{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:E6ISNIQV7L2SQ73BPFU4BJLQCR","short_pith_number":"pith:E6ISNIQV","canonical_record":{"source":{"id":"1806.09821","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-06-26T07:29:37Z","cross_cats_sorted":[],"title_canon_sha256":"588e32a8490cf05bd36e996130e512d9464e9ca7f5d15b2e394d2a825a214e54","abstract_canon_sha256":"67e950010b6b4a5179f0ab6bb542afa9925dd000e2d039b63ec469223721aa54"},"schema_version":"1.0"},"canonical_sha256":"279126a215faf5287f617969c0a5701444327fa1d8071eeb8720e82c1e254b72","source":{"kind":"arxiv","id":"1806.09821","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.09821","created_at":"2026-05-18T00:12:23Z"},{"alias_kind":"arxiv_version","alias_value":"1806.09821v1","created_at":"2026-05-18T00:12:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.09821","created_at":"2026-05-18T00:12:23Z"},{"alias_kind":"pith_short_12","alias_value":"E6ISNIQV7L2S","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"E6ISNIQV7L2SQ73B","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"E6ISNIQV","created_at":"2026-05-18T12:32:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:E6ISNIQV7L2SQ73BPFU4BJLQCR","target":"record","payload":{"canonical_record":{"source":{"id":"1806.09821","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-06-26T07:29:37Z","cross_cats_sorted":[],"title_canon_sha256":"588e32a8490cf05bd36e996130e512d9464e9ca7f5d15b2e394d2a825a214e54","abstract_canon_sha256":"67e950010b6b4a5179f0ab6bb542afa9925dd000e2d039b63ec469223721aa54"},"schema_version":"1.0"},"canonical_sha256":"279126a215faf5287f617969c0a5701444327fa1d8071eeb8720e82c1e254b72","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:23.244009Z","signature_b64":"7ivG0Ecx+Ukrc+uhz9Mk0pig4r/G4Qtf8OT+vJwXpJnZ8DOCSX6XLV++JPlwU7BxIZ3Q3tANqoBpXvUot5uoCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"279126a215faf5287f617969c0a5701444327fa1d8071eeb8720e82c1e254b72","last_reissued_at":"2026-05-18T00:12:23.243305Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:23.243305Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.09821","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:12:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bCvo0dzQE+KNbe6C1C9ToOj8SL2ZzctBWf7AIIIZOS8PiDM8dNOeUpDcZRe2bs5Ga9rUy+liMovQj2sjykixDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T16:12:50.534145Z"},"content_sha256":"fbbd9930d4c6ae51a8ed82c878972b2968e58662890e5a83f75f0c1f8bd84df8","schema_version":"1.0","event_id":"sha256:fbbd9930d4c6ae51a8ed82c878972b2968e58662890e5a83f75f0c1f8bd84df8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:E6ISNIQV7L2SQ73BPFU4BJLQCR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Shape Optimization using the Finite Element Method on Multiple Meshes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"August Johansson, Jorgen S. Dokken, Simon W. Funke, Stephan Schmidt","submitted_at":"2018-06-26T07:29:37Z","abstract_excerpt":"An important step in shape optimization with partial differential equation constraints is to adapt the geometry during each optimization iteration. Common strategies are to employ mesh-deformation or re-meshing, where one or the other typically lacks robustness or is computationally expensive. This paper proposes a different approach, in which the computational domain is represented by multiple, independent meshes. A Nitsche based finite element method is used to weakly enforce continuity over the non-matching mesh interfaces. The optimization is preformed using an iterative gradient method, i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.09821","kind":"arxiv","version":1},"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":"2026-05-18T00:12:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0/ENI9zyUl1ELfU10rDve06wAeGJVqBsRBO60okl09sYTuPjU+TCUNiWJpzsGK2gIzuNooHMiihUGFRIo6dsBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T16:12:50.534515Z"},"content_sha256":"f06c18909d050706ce17bb23d95cbbc9aab732dad5573fe0cbde9f884ad15812","schema_version":"1.0","event_id":"sha256:f06c18909d050706ce17bb23d95cbbc9aab732dad5573fe0cbde9f884ad15812"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/E6ISNIQV7L2SQ73BPFU4BJLQCR/bundle.json","state_url":"https://