{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:LHSVEWGUTIH7OVSXZVS2G3C2VL","short_pith_number":"pith:LHSVEWGU","canonical_record":{"source":{"id":"1203.1493","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-03-07T15:13:08Z","cross_cats_sorted":[],"title_canon_sha256":"5585054af0a24b6c42d10e7a37c578ad9ae2ded8df7e6972bee22ccb9f4c8ab0","abstract_canon_sha256":"4da2e4f0ebc554905275155317e8318e8009366b9e4d22eb7f4c2aeeb2d36649"},"schema_version":"1.0"},"canonical_sha256":"59e55258d49a0ff75657cd65a36c5aaaf06afac6031028694efd04fcf8a5f2cc","source":{"kind":"arxiv","id":"1203.1493","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.1493","created_at":"2026-05-18T02:52:04Z"},{"alias_kind":"arxiv_version","alias_value":"1203.1493v2","created_at":"2026-05-18T02:52:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.1493","created_at":"2026-05-18T02:52:04Z"},{"alias_kind":"pith_short_12","alias_value":"LHSVEWGUTIH7","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"LHSVEWGUTIH7OVSX","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"LHSVEWGU","created_at":"2026-05-18T12:27:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:LHSVEWGUTIH7OVSXZVS2G3C2VL","target":"record","payload":{"canonical_record":{"source":{"id":"1203.1493","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-03-07T15:13:08Z","cross_cats_sorted":[],"title_canon_sha256":"5585054af0a24b6c42d10e7a37c578ad9ae2ded8df7e6972bee22ccb9f4c8ab0","abstract_canon_sha256":"4da2e4f0ebc554905275155317e8318e8009366b9e4d22eb7f4c2aeeb2d36649"},"schema_version":"1.0"},"canonical_sha256":"59e55258d49a0ff75657cd65a36c5aaaf06afac6031028694efd04fcf8a5f2cc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:52:04.405481Z","signature_b64":"ZrizyH6/aTe/rWDqteIvtXqaQk2ZBjZ19ze2eWKyIphGiBhSjWDyCdqJrXc0nHCFD99wZsGT4rUndEUQ+yj0BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"59e55258d49a0ff75657cd65a36c5aaaf06afac6031028694efd04fcf8a5f2cc","last_reissued_at":"2026-05-18T02:52:04.404986Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:52:04.404986Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1203.1493","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":"2026-05-18T02:52:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"63med/g5pbc8cdu8y91Xeic+f4yeChUCyVeencNBm4eY6nyqpqGdYdtT7jTHzlUWLaojwLDE1C9B8NGff2LWBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T22:14:39.482744Z"},"content_sha256":"14d667e7716557004a5b35fce2fd3ea406344aa03ff830a2bde39e5c11ad13c8","schema_version":"1.0","event_id":"sha256:14d667e7716557004a5b35fce2fd3ea406344aa03ff830a2bde39e5c11ad13c8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:LHSVEWGUTIH7OVSXZVS2G3C2VL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Riemannian View on Shape Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Volker Schulz","submitted_at":"2012-03-07T15:13:08Z","abstract_excerpt":"Shape optimization based on the shape calculus is numerically mostly performed by means of steepest descent methods. This paper provides a novel framework to analyze shape-Newton optimization methods by exploiting a Riemannian perspective. A Riemannian shape Hessian is defined yielding often sought properties like symmetry and quadratic convergence for Newton optimization methods."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.1493","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":"2026-05-18T02:52:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PRjzQetXr2fbfs6IErI5ZRphukdE1N0Adu+InkZf6k7xghNi//1/aGDimqzNlZwwWmrpBmmPQjnbdI5QbatVBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T22:14:39.483437Z"},"content_sha256":"69e4047dee6122b6883bbae78c45c091a77be5ce90386e289202575f60288355","schema_version":"1.0","event_id":"sha256:69e4047dee6122b6883bbae78c45c091a77be5ce90386e289202575f60288355"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LHSVEWGUTIH7OVSXZVS2G3C2VL/bundle.json","state_url":"https://