{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:LAYAPZXDNDYZT62WNBV6DKY3OZ","short_pith_number":"pith:LAYAPZXD","canonical_record":{"source":{"id":"1608.02699","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-08-09T05:59:47Z","cross_cats_sorted":[],"title_canon_sha256":"917ce9368a46c64b816e00126fd684e40cce329a98aa0e687e928015463ec7f3","abstract_canon_sha256":"e984e4eab026e2bd37e049080175d803d8c613b5a7d2cb2f9d6762f4b20a8d0d"},"schema_version":"1.0"},"canonical_sha256":"583007e6e368f199fb56686be1ab1b76426cf967f55889dba0e617fff00698c7","source":{"kind":"arxiv","id":"1608.02699","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.02699","created_at":"2026-05-18T00:06:31Z"},{"alias_kind":"arxiv_version","alias_value":"1608.02699v2","created_at":"2026-05-18T00:06:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.02699","created_at":"2026-05-18T00:06:31Z"},{"alias_kind":"pith_short_12","alias_value":"LAYAPZXDNDYZ","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LAYAPZXDNDYZT62W","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LAYAPZXD","created_at":"2026-05-18T12:30:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:LAYAPZXDNDYZT62WNBV6DKY3OZ","target":"record","payload":{"canonical_record":{"source":{"id":"1608.02699","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-08-09T05:59:47Z","cross_cats_sorted":[],"title_canon_sha256":"917ce9368a46c64b816e00126fd684e40cce329a98aa0e687e928015463ec7f3","abstract_canon_sha256":"e984e4eab026e2bd37e049080175d803d8c613b5a7d2cb2f9d6762f4b20a8d0d"},"schema_version":"1.0"},"canonical_sha256":"583007e6e368f199fb56686be1ab1b76426cf967f55889dba0e617fff00698c7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:31.181931Z","signature_b64":"ADp8U0uh6KADLqOxBAp/m/Yv8PvAYZsJOESKJMmzhb2S1NnRJEscwJ5xzbvGnJKKqk0HNiUcheHp7i/BEvWZDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"583007e6e368f199fb56686be1ab1b76426cf967f55889dba0e617fff00698c7","last_reissued_at":"2026-05-18T00:06:31.181530Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:31.181530Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.02699","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":"2026-05-18T00:06:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l0YTwihHgEWnzk3Ux8tXSUiqi8aQl5/T5SwVVxeq+cX4DzbCRIT67mBksfMA00pg1+cmciEKBspJbI7QiSo9CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T16:56:00.105150Z"},"content_sha256":"5ff3a7eaf65f702fee09e0ccd233731d02537d830c3bd5f7055c5cc1ecd91cd3","schema_version":"1.0","event_id":"sha256:5ff3a7eaf65f702fee09e0ccd233731d02537d830c3bd5f7055c5cc1ecd91cd3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:LAYAPZXDNDYZT62WNBV6DKY3OZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Convergence of Newton's method in shape optimisation via approximate normal functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Kevin Sturm","submitted_at":"2016-08-09T05:59:47Z","abstract_excerpt":"In this paper we propose a Newton method for shape functions defined on an image set generated by the (Micheletti) metric group. We review basic properties of the metric group and a quotient associated with the metric group and a fixed domain. Taking into account the special structure of the second shape derivative and its symmetric part allows us to distinguish between two Hessians, the domain shape Hessian and the boundary shape Hessian. Using the domain Hessian we define a Newton method on the metric group by discretising the tangent space of the quotient via approximate normal functions us"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.02699","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":"2026-05-18T00:06:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"29ocnmw9GYIEEDdbAMZHzPl9MPRaqOt+2CqgXSIqSUNXxUSM7E0c/3UqI9BTP5U5/E5exqW4ZkAgY87L5cFJBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T16:56:00.105526Z"},"content_sha256":"2da0c18aeac84e4ccc0840e25cee05f421a6503c044e5ef5398c9f7bfef7981b","schema_version":"1.0","event_id":"sha256:2da0c18aeac84e4ccc0840e25cee05f421a6503c044e5ef5398c9f7bfef7981b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LAYAPZXDNDYZT62WNBV6DKY3OZ/bundle.json","state_url":