pith.science/pith/E6ISNIQV7L2SQ73BPFU4BJLQCR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/E6ISNIQV7L2SQ73BPFU4BJLQCR/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":"2026-06-22T16:12:50Z","links":{"resolver":"https://pith.science/pith/E6ISNIQV7L2SQ73BPFU4BJLQCR","bundle":"https://pith.science/pith/E6ISNIQV7L2SQ73BPFU4BJLQCR/bundle.json","state":"https://pith.science/pith/E6ISNIQV7L2SQ73BPFU4BJLQCR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/E6ISNIQV7L2SQ73BPFU4BJLQCR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:E6ISNIQV7L2SQ73BPFU4BJLQCR","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":"67e950010b6b4a5179f0ab6bb542afa9925dd000e2d039b63ec469223721aa54","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-06-26T07:29:37Z","title_canon_sha256":"588e32a8490cf05bd36e996130e512d9464e9ca7f5d15b2e394d2a825a214e54"},"schema_version":"1.0","source":{"id":"1806.09821","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.09821","created_at":"2026-05-18T00:12:23Z"},{"alias_kind":"arxiv_version","alias_value":"1806.09821v1","created_at":"2026-05-18T00:12:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.09821","created_at":"2026-05-18T00:12:23Z"},{"alias_kind":"pith_short_12","alias_value":"E6ISNIQV7L2S","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"E6ISNIQV7L2SQ73B","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"E6ISNIQV","created_at":"2026-05-18T12:32:19Z"}],"graph_snapshots":[{"event_id":"sha256:f06c18909d050706ce17bb23d95cbbc9aab732dad5573fe0cbde9f884ad15812","target":"graph","created_at":"2026-05-18T00:12:23Z","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":"An important step in shape optimization with partial differential equation constraints is to adapt the geometry during each optimization iteration. Common strategies are to employ mesh-deformation or re-meshing, where one or the other typically lacks robustness or is computationally expensive. This paper proposes a different approach, in which the computational domain is represented by multiple, independent meshes. A Nitsche based finite element method is used to weakly enforce continuity over the non-matching mesh interfaces. The optimization is preformed using an iterative gradient method, i","authors_text":"August Johansson, Jorgen S. Dokken, Simon W. Funke, Stephan Schmidt","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-06-26T07:29:37Z","title":"Shape Optimization using the Finite Element Method on Multiple Meshes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.09821","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:fbbd9930d4c6ae51a8ed82c878972b2968e58662890e5a83f75f0c1f8bd84df8","target":"record","created_at":"2026-05-18T00:12:23Z","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":"67e950010b6b4a5179f0ab6bb542afa9925dd000e2d039b63ec469223721aa54","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-06-26T07:29:37Z","title_canon_sha256":"588e32a8490cf05bd36e996130e512d9464e9ca7f5d15b2e394d2a825a214e54"},"schema_version":"1.0","source":{"id":"1806.09821","kind":"arxiv","version":1}},"canonical_sha256":"279126a215faf5287f617969c0a5701444327fa1d8071eeb8720e82c1e254b72","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"279126a215faf5287f617969c0a5701444327fa1d8071eeb8720e82c1e254b72","first_computed_at":"2026-05-18T00:12:23.243305Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:23.243305Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7ivG0Ecx+Ukrc+uhz9Mk0pig4r/G4Qtf8OT+vJwXpJnZ8DOCSX6XLV++JPlwU7BxIZ3Q3tANqoBpXvUot5uoCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:23.244009Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.09821","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fbbd9930d4c6ae51a8ed82c878972b2968e58662890e5a83f75f0c1f8bd84df8","sha256:f06c18909d050706ce17bb23d95cbbc9aab732dad5573fe0cbde9f884ad15812"],"state_sha256":"c5b5ff37cd8e5fe124a710479c2c2d2e23f9a77ed82184338af0fe72b3f56431"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nCA4IzVuCTR6aC3KEd2isQ+Av5XE1M8NoRv3wwljKlkOd86cQ2wgylauLgbtLKLnp9odctLET7OcyxLJ1eMtDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T16:12:50.536446Z","bundle_sha256":"204ecabb9e7e6b109a110c27f80c007dce4b2d9a94616c970168b7c61db19f6e"}}