{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:TDNUVJLNCOWAZRBA4JVIALR5US","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":"cf1ae92f37c490aa11dc5ea1f707db322a0dece9ae9afeca58faed6a5dfe4b36","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-09-27T17:14:34Z","title_canon_sha256":"54e576223582e626e1f06b5860176f036fbc8963058a000722c48e8bd5914531"},"schema_version":"1.0","source":{"id":"1809.10645","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.10645","created_at":"2026-05-18T00:04:12Z"},{"alias_kind":"arxiv_version","alias_value":"1809.10645v2","created_at":"2026-05-18T00:04:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.10645","created_at":"2026-05-18T00:04:12Z"},{"alias_kind":"pith_short_12","alias_value":"TDNUVJLNCOWA","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"TDNUVJLNCOWAZRBA","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"TDNUVJLN","created_at":"2026-05-18T12:32:53Z"}],"graph_snapshots":[{"event_id":"sha256:9db7bc444a88ee551ffb8eda8ce0738f31a4bce9637d9f0a342c491afe74735a","target":"graph","created_at":"2026-05-18T00:04:12Z","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 note, we consider the existence and uniqueness of the solution of a time-dependent optimal control problem constrained by a partial differential equation with uncertain inputs. Relying on the Lions' Lemma for deterministic problems, we furthermore characterize the optimal control of the stochastic problem.","authors_text":"Akwum Onwunta, Martin Stoll, Peter Benner","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-09-27T17:14:34Z","title":"On the existence and uniqueness of the solution of a parabolic optimal control problem with uncertain inputs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.10645","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":"sha256:21d06f7d6024a0620aaa74054dc3170503aab6633be4e420e2604720c2cb7016","target":"record","created_at":"2026-05-18T00:04:12Z","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":"cf1ae92f37c490aa11dc5ea1f707db322a0dece9ae9afeca58faed6a5dfe4b36","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-09-27T17:14:34Z","title_canon_sha256":"54e576223582e626e1f06b5860176f036fbc8963058a000722c48e8bd5914531"},"schema_version":"1.0","source":{"id":"1809.10645","kind":"arxiv","version":2}},"canonical_sha256":"98db4aa56d13ac0cc420e26a802e3da4bc03e69efc60ec060d3d28b97419d8cb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"98db4aa56d13ac0cc420e26a802e3da4bc03e69efc60ec060d3d28b97419d8cb","first_computed_at":"2026-05-18T00:04:12.393757Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:12.393757Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mY0J4BfoR5yPYKF/OY/plmyDIh7ySJKB2Ndux8hFUWI4gaUu5KHtt0Jgho/A///AcGPkFSYMP/QhxK2ZqVjwCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:12.394556Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.10645","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:21d06f7d6024a0620aaa74054dc3170503aab6633be4e420e2604720c2cb7016","sha256:9db7bc444a88ee551ffb8eda8ce0738f31a4bce9637d9f0a342c491afe74735a"],"state_sha256":"f11ad1132f0a07dcd69bd929dd5c128a382d26ba76ba6c186c634d09bd2c7432"}