{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:TXHJY6QSSBYRQ4JH4ZJ3A4Y5W4","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":"e39fede121f70becbd3991130106b6537749edd18cf64333d18f7e115309f6cc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-05-03T13:45:22Z","title_canon_sha256":"9438a43979b27fe78e54edd65470e08f2a5fdce7ca8a85aba8531719d4642311"},"schema_version":"1.0","source":{"id":"1705.01427","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.01427","created_at":"2026-05-18T00:45:05Z"},{"alias_kind":"arxiv_version","alias_value":"1705.01427v1","created_at":"2026-05-18T00:45:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.01427","created_at":"2026-05-18T00:45:05Z"},{"alias_kind":"pith_short_12","alias_value":"TXHJY6QSSBYR","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"TXHJY6QSSBYRQ4JH","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"TXHJY6QS","created_at":"2026-05-18T12:31:46Z"}],"graph_snapshots":[{"event_id":"sha256:17ba52ed9233fe78d40eb357475e9ebc800f7cda2dbabdc787738a8928652a83","target":"graph","created_at":"2026-05-18T00:45:05Z","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 article, we consider the Tikhonov regularization of an optimal control problem of semilinear partial differential equations with box constraints on the control. We derive a-priori regularization error estimates for the control under suitable conditions. These conditions comprise second-order sufficient optimality conditions as well as regularity conditions on the control, which consists of a source condition and a condition on the active sets. In addition, we show that these conditions are necessary for convergence rates under certain conditions. We also consider sparse optimal control","authors_text":"Daniel Wachsmuth, Frank P\\\"orner","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-05-03T13:45:22Z","title":"Tikhonov regularization of optimal control problems governed by semi-linear partial differential equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.01427","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":"sha256:3a53f135b0d88891297a4ca87e3ccccfe39b783c1458231cec38854de5201955","target":"record","created_at":"2026-05-18T00:45:05Z","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":"e39fede121f70becbd3991130106b6537749edd18cf64333d18f7e115309f6cc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-05-03T13:45:22Z","title_canon_sha256":"9438a43979b27fe78e54edd65470e08f2a5fdce7ca8a85aba8531719d4642311"},"schema_version":"1.0","source":{"id":"1705.01427","kind":"arxiv","version":1}},"canonical_sha256":"9dce9c7a129071187127e653b0731db70372ac3bf14951ee2fd8c88fe9423dfa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9dce9c7a129071187127e653b0731db70372ac3bf14951ee2fd8c88fe9423dfa","first_computed_at":"2026-05-18T00:45:05.200407Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:05.200407Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"z4D03UlGh4K+pqgUiQIAHk5Asg6b7cdj9VotRn9RLid1XaR0Ow8ySgvQtqXINeUf4+4Cuwee/WBO95mo0Ws3Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:05.200899Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.01427","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3a53f135b0d88891297a4ca87e3ccccfe39b783c1458231cec38854de5201955","sha256:17ba52ed9233fe78d40eb357475e9ebc800f7cda2dbabdc787738a8928652a83"],"state_sha256":"80a59f74b3290b68b493d20bb64f2c3c6e97e9ef4497c202f9c7d7f53e7d08db"}