{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:AR64E2DTO7GXC76D5F6RLS43NU","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":"4befebf18a1c9100ac197ab499a30371cfc8dc259d977491670c8b13f837cfef","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-03-27T16:38:48Z","title_canon_sha256":"c775de4584dcee713df0daae7d876bd741e7323d7bf3d77baaf97c3a03e364b3"},"schema_version":"1.0","source":{"id":"1603.08235","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.08235","created_at":"2026-05-18T01:17:49Z"},{"alias_kind":"arxiv_version","alias_value":"1603.08235v2","created_at":"2026-05-18T01:17:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.08235","created_at":"2026-05-18T01:17:49Z"},{"alias_kind":"pith_short_12","alias_value":"AR64E2DTO7GX","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"AR64E2DTO7GXC76D","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"AR64E2DT","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:ac85715580b0ecd97022b8786fdce87cd9e45cc6f2f05d3d7aaf2db2f99f472d","target":"graph","created_at":"2026-05-18T01:17:49Z","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":"This paper is concerned with the study of a class of nonsmooth cost functions subject to a quasi-linear PDE in Lipschitz domains in dimension two. We derive the Eulerian semi-derivative of the cost function by employing the averaged adjoint approach and maximal elliptic regularity. Furthermore we characterise stationary points and show how to compute steepest descent direc- tions theoretically and practically. Finally, we present some numerical results for a simple toy problem and compare them with the smooth case. We also compare the convergence rates and obtain higher rates in the nonsmooth ","authors_text":"Kevin Sturm","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-03-27T16:38:48Z","title":"Shape optimisation with nonsmooth cost functions: from theory to numerics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.08235","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:d868d1c0a5e93cd77e08d246cbca4ff009e8c8b8e11a0cd65af311277ca760f1","target":"record","created_at":"2026-05-18T01:17:49Z","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":"4befebf18a1c9100ac197ab499a30371cfc8dc259d977491670c8b13f837cfef","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-03-27T16:38:48Z","title_canon_sha256":"c775de4584dcee713df0daae7d876bd741e7323d7bf3d77baaf97c3a03e364b3"},"schema_version":"1.0","source":{"id":"1603.08235","kind":"arxiv","version":2}},"canonical_sha256":"047dc2687377cd717fc3e97d15cb9b6d176e5ed6578b748bec1b54faff19848b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"047dc2687377cd717fc3e97d15cb9b6d176e5ed6578b748bec1b54faff19848b","first_computed_at":"2026-05-18T01:17:49.867279Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:49.867279Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TbQ35gczb0xkoafH+qlxJq4WRCl8gUhNTwCyp1MBF5jn4ytXe5goUwNB6pKcowj2R46KnTQJ7Tn5ESZ19Hv/Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:49.867960Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.08235","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d868d1c0a5e93cd77e08d246cbca4ff009e8c8b8e11a0cd65af311277ca760f1","sha256:ac85715580b0ecd97022b8786fdce87cd9e45cc6f2f05d3d7aaf2db2f99f472d"],"state_sha256":"2e6e41337269d6f4eba372bb49f8bd8ca13ceed9cd63a68c4367ec510e796512"}