{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:E2ACZF2EMAXNQPEMNY5EXHQNHA","short_pith_number":"pith:E2ACZF2E","canonical_record":{"source":{"id":"1704.08899","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-04-28T12:23:37Z","cross_cats_sorted":[],"title_canon_sha256":"305023ac9dbe12284f02457a189a433263169801b030058a3ee40c4a0b25c63c","abstract_canon_sha256":"a79f0f72672fd72188c42c08b2f0c064b8870b78ea56f18b17c049bf0dea2379"},"schema_version":"1.0"},"canonical_sha256":"26802c9744602ed83c8c6e3a4b9e0d380855d8f23a0f4600eff819bd153d9945","source":{"kind":"arxiv","id":"1704.08899","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.08899","created_at":"2026-05-18T00:01:15Z"},{"alias_kind":"arxiv_version","alias_value":"1704.08899v4","created_at":"2026-05-18T00:01:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.08899","created_at":"2026-05-18T00:01:15Z"},{"alias_kind":"pith_short_12","alias_value":"E2ACZF2EMAXN","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"E2ACZF2EMAXNQPEM","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"E2ACZF2E","created_at":"2026-05-18T12:31:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:E2ACZF2EMAXNQPEMNY5EXHQNHA","target":"record","payload":{"canonical_record":{"source":{"id":"1704.08899","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-04-28T12:23:37Z","cross_cats_sorted":[],"title_canon_sha256":"305023ac9dbe12284f02457a189a433263169801b030058a3ee40c4a0b25c63c","abstract_canon_sha256":"a79f0f72672fd72188c42c08b2f0c064b8870b78ea56f18b17c049bf0dea2379"},"schema_version":"1.0"},"canonical_sha256":"26802c9744602ed83c8c6e3a4b9e0d380855d8f23a0f4600eff819bd153d9945","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:15.433949Z","signature_b64":"kHFf44/JAwsHUQpoDRmAXzApn0usNKkUshW9qhyAew9nGjkzZHwkIQ4hiCQPP+K3D0rlFAdmPK8wGQrBNZ08Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"26802c9744602ed83c8c6e3a4b9e0d380855d8f23a0f4600eff819bd153d9945","last_reissued_at":"2026-05-18T00:01:15.433570Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:15.433570Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.08899","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:01:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IDbs4HihLsGF4k4A8kgdybpdpWYVThe5vBwrrn1RRN5WgkBDkMz9boWQRNjX4FhJDJOURvLtWhtcpi3HwSftBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T04:09:45.400911Z"},"content_sha256":"747670485ec33a781526bb8e2f0a4f79f19c0eac098679317257942cb48c1ef6","schema_version":"1.0","event_id":"sha256:747670485ec33a781526bb8e2f0a4f79f19c0eac098679317257942cb48c1ef6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:E2ACZF2EMAXNQPEMNY5EXHQNHA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Hida-Malliavin white noise calculus approach to optimal control","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Bernt {\\O}ksendal, Nacira Agram","submitted_at":"2017-04-28T12:23:37Z","abstract_excerpt":"The classical maximum principle for optimal stochastic control states that if a control $\\hat{u}$ is optimal, then the corresponding Hamiltonian has a maximum at $u=\\hat{u}$. The first proofs for this result assumed that the control did not enter the diffusion coefficient. Moreover, it was assumed that there were no jumps in the system. Subsequently it was discovered by Shige Peng (still assuming no jumps) that one could also allow the diffusion coefficient to depend on the control, provided that the corresponding adjoint backward stochastic differential equation (BSDE) for the first order der"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.08899","kind":"arxiv","version":4},"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":"2026-05-18T00:01:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9eZ/KZanKrypF7QufX2jydiSG1Tys2cg6XQv9Tzw4Iq8buyArnfQOeKqnOu8TIbrfemED3Yyo8y1/JO1wgVsBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T04:09:45.401653Z"},"content_sha256":"51b478e803826d7f0674e0909c6c1de41f27f79db862cb9d3559f94d3aaa2b96","schema_version":"1.0","event_id":"sha256:51b478e803826d7f0674e0909c6c1de41f27f79db862cb9d3559f94d3aaa2b96"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/E2ACZF2EMAXNQPEMNY5EXHQNHA/bundle.json","state_url":"https://pith.science