pith.science/pith/LHSVEWGUTIH7OVSXZVS2G3C2VL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LHSVEWGUTIH7OVSXZVS2G3C2VL/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":"2026-06-06T22:14:39Z","links":{"resolver":"https://pith.science/pith/LHSVEWGUTIH7OVSXZVS2G3C2VL","bundle":"https://pith.science/pith/LHSVEWGUTIH7OVSXZVS2G3C2VL/bundle.json","state":"https://pith.science/pith/LHSVEWGUTIH7OVSXZVS2G3C2VL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LHSVEWGUTIH7OVSXZVS2G3C2VL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:LHSVEWGUTIH7OVSXZVS2G3C2VL","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":"4da2e4f0ebc554905275155317e8318e8009366b9e4d22eb7f4c2aeeb2d36649","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-03-07T15:13:08Z","title_canon_sha256":"5585054af0a24b6c42d10e7a37c578ad9ae2ded8df7e6972bee22ccb9f4c8ab0"},"schema_version":"1.0","source":{"id":"1203.1493","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.1493","created_at":"2026-05-18T02:52:04Z"},{"alias_kind":"arxiv_version","alias_value":"1203.1493v2","created_at":"2026-05-18T02:52:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.1493","created_at":"2026-05-18T02:52:04Z"},{"alias_kind":"pith_short_12","alias_value":"LHSVEWGUTIH7","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"LHSVEWGUTIH7OVSX","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"LHSVEWGU","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:69e4047dee6122b6883bbae78c45c091a77be5ce90386e289202575f60288355","target":"graph","created_at":"2026-05-18T02:52:04Z","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":"Shape optimization based on the shape calculus is numerically mostly performed by means of steepest descent methods. This paper provides a novel framework to analyze shape-Newton optimization methods by exploiting a Riemannian perspective. A Riemannian shape Hessian is defined yielding often sought properties like symmetry and quadratic convergence for Newton optimization methods.","authors_text":"Volker Schulz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-03-07T15:13:08Z","title":"A Riemannian View on Shape Optimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.1493","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":"sha256:14d667e7716557004a5b35fce2fd3ea406344aa03ff830a2bde39e5c11ad13c8","target":"record","created_at":"2026-05-18T02:52:04Z","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":"4da2e4f0ebc554905275155317e8318e8009366b9e4d22eb7f4c2aeeb2d36649","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-03-07T15:13:08Z","title_canon_sha256":"5585054af0a24b6c42d10e7a37c578ad9ae2ded8df7e6972bee22ccb9f4c8ab0"},"schema_version":"1.0","source":{"id":"1203.1493","kind":"arxiv","version":2}},"canonical_sha256":"59e55258d49a0ff75657cd65a36c5aaaf06afac6031028694efd04fcf8a5f2cc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"59e55258d49a0ff75657cd65a36c5aaaf06afac6031028694efd04fcf8a5f2cc","first_computed_at":"2026-05-18T02:52:04.404986Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:52:04.404986Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZrizyH6/aTe/rWDqteIvtXqaQk2ZBjZ19ze2eWKyIphGiBhSjWDyCdqJrXc0nHCFD99wZsGT4rUndEUQ+yj0BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:52:04.405481Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.1493","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:14d667e7716557004a5b35fce2fd3ea406344aa03ff830a2bde39e5c11ad13c8","sha256:69e4047dee6122b6883bbae78c45c091a77be5ce90386e289202575f60288355"],"state_sha256":"09a5c41ff5b816051ce9b0b050227cabb1c3685effeb6b48f747b82a7863ad37"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LfgYE7QxlE329Ozy0K/49COnAOt7jg4np+o45B0xZxtZQnlKchbilE2b88ISHks+trJ9APH2tzg2SY6dxxP3BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T22:14:39.487674Z","bundle_sha256":"92ca42af480cf69887f21f2dc8fc30ea8a6be3ca21500504d8cacd0940644c52"}}