{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:ZCFE76EJ2U64BEKOGGGUUJGGFK","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":"a8fd66cebb65ff5362b1404ce0013ba556d5c189490f8b3284c1c3d7b2f31777","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-07-21T12:35:23Z","title_canon_sha256":"3c762c94a14d1f1b64789dfddaf56e43911dafba5e1f522a59a4e5fcec94102e"},"schema_version":"1.0","source":{"id":"1407.5470","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.5470","created_at":"2026-05-18T02:47:13Z"},{"alias_kind":"arxiv_version","alias_value":"1407.5470v1","created_at":"2026-05-18T02:47:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.5470","created_at":"2026-05-18T02:47:13Z"},{"alias_kind":"pith_short_12","alias_value":"ZCFE76EJ2U64","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZCFE76EJ2U64BEKO","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZCFE76EJ","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:fcea2940b5a09e635f79a6a289bf7b403a4a0f7b576272706464ab0755fa29d2","target":"graph","created_at":"2026-05-18T02:47:13Z","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":"We apply a phase field approach for a general shape optimization problem of a stationary Navier-Stokes flow. To be precise we add a multiple of the Ginzburg--Landau energy as a regularization to the objective functional and relax the non-permeability of the medium outside the fluid region. The resulting diffuse interface problem can be shown to be well-posed and optimality conditions are derived. We state suitable assumptions on the problem in order to derive a sharp interface limit for the minimizers and the optimality conditions. Additionally, we can derive a necessary optimality system for ","authors_text":"Claudia Hecht, Harald Garcke","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-07-21T12:35:23Z","title":"Applying a phase field approach for shape optimization of a stationary Navier-Stokes flow"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.5470","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:cf79a507200dc6806ed6c71cbd87661892125f9f46ccb6696c23cc9094a99747","target":"record","created_at":"2026-05-18T02:47:13Z","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":"a8fd66cebb65ff5362b1404ce0013ba556d5c189490f8b3284c1c3d7b2f31777","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-07-21T12:35:23Z","title_canon_sha256":"3c762c94a14d1f1b64789dfddaf56e43911dafba5e1f522a59a4e5fcec94102e"},"schema_version":"1.0","source":{"id":"1407.5470","kind":"arxiv","version":1}},"canonical_sha256":"c88a4ff889d53dc0914e318d4a24c62abb253ce25012edcac645715bb656e459","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c88a4ff889d53dc0914e318d4a24c62abb253ce25012edcac645715bb656e459","first_computed_at":"2026-05-18T02:47:13.948951Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:47:13.948951Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"i47clSzgYbKSpmMUKw1E/wCvoqntsHBaTbW5gX6M3q59JJ42GOpNMCpLu6bufFBRSnKn2JLv/G5PxGfy1G4vBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:47:13.949509Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.5470","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cf79a507200dc6806ed6c71cbd87661892125f9f46ccb6696c23cc9094a99747","sha256:fcea2940b5a09e635f79a6a289bf7b403a4a0f7b576272706464ab0755fa29d2"],"state_sha256":"3eac983b3621c3902bfd68499cce6b6187481e0532d1469c2b290c2cc481861e"}