{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:LCPWPNF7C2DMGAJPPSC2J2XGHY","short_pith_number":"pith:LCPWPNF7","canonical_record":{"source":{"id":"1805.07957","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-05-21T09:22:04Z","cross_cats_sorted":[],"title_canon_sha256":"770b0caef5c689497595623abe1c51afe5eab08545676af58917a46f909b333c","abstract_canon_sha256":"bb187ff848e4a0cbf4aac4331be70dcc71eda561ba2f0c5d89ffb0ce774874ba"},"schema_version":"1.0"},"canonical_sha256":"589f67b4bf1686c3012f7c85a4eae63e1520e9a45d2e9f2fb3f1c669389fe2f7","source":{"kind":"arxiv","id":"1805.07957","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.07957","created_at":"2026-05-17T23:59:43Z"},{"alias_kind":"arxiv_version","alias_value":"1805.07957v2","created_at":"2026-05-17T23:59:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.07957","created_at":"2026-05-17T23:59:43Z"},{"alias_kind":"pith_short_12","alias_value":"LCPWPNF7C2DM","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"LCPWPNF7C2DMGAJP","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"LCPWPNF7","created_at":"2026-05-18T12:32:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:LCPWPNF7C2DMGAJPPSC2J2XGHY","target":"record","payload":{"canonical_record":{"source":{"id":"1805.07957","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-05-21T09:22:04Z","cross_cats_sorted":[],"title_canon_sha256":"770b0caef5c689497595623abe1c51afe5eab08545676af58917a46f909b333c","abstract_canon_sha256":"bb187ff848e4a0cbf4aac4331be70dcc71eda561ba2f0c5d89ffb0ce774874ba"},"schema_version":"1.0"},"canonical_sha256":"589f67b4bf1686c3012f7c85a4eae63e1520e9a45d2e9f2fb3f1c669389fe2f7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:59:43.657220Z","signature_b64":"HGFR3ODddzl61LJcnVTdge2XDnuVnczHSLOKobEbFeFYMnNURuLB9RqXilLx7oGrQJj4GIgljnBE16jhqtaUDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"589f67b4bf1686c3012f7c85a4eae63e1520e9a45d2e9f2fb3f1c669389fe2f7","last_reissued_at":"2026-05-17T23:59:43.656638Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:59:43.656638Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.07957","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":"2026-05-17T23:59:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JYjFB+uDrv8KP4xj8zI7ABxJNjjAC+ShxQe4NmFbSa4MiaIrXjX1g/yMlQ9s4FZ4jHDnNvgI7ukOXHFgQt67Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T21:08:51.964454Z"},"content_sha256":"d26a649e5cb85ca3ae9869006e2e8a5d9099878233e1761253d285041c9d8df9","schema_version":"1.0","event_id":"sha256:d26a649e5cb85ca3ae9869006e2e8a5d9099878233e1761253d285041c9d8df9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:LCPWPNF7C2DMGAJPPSC2J2XGHY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stochastic maximum principle for equations with delay: the non-convex case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Federica Masiero, Giuseppina Guatteri","submitted_at":"2018-05-21T09:22:04Z","abstract_excerpt":"In this paper we develop necessary conditions for optimality, in the form of the stochastic Pontryagin maximum principle, for controlled equations with pointwise delay in the state and with control dependent noise, in the general case of controls $u \\in U$ with $U$ not necessarily convex. The maximum principle is formulated by means of first and second order adjoint BSDEs. We also outline how to deal with control problems with pointwise delay both in the state and in the control."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.07957","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":""},"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":"2026-05-17T23:59:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Wlz+FvuPHjus2aS9eODCSAhewt0o+Mh+KS4d88Xm8NHfmcHMu2VwCbAWrRHDZl6PbFJDSMjFMeEAwjPUAl5WCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T21:08:51.964801Z"},"content_sha256":"3ec351809c4e146a30bc0883a8b96e138ae949bf21f8b8ead702888f05c244be","schema_version":"1.0","event_id":"sha256:3ec351809c4e146a30bc0883a8b96e138ae949bf21f8b8ead702888f05c244be"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LCPWPNF7C2DMGAJPPSC2J2XGHY/bundle.json","state_url":"https://pith.science/pith/LCPWPNF7C2DMGAJPPSC2J2XGHY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LCPWPNF7C2DMGAJPPSC2J2XGHY/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":"2026-05-29T21:08:51Z","links":{"resolver":"https://pith.science/pith/LCPWPNF7C2DMGAJPPSC2J2XGHY","bundle":"https://pith.science/pith/LCPWPNF7C2DMGAJPPSC2J2XGHY/bundle.json","state":"https://pith.science/pith/LCPWPNF7C2DMGAJPPSC2J2XGHY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LCPWPNF7C2DMGAJPPSC2J2XGHY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:LCPWPNF7C2DMGAJPPSC2J2XGHY","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":"bb187ff848e4a0cbf4aac4331be70dcc71eda561ba2f0c5d89ffb0ce774874ba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-05-21T09:22:04Z","title_canon_sha256":"770b0caef5c689497595623abe1c51afe5eab08545676af58917a46f909b333c"},"schema_version":"1.0","source":{"id":"1805.07957","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.07957","created_at":"2026-05-17T23:59:43Z"},{"alias_kind":"arxiv_version","alias_value":"1805.07957v2","created_at":"2026-05-17T23:59:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.07957","created_at":"2026-05-17T23:59:43Z"},{"alias_kind":"pith_short_12","alias_value":"LCPWPNF7C2DM","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"LCPWPNF7C2DMGAJP","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"LCPWPNF7","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:3ec351809c4e146a30bc0883a8b96e138ae949bf21f8b8ead702888f05c244be","target":"graph","created_at":"2026-05-17T23:59:43Z","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":"In this paper we develop necessary conditions for optimality, in the form of the stochastic Pontryagin maximum principle, for controlled equations with pointwise delay in the state and with control dependent noise, in the general case of controls $u \\in U$ with $U$ not necessarily convex. The maximum principle is formulated by means of first and second order adjoint BSDEs. We also outline how to deal with control problems with pointwise delay both in the state and in the control.","authors_text":"Federica Masiero, Giuseppina Guatteri","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-05-21T09:22:04Z","title":"Stochastic maximum principle for equations with delay: the non-convex case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.07957","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:d26a649e5cb85ca3ae9869006e2e8a5d9099878233e1761253d285041c9d8df9","target":"record","created_at":"2026-05-17T23:59:43Z","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":"bb187ff848e4a0cbf4aac4331be70dcc71eda561ba2f0c5d89ffb0ce774874ba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-05-21T09:22:04Z","title_canon_sha256":"770b0caef5c689497595623abe1c51afe5eab08545676af58917a46f909b333c"},"schema_version":"1.0","source":{"id":"1805.07957","kind":"arxiv","version":2}},"canonical_sha256":"589f67b4bf1686c3012f7c85a4eae63e1520e9a45d2e9f2fb3f1c669389fe2f7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"589f67b4bf1686c3012f7c85a4eae63e1520e9a45d2e9f2fb3f1c669389fe2f7","first_computed_at":"2026-05-17T23:59:43.656638Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:59:43.656638Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HGFR3ODddzl61LJcnVTdge2XDnuVnczHSLOKobEbFeFYMnNURuLB9RqXilLx7oGrQJj4GIgljnBE16jhqtaUDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:59:43.657220Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.07957","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d26a649e5cb85ca3ae9869006e2e8a5d9099878233e1761253d285041c9d8df9","sha256:3ec351809c4e146a30bc0883a8b96e138ae949bf21f8b8ead702888f05c244be"],"state_sha256":"15bb6e6b1055059025a7411655266d598b22175614ead1593687c77c8691a396"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jNLnDoKKU69i5lzY6n+O8mUeqrw0ZUMgNeVHV83pM8Z5c5tAaOrQNyM3WgVGsSTjsHGaFbAePsV8Drp1KId9Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T21:08:51.967163Z","bundle_sha256":"ad30e1bb9329c650502192e7778a4a65098bf4dc1449d6b17072deef1ae3f5cd"}}