{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:ZKPILXG4FHZ4TA557JDKV23APD","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":"8db13f103ba159d7cbc1034beca8ec094569b6931b8829895172f1156d15d649","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-05-31T11:01:13Z","title_canon_sha256":"b6d639d4407038cfa7ccfe940df06d285519e4bc94e4a6c81d13723359d3e643"},"schema_version":"1.0","source":{"id":"1705.11031","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.11031","created_at":"2026-05-18T00:43:19Z"},{"alias_kind":"arxiv_version","alias_value":"1705.11031v1","created_at":"2026-05-18T00:43:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.11031","created_at":"2026-05-18T00:43:19Z"},{"alias_kind":"pith_short_12","alias_value":"ZKPILXG4FHZ4","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZKPILXG4FHZ4TA55","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZKPILXG4","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:d991325a65934b3352ad648c2afa97be47b5cca9b1fef7ccfb12c5d5f3db8d32","target":"graph","created_at":"2026-05-18T00:43:19Z","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":"This paper is concerned with the optimal control of hysteresis-reaction-diffusion systems. We study a control problem with two sorts of controls, namely distributed control functions, or controls which act on a part of the boundary of the domain. The state equation is given by a reaction-diffusion system with the additional challenge that the reaction term includes a scalar stop operator. We choose a variational inequality to represent the hysteresis. In this paper, we prove first order necessary optimality conditions. In particular, under certain regularity assumptions, we derive results abou","authors_text":"Christian M\\\"unch","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-05-31T11:01:13Z","title":"Optimal control of reaction-diffusion systems with hysteresis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.11031","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":"sha256:364633e4ddd3c4ede6388c43c0a7ea2699f55bc58855d23683839165155f9fbd","target":"record","created_at":"2026-05-18T00:43:19Z","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":"8db13f103ba159d7cbc1034beca8ec094569b6931b8829895172f1156d15d649","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-05-31T11:01:13Z","title_canon_sha256":"b6d639d4407038cfa7ccfe940df06d285519e4bc94e4a6c81d13723359d3e643"},"schema_version":"1.0","source":{"id":"1705.11031","kind":"arxiv","version":1}},"canonical_sha256":"ca9e85dcdc29f3c983bdfa46aaeb6078cb54ef3fcea11f561d32e9325f584ad4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ca9e85dcdc29f3c983bdfa46aaeb6078cb54ef3fcea11f561d32e9325f584ad4","first_computed_at":"2026-05-18T00:43:19.484176Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:19.484176Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GYeaDTK94jFadhOIUQPwDAc0vCVj4QqNVvY14ZL3lHMcm2xra9HDkw+8HUsSxMGlIKILBbVUqcAY4zYqR3qhDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:19.484822Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.11031","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:364633e4ddd3c4ede6388c43c0a7ea2699f55bc58855d23683839165155f9fbd","sha256:d991325a65934b3352ad648c2afa97be47b5cca9b1fef7ccfb12c5d5f3db8d32"],"state_sha256":"18794e6dba9d3749756f6a732f8cf845280dddcee7e0c9582b0cb871ece6fcf7"}