{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:R6EBUNO7N2Z7I5TLHEDSHCATQZ","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":"45d6228f4fc5b3ba58692eb6cd0fa0697f8fc3e4d17fbe2fecf52ece449fe362","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-01-08T14:54:18Z","title_canon_sha256":"8660c95049061c1442bfb070425a074bfda0052f032146281db59478be805789"},"schema_version":"1.0","source":{"id":"2501.04548","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.04548","created_at":"2026-05-20T01:04:51Z"},{"alias_kind":"arxiv_version","alias_value":"2501.04548v2","created_at":"2026-05-20T01:04:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.04548","created_at":"2026-05-20T01:04:51Z"},{"alias_kind":"pith_short_12","alias_value":"R6EBUNO7N2Z7","created_at":"2026-05-20T01:04:51Z"},{"alias_kind":"pith_short_16","alias_value":"R6EBUNO7N2Z7I5TL","created_at":"2026-05-20T01:04:51Z"},{"alias_kind":"pith_short_8","alias_value":"R6EBUNO7","created_at":"2026-05-20T01:04:51Z"}],"graph_snapshots":[{"event_id":"sha256:8eca6375516486e9bd2f3f4ea205dc8aec8f4c6a3e866c0ae0bfb47579371c05","target":"graph","created_at":"2026-05-20T01:04:51Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2501.04548/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this work we study an optimal control problem subject to the instationary Navier-Stokes equations, where the control enters via an inhomogeneous Neumann/Do-Nothing boundary condition. Despite the Navier-Stokes equations with these boundary conditions not being well-posed for large times and/or data, we obtain wellposedness of the optimal control problem by choosing a proper tracking type term. In order to discuss the regularity of the optimal control, state and adjoint state, we present new results on $L^2(I;H^2(\\Omega))$ regularity of solutions to a Stokes problem with mixed inhomogeneous ","authors_text":"Boris Vexler, Jakob Wagner","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-01-08T14:54:18Z","title":"Optimal Control of the Navier-Stokes equations via Pressure Boundary Conditions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.04548","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:da0e17349a63cbd09e4d5bd17d68b311d22645e4bdefe66006a80f5c4247f76f","target":"record","created_at":"2026-05-20T01:04:51Z","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":"45d6228f4fc5b3ba58692eb6cd0fa0697f8fc3e4d17fbe2fecf52ece449fe362","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-01-08T14:54:18Z","title_canon_sha256":"8660c95049061c1442bfb070425a074bfda0052f032146281db59478be805789"},"schema_version":"1.0","source":{"id":"2501.04548","kind":"arxiv","version":2}},"canonical_sha256":"8f881a35df6eb3f4766b39072388138674f396712f203e93099c52b190bd89fb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8f881a35df6eb3f4766b39072388138674f396712f203e93099c52b190bd89fb","first_computed_at":"2026-05-20T01:04:51.616988Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T01:04:51.616988Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"D1Yz/TtZ/irOtrOEFp6i4h5sFI3/DFe8PuahbmeiP9fDZHL41bYMP0tEdqhd7rcVXTf4biAYAg/tqBpyZmXGAw==","signature_status":"signed_v1","signed_at":"2026-05-20T01:04:51.617632Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.04548","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:da0e17349a63cbd09e4d5bd17d68b311d22645e4bdefe66006a80f5c4247f76f","sha256:8eca6375516486e9bd2f3f4ea205dc8aec8f4c6a3e866c0ae0bfb47579371c05"],"state_sha256":"32d438675bdf43cbb18e39692715dd2a1f926cd96860cf82a917c738585dc7c1"}