{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:7VW42PS4CU6M2KCFK4NS5K6ERC","short_pith_number":"pith:7VW42PS4","schema_version":"1.0","canonical_sha256":"fd6dcd3e5c153ccd2845571b2eabc488a94648cf7873295a5c25f15c9e4cbc21","source":{"kind":"arxiv","id":"2209.04538","version":3},"attestation_state":"computed","paper":{"title":"Phase field model for multi-material shape optimization of inextensible rods","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math-ph","math.MP","math.NA"],"primary_cat":"math.OC","authors_text":"Alberto Maione, Patrick Dondl, Steve Wolff-Vorbeck","submitted_at":"2022-09-09T21:58:44Z","abstract_excerpt":"We derive a model for the optimization of the bending and torsional rigidities of non-homogeneous elastic rods. This is achieved by studying a sharp interface shape optimization problem with perimeter penalization, that treats both rigidities as objectives. We then formulate a phase field approximation of the optimization problem and show the convergence to the aforementioned sharp interface model via $\\Gamma$-convergence. In the final part of this work we numerically approximate minimizers of the phase field problem by using a steepest descent approach and relate the resulting optimal shapes "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2209.04538","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2022-09-09T21:58:44Z","cross_cats_sorted":["cs.NA","math-ph","math.MP","math.NA"],"title_canon_sha256":"abc85aa294cce7d75817318ec50aa2badf8dba7b605d2bd9d82a2aa29bd5c1ce","abstract_canon_sha256":"e89b04ff5effedd9bd980b0b01e3b378b8a96b06e52c1d9f8607e1c36573d376"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:13:24.600175Z","signature_b64":"grXaNTzeMxiRuaTZvIIEp8fnUmlq4q8SpIXwxAOYVrS6I42zuX3IlgS0Wl0FKEtEtzgBxvKak/qzDJwZiHm6Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fd6dcd3e5c153ccd2845571b2eabc488a94648cf7873295a5c25f15c9e4cbc21","last_reissued_at":"2026-07-05T08:13:24.599772Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:13:24.599772Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Phase field model for multi-material shape optimization of inextensible rods","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math-ph","math.MP","math.NA"],"primary_cat":"math.OC","authors_text":"Alberto Maione, Patrick Dondl, Steve Wolff-Vorbeck","submitted_at":"2022-09-09T21:58:44Z","abstract_excerpt":"We derive a model for the optimization of the bending and torsional rigidities of non-homogeneous elastic rods. This is achieved by studying a sharp interface shape optimization problem with perimeter penalization, that treats both rigidities as objectives. We then formulate a phase field approximation of the optimization problem and show the convergence to the aforementioned sharp interface model via $\\Gamma$-convergence. In the final part of this work we numerically approximate minimizers of the phase field problem by using a steepest descent approach and relate the resulting optimal shapes "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.04538","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2209.04538/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2209.04538","created_at":"2026-07-05T08:13:24.599834+00:00"},{"alias_kind":"arxiv_version","alias_value":"2209.04538v3","created_at":"2026-07-05T08:13:24.599834+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.04538","created_at":"2026-07-05T08:13:24.599834+00:00"},{"alias_kind":"pith_short_12","alias_value":"7VW42PS4CU6M","created_at":"2026-07-05T08:13:24.599834+00:00"},{"alias_kind":"pith_short_16","alias_value":"7VW42PS4CU6M2KCF","created_at":"2026-07-05T08:13:24.599834+00:00"},{"alias_kind":"pith_short_8","alias_value":"7VW42PS4","created_at":"2026-07-05T08:13:24.599834+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2505.18953","citing_title":"Evaluating AI for Finance: Is AI Credible at Assessing Investment Risk?","ref_index":14,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7VW42PS4CU6M2KCFK4NS5K6ERC","json":"https://pith.science/pith/7VW42PS4CU6M2KCFK4NS5K6ERC.json","graph_json":"https://pith.science/api/pith-number/7VW42PS4CU6M2KCFK4NS5K6ERC/graph.json","events_json":"https://pith.science/api/pith-number/7VW42PS4CU6M2KCFK4NS5K6ERC/events.json","paper":"https://pith.science/paper/7VW42PS4"},"agent_actions":{"view_html":"https://pith.science/pith/7VW42PS4CU6M2KCFK4NS5K6ERC","download_json":"https://pith.science/pith/7VW42PS4CU6M2KCFK4NS5K6ERC.json","view_paper":"https://pith.science/paper/7VW42PS4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2209.04538&json=true","fetch_graph":"https://pith.science/api/pith-number/7VW42PS4CU6M2KCFK4NS5K6ERC/graph.json","fetch_events":"https://pith.science/api/pith-number/7VW42PS4CU6M2KCFK4NS5K6ERC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7VW42PS4CU6M2KCFK4NS5K6ERC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7VW42PS4CU6M2KCFK4NS5K6ERC/action/storage_attestation","attest_author":"https://pith.science/pith/7VW42PS4CU6M2KCFK4NS5K6ERC/action/author_attestation","sign_citation":"https://pith.science/pith/7VW42PS4CU6M2KCFK4NS5K6ERC/action/citation_signature","submit_replication":"https://pith.science/pith/7VW42PS4CU6M2KCFK4NS5K6ERC/action/replication_record"}},"created_at":"2026-07-05T08:13:24.599834+00:00","updated_at":"2026-07-05T08:13:24.599834+00:00"}