{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:55XVHFKVKJZH4ET27TGW6H5N2J","short_pith_number":"pith:55XVHFKV","canonical_record":{"source":{"id":"1702.03855","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-02-13T16:23:03Z","cross_cats_sorted":[],"title_canon_sha256":"92729c4bf9116d880e419c7073995f285ed9b64f10a8523009eb9b3acbacedac","abstract_canon_sha256":"27a34c9e597ff9e15d93e795ce5edafee25831f410cbae2d7e2a938fbcfaa510"},"schema_version":"1.0"},"canonical_sha256":"ef6f53955552727e127afccd6f1fadd270686087d710d7c9eb8893f6d29890b1","source":{"kind":"arxiv","id":"1702.03855","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.03855","created_at":"2026-05-17T23:59:26Z"},{"alias_kind":"arxiv_version","alias_value":"1702.03855v2","created_at":"2026-05-17T23:59:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.03855","created_at":"2026-05-17T23:59:26Z"},{"alias_kind":"pith_short_12","alias_value":"55XVHFKVKJZH","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"55XVHFKVKJZH4ET2","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"55XVHFKV","created_at":"2026-05-18T12:31:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:55XVHFKVKJZH4ET27TGW6H5N2J","target":"record","payload":{"canonical_record":{"source":{"id":"1702.03855","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-02-13T16:23:03Z","cross_cats_sorted":[],"title_canon_sha256":"92729c4bf9116d880e419c7073995f285ed9b64f10a8523009eb9b3acbacedac","abstract_canon_sha256":"27a34c9e597ff9e15d93e795ce5edafee25831f410cbae2d7e2a938fbcfaa510"},"schema_version":"1.0"},"canonical_sha256":"ef6f53955552727e127afccd6f1fadd270686087d710d7c9eb8893f6d29890b1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:59:26.623033Z","signature_b64":"LeLVpQGs1EpvdmAz/VzhLyhQti3Cz9QzJ+cpzVxa9BUMIhM2cIGeqiC00t8N/V9cBvku9Zsr83Kvy5d6OviFAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ef6f53955552727e127afccd6f1fadd270686087d710d7c9eb8893f6d29890b1","last_reissued_at":"2026-05-17T23:59:26.622192Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:59:26.622192Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1702.03855","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:59:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SnRp8YU3lesYqIGhbxbJeN34oU1sqPTvMQd9vw7RYxW4voNIO6p4CTQKdnV7B+55svAViJzq1y/Le2TdA7KxBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T17:18:29.312349Z"},"content_sha256":"70a851b037609038e3459443d8d6547aaa5e04809f14178ec4d66d242ec19745","schema_version":"1.0","event_id":"sha256:70a851b037609038e3459443d8d6547aaa5e04809f14178ec4d66d242ec19745"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:55XVHFKVKJZH4ET27TGW6H5N2J","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A phase field approach to shape optimization in Navier--Stokes flow with integral state constraint","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Christian Kahle, Harald Garcke, Kei Fong Lam, Michael Hinze","submitted_at":"2017-02-13T16:23:03Z","abstract_excerpt":"We consider the shape optimization of an object in Navier--Stokes flow by employing a combined phase field and porous medium approach, along with additional perimeter regularization. By considering integral control and state constraints, we extend the results of earlier works concerning the existence of optimal shapes and the derivation of first order optimality conditions. The control variable is a phase field function that prescribes the shape and topology of the object, while the state variables are the velocity and the pressure of the fluid. In our analysis, we cover a multitude of constra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.03855","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:59:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"okrgihL75CZMrts+gRGV3mTyL7ET+bPAZoqKoFMX5b7ilL15L9K7Kg/RLyQjqTPeM+pOGodOn40GxCU4xM/MAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T17:18:29.312701Z"},"content_sha256":"5f228344e399dcf64452a47af616da75a36eb01b741671d90c831f3850bd5075","schema_version":"1.0","event_id":"sha256:5f228344e399dcf64452a47af616da75a36eb01b741671d90c831f3850bd5075"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/55XVHFKVKJZH4ET27TGW6H5N2J/bundle.json","state_url":"https://pith.science/pith/55XVHFKVKJZH4ET27TGW6H5N2J/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/55XVHFKVKJZH4ET27TGW6H5N2J/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-25T17:18:29Z","links":{"resolver":"https://pith.science/pith/55XVHFKVKJZH4ET27TGW6H5N2J","bundle":"https://pith.science/pith/55XVHFKVKJZH4ET27TGW6H5N2J/bundle.json","state":"https://pith.science/pith/55XVHFKVKJZH4ET27TGW6H5N2J/state.json","well_known_bundle":"https://pith.science/.well-known/pith/55XVHFKVKJZH4ET27TGW6H5N2J/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:55XVHFKVKJZH4ET27TGW6H5N2J","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":"27a34c9e597ff9e15d93e795ce5edafee25831f410cbae2d7e2a938fbcfaa510","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-02-13T16:23:03Z","title_canon_sha256":"92729c4bf9116d880e419c7073995f285ed9b64f10a8523009eb9b3acbacedac"},"schema_version":"1.0","source":{"id":"1702.03855","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.03855","created_at":"2026-05-17T23:59:26Z"},{"alias_kind":"arxiv_version","alias_value":"1702.03855v2","created_at":"2026-05-17T23:59:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.03855","created_at":"2026-05-17T23:59:26Z"},{"alias_kind":"pith_short_12","alias_value":"55XVHFKVKJZH","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"55XVHFKVKJZH4ET2","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"55XVHFKV","created_at":"2026-05-18T12:31:00Z"}],"graph_snapshots":[{"event_id":"sha256:5f228344e399dcf64452a47af616da75a36eb01b741671d90c831f3850bd5075","target":"graph","created_at":"2026-05-17T23:59:26Z","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 consider the shape optimization of an object in Navier--Stokes flow by employing a combined phase field and porous medium approach, along with additional perimeter regularization. By considering integral control and state constraints, we extend the results of earlier works concerning the existence of optimal shapes and the derivation of first order optimality conditions. The control variable is a phase field function that prescribes the shape and topology of the object, while the state variables are the velocity and the pressure of the fluid. In our analysis, we cover a multitude of constra","authors_text":"Christian Kahle, Harald Garcke, Kei Fong Lam, Michael Hinze","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-02-13T16:23:03Z","title":"A phase field approach to shape optimization in Navier--Stokes flow with integral state constraint"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.03855","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":"sha256:70a851b037609038e3459443d8d6547aaa5e04809f14178ec4d66d242ec19745","target":"record","created_at":"2026-05-17T23:59:26Z","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":"27a34c9e597ff9e15d93e795ce5edafee25831f410cbae2d7e2a938fbcfaa510","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-02-13T16:23:03Z","title_canon_sha256":"92729c4bf9116d880e419c7073995f285ed9b64f10a8523009eb9b3acbacedac"},"schema_version":"1.0","source":{"id":"1702.03855","kind":"arxiv","version":2}},"canonical_sha256":"ef6f53955552727e127afccd6f1fadd270686087d710d7c9eb8893f6d29890b1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ef6f53955552727e127afccd6f1fadd270686087d710d7c9eb8893f6d29890b1","first_computed_at":"2026-05-17T23:59:26.622192Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:59:26.622192Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LeLVpQGs1EpvdmAz/VzhLyhQti3Cz9QzJ+cpzVxa9BUMIhM2cIGeqiC00t8N/V9cBvku9Zsr83Kvy5d6OviFAA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:59:26.623033Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.03855","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:70a851b037609038e3459443d8d6547aaa5e04809f14178ec4d66d242ec19745","sha256:5f228344e399dcf64452a47af616da75a36eb01b741671d90c831f3850bd5075"],"state_sha256":"bd2d376da3eab36a32096e7d88c44d810c2162cfc489b1ed9f86b4780f4b17d1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZgbCCVyG4fbt4q9CXQibmSFoW5+xyGIkHa0EbQdXCY1E6jQXTQCTCSily9+u4OpGjLnB6OCeQRimJBpHF36+Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T17:18:29.314642Z","bundle_sha256":"d4777894f3f429d07770f86d1962c065f687954858ac7e299b59463046f05685"}}