/pith/E2ACZF2EMAXNQPEMNY5EXHQNHA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/E2ACZF2EMAXNQPEMNY5EXHQNHA/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":"2026-06-09T04:09:45Z","links":{"resolver":"https://pith.science/pith/E2ACZF2EMAXNQPEMNY5EXHQNHA","bundle":"https://pith.science/pith/E2ACZF2EMAXNQPEMNY5EXHQNHA/bundle.json","state":"https://pith.science/pith/E2ACZF2EMAXNQPEMNY5EXHQNHA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/E2ACZF2EMAXNQPEMNY5EXHQNHA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:E2ACZF2EMAXNQPEMNY5EXHQNHA","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":"a79f0f72672fd72188c42c08b2f0c064b8870b78ea56f18b17c049bf0dea2379","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-04-28T12:23:37Z","title_canon_sha256":"305023ac9dbe12284f02457a189a433263169801b030058a3ee40c4a0b25c63c"},"schema_version":"1.0","source":{"id":"1704.08899","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.08899","created_at":"2026-05-18T00:01:15Z"},{"alias_kind":"arxiv_version","alias_value":"1704.08899v4","created_at":"2026-05-18T00:01:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.08899","created_at":"2026-05-18T00:01:15Z"},{"alias_kind":"pith_short_12","alias_value":"E2ACZF2EMAXN","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"E2ACZF2EMAXNQPEM","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"E2ACZF2E","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:51b478e803826d7f0674e0909c6c1de41f27f79db862cb9d3559f94d3aaa2b96","target":"graph","created_at":"2026-05-18T00:01:15Z","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":"The classical maximum principle for optimal stochastic control states that if a control $\\hat{u}$ is optimal, then the corresponding Hamiltonian has a maximum at $u=\\hat{u}$. The first proofs for this result assumed that the control did not enter the diffusion coefficient. Moreover, it was assumed that there were no jumps in the system. Subsequently it was discovered by Shige Peng (still assuming no jumps) that one could also allow the diffusion coefficient to depend on the control, provided that the corresponding adjoint backward stochastic differential equation (BSDE) for the first order der","authors_text":"Bernt {\\O}ksendal, Nacira Agram","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-04-28T12:23:37Z","title":"A Hida-Malliavin white noise calculus approach to optimal control"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.08899","kind":"arxiv","version":4},"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":"sha256:747670485ec33a781526bb8e2f0a4f79f19c0eac098679317257942cb48c1ef6","target":"record","created_at":"2026-05-18T00:01:15Z","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":"a79f0f72672fd72188c42c08b2f0c064b8870b78ea56f18b17c049bf0dea2379","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-04-28T12:23:37Z","title_canon_sha256":"305023ac9dbe12284f02457a189a433263169801b030058a3ee40c4a0b25c63c"},"schema_version":"1.0","source":{"id":"1704.08899","kind":"arxiv","version":4}},"canonical_sha256":"26802c9744602ed83c8c6e3a4b9e0d380855d8f23a0f4600eff819bd153d9945","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"26802c9744602ed83c8c6e3a4b9e0d380855d8f23a0f4600eff819bd153d9945","first_computed_at":"2026-05-18T00:01:15.433570Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:15.433570Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kHFf44/JAwsHUQpoDRmAXzApn0usNKkUshW9qhyAew9nGjkzZHwkIQ4hiCQPP+K3D0rlFAdmPK8wGQrBNZ08Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:15.433949Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.08899","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:747670485ec33a781526bb8e2f0a4f79f19c0eac098679317257942cb48c1ef6","sha256:51b478e803826d7f0674e0909c6c1de41f27f79db862cb9d3559f94d3aaa2b96"],"state_sha256":"6519adb0d2c8b6d2e646de67ddd728e3faadb002a1db75f31d19b2361b3c0a31"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AbCpx3uTAUWDogeraAW14/XR0FONh44E7miH1WgE3k7PGPNrbZqWuPHz1T+WBDFHKtS0WDv5fHNZbZSm+zQGAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T04:09:45.405959Z","bundle_sha256":"efcfc8ed31c6ffa69ebebdc86e64b546bc700683b62a6c4e77c19767c9e89d06"}}