06071","created_at":"2026-05-18T00:39:47Z"},{"alias_kind":"arxiv_version","alias_value":"1603.06071v3","created_at":"2026-05-18T00:39:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.06071","created_at":"2026-05-18T00:39:47Z"},{"alias_kind":"pith_short_12","alias_value":"MSN5M7KN5BXS","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"MSN5M7KN5BXSQ4IC","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"MSN5M7KN","created_at":"2026-05-18T12:30:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:MSN5M7KN5BXSQ4IC5UMCCXS23E","target":"record","payload":{"canonical_record":{"source":{"id":"1603.06071","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-03-19T09:52:43Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"bcee541fff9a3ff670b1f009087a515af1ddd0c135f1fe30792ddcd7db6c5f6f","abstract_canon_sha256":"1a39ad9acdcc4c5ffc53e4c3da8c21e4cb1a37d93ffd8323a6f4118ffa38e0cd"},"schema_version":"1.0"},"canonical_sha256":"649bd67d4de86f287102ed18215e5ad92549303fb62872174247370779a0cce6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:47.881226Z","signature_b64":"hHDdrZXRsEEUA8Pdar5VAoZA3zmbMXSQRGPEpBf5hXzXoq53AzxCIyCCQKX0FVdVJW0/xUMS/1CUdnUpjLkMCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"649bd67d4de86f287102ed18215e5ad92549303fb62872174247370779a0cce6","last_reissued_at":"2026-05-18T00:39:47.880378Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:47.880378Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.06071","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":"2026-05-18T00:39:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bzS6cROTUC+6ePEWBFvtSg6JVZ6/EfZF0uEtHX8Bm6uxexsXvZUNYYG9T9y2xDSfteaf1AbGJeMmiK4xQ3LVAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T16:36:17.337775Z"},"content_sha256":"c0f75772a0ad8d88f7864cbbaaa55423cba092cb75a6b1053c925a7ff560e2a3","schema_version":"1.0","event_id":"sha256:c0f75772a0ad8d88f7864cbbaaa55423cba092cb75a6b1053c925a7ff560e2a3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:MSN5M7KN5BXSQ4IC5UMCCXS23E","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal control and zero-sum stochastic differential game problems of mean-field type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.PR","authors_text":"Boualem Djehiche, Said Hamad\\`ene","submitted_at":"2016-03-19T09:52:43Z","abstract_excerpt":"We establish existence of nearly-optimal controls, conditions for existence of an optimal control and a saddle-point for respectively a control problem and zero-sum differential game associated with payoff functionals of mean-field type, under dynamics driven by weak solutions of stochastic differential equations of mean-field type."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.06071","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":""},"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":"2026-05-18T00:39:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j58MRJCKqZ7KfB0HY9NnDi0Rolt0RkxdL2PFxx6lqR1XXq1H/JafQWVGXJyfy8teKapqEl58ul0qL0zMFrblBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T16:36:17.338483Z"},"content_sha256":"d2f452903c35992160c1070ddd84211e303b93065086ee46d1ca8efc4bb005c8","schema_version":"1.0","event_id":"sha256:d2f452903c35992160c1070ddd84211e303b93065086ee46d1ca8efc4bb005c8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MSN5M7KN5BXSQ4IC5UMCCXS23E/bundle.json","state_url":"https://pith.science/pith/MSN5M7KN5BXSQ4IC5UMCCXS23E/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MSN5M7KN5BXSQ4IC5UMCCXS23E/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":"2026-05-29T16:36:17Z","links":{"resolver":"https://pith.science/pith/MSN5M7KN5BXSQ4IC5UMCCXS23E","bundle":"https://pith.science/pith/MSN5M7KN5BXSQ4IC5UMCCXS23E/bundle.json","state":"https://pith.science/pith/MSN5M7KN5BXSQ4IC5UMCCXS23E/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MSN5M7KN5BXSQ4IC5UMCCXS23E/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:MSN5M7KN5BXSQ4IC5UMCCXS23E","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":"1a39ad9acdcc4c5ffc53e4c3da8c21e4cb1a37d93ffd8323a6f4118ffa38e0cd","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-03-19T09:52:43Z","title_canon_sha256":"bcee541fff9a3ff670b1f009087a515af1ddd0c135f1fe30792ddcd7db6c5f6f"},"schema_version":"1.0","source":{"id":"1603.06071","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.06071","created_at":"2026-05-18T00:39:47Z"},{"alias_kind":"arxiv_version","alias_value":"1603.06071v3","created_at":"2026-05-18T00:39:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.06071","created_at":"2026-05-18T00:39:47Z"},{"alias_kind":"pith_short_12","alias_value":"MSN5M7KN5BXS","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"MSN5M7KN5BXSQ4IC","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"MSN5M7KN","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:d2f452903c35992160c1070ddd84211e303b93065086ee46d1ca8efc4bb005c8","target":"graph","created_at":"2026-05-18T00:39:47Z","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 establish existence of nearly-optimal controls, conditions for existence of an optimal control and a saddle-point for respectively a control problem and zero-sum differential game associated with payoff functionals of mean-field type, under dynamics driven by weak solutions of stochastic differential equations of mean-field type.","authors_text":"Boualem Djehiche, Said Hamad\\`ene","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-03-19T09:52:43Z","title":"Optimal control and zero-sum stochastic differential game problems of mean-field type"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.06071","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:c0f75772a0ad8d88f7864cbbaaa55423cba092cb75a6b1053c925a7ff560e2a3","target":"record","created_at":"2026-05-18T00:39:47Z","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":"1a39ad9acdcc4c5ffc53e4c3da8c21e4cb1a37d93ffd8323a6f4118ffa38e0cd","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-03-19T09:52:43Z","title_canon_sha256":"bcee541fff9a3ff670b1f009087a515af1ddd0c135f1fe30792ddcd7db6c5f6f"},"schema_version":"1.0","source":{"id":"1603.06071","kind":"arxiv","version":3}},"canonical_sha256":"649bd67d4de86f287102ed18215e5ad92549303fb62872174247370779a0cce6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"649bd67d4de86f287102ed18215e5ad92549303fb62872174247370779a0cce6","first_computed_at":"2026-05-18T00:39:47.880378Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:39:47.880378Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hHDdrZXRsEEUA8Pdar5VAoZA3zmbMXSQRGPEpBf5hXzXoq53AzxCIyCCQKX0FVdVJW0/xUMS/1CUdnUpjLkMCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:39:47.881226Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.06071","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c0f75772a0ad8d88f7864cbbaaa55423cba092cb75a6b1053c925a7ff560e2a3","sha256:d2f452903c35992160c1070ddd84211e303b93065086ee46d1ca8efc4bb005c8"],"state_sha256":"500536d455f9188e0c9216c7bc40e0723a60437ecd09e77dc4ef988a809ac724"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AslcjqeGbnr09yhuS9nTGfyKjTmMlkOxP2CYSEX88REnBaWJgY2i1bvzjgqU75JNDLkLH7+0arVkb6oBRn0dCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T16:36:17.342154Z","bundle_sha256":"d6e0d6e80bd50da33970b25f915aadeb959c0560eca3853e5198f7c699933c8b"}}