"https://pith.science/pith/LAYAPZXDNDYZT62WNBV6DKY3OZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LAYAPZXDNDYZT62WNBV6DKY3OZ/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":"2026-06-01T16:56:00Z","links":{"resolver":"https://pith.science/pith/LAYAPZXDNDYZT62WNBV6DKY3OZ","bundle":"https://pith.science/pith/LAYAPZXDNDYZT62WNBV6DKY3OZ/bundle.json","state":"https://pith.science/pith/LAYAPZXDNDYZT62WNBV6DKY3OZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LAYAPZXDNDYZT62WNBV6DKY3OZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:LAYAPZXDNDYZT62WNBV6DKY3OZ","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":"e984e4eab026e2bd37e049080175d803d8c613b5a7d2cb2f9d6762f4b20a8d0d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-08-09T05:59:47Z","title_canon_sha256":"917ce9368a46c64b816e00126fd684e40cce329a98aa0e687e928015463ec7f3"},"schema_version":"1.0","source":{"id":"1608.02699","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.02699","created_at":"2026-05-18T00:06:31Z"},{"alias_kind":"arxiv_version","alias_value":"1608.02699v2","created_at":"2026-05-18T00:06:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.02699","created_at":"2026-05-18T00:06:31Z"},{"alias_kind":"pith_short_12","alias_value":"LAYAPZXDNDYZ","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LAYAPZXDNDYZT62W","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LAYAPZXD","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:2da0c18aeac84e4ccc0840e25cee05f421a6503c044e5ef5398c9f7bfef7981b","target":"graph","created_at":"2026-05-18T00:06:31Z","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 paper we propose a Newton method for shape functions defined on an image set generated by the (Micheletti) metric group. We review basic properties of the metric group and a quotient associated with the metric group and a fixed domain. Taking into account the special structure of the second shape derivative and its symmetric part allows us to distinguish between two Hessians, the domain shape Hessian and the boundary shape Hessian. Using the domain Hessian we define a Newton method on the metric group by discretising the tangent space of the quotient via approximate normal functions us","authors_text":"Kevin Sturm","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-08-09T05:59:47Z","title":"Convergence of Newton's method in shape optimisation via approximate normal functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.02699","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":"sha256:5ff3a7eaf65f702fee09e0ccd233731d02537d830c3bd5f7055c5cc1ecd91cd3","target":"record","created_at":"2026-05-18T00:06:31Z","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":"e984e4eab026e2bd37e049080175d803d8c613b5a7d2cb2f9d6762f4b20a8d0d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-08-09T05:59:47Z","title_canon_sha256":"917ce9368a46c64b816e00126fd684e40cce329a98aa0e687e928015463ec7f3"},"schema_version":"1.0","source":{"id":"1608.02699","kind":"arxiv","version":2}},"canonical_sha256":"583007e6e368f199fb56686be1ab1b76426cf967f55889dba0e617fff00698c7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"583007e6e368f199fb56686be1ab1b76426cf967f55889dba0e617fff00698c7","first_computed_at":"2026-05-18T00:06:31.181530Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:31.181530Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ADp8U0uh6KADLqOxBAp/m/Yv8PvAYZsJOESKJMmzhb2S1NnRJEscwJ5xzbvGnJKKqk0HNiUcheHp7i/BEvWZDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:31.181931Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.02699","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5ff3a7eaf65f702fee09e0ccd233731d02537d830c3bd5f7055c5cc1ecd91cd3","sha256:2da0c18aeac84e4ccc0840e25cee05f421a6503c044e5ef5398c9f7bfef7981b"],"state_sha256":"ad4ee4f4f853bb0d03b0434b5352e25b884b5646405c825693c8ebc707d6e6e7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3hEaCC3s0pWiZMWF6YT/ubB3hF9g5XuGUkX3ANWygVcgPF4ZrwtJzeEQFTIH8PnTkoxyFjFS/wVTMJOw46foCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T16:56:00.107655Z","bundle_sha256":"162176fa7cd3788e8c57bb29733eee37330cfdc7c6ed1eaeea9e354dde8aee73"}}