{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:7VW42PS4CU6M2KCFK4NS5K6ERC","short_pith_number":"pith:7VW42PS4","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"},"canonical_sha256":"fd6dcd3e5c153ccd2845571b2eabc488a94648cf7873295a5c25f15c9e4cbc21","source":{"kind":"arxiv","id":"2209.04538","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2209.04538","created_at":"2026-07-05T08:13:24Z"},{"alias_kind":"arxiv_version","alias_value":"2209.04538v3","created_at":"2026-07-05T08:13:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.04538","created_at":"2026-07-05T08:13:24Z"},{"alias_kind":"pith_short_12","alias_value":"7VW42PS4CU6M","created_at":"2026-07-05T08:13:24Z"},{"alias_kind":"pith_short_16","alias_value":"7VW42PS4CU6M2KCF","created_at":"2026-07-05T08:13:24Z"},{"alias_kind":"pith_short_8","alias_value":"7VW42PS4","created_at":"2026-07-05T08:13:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:7VW42PS4CU6M2KCFK4NS5K6ERC","target":"record","payload":{"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"},"canonical_sha256":"fd6dcd3e5c153ccd2845571b2eabc488a94648cf7873295a5c25f15c9e4cbc21","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"},"source_kind":"arxiv","source_id":"2209.04538","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T08:13:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5j/QBbb4y8igKf5cClOOwaiYz+XnD29V7iVt89NEn9ba6W9QtHMJTkDuql2UzV55QL9XNYTaqu0b2WbBxLCeCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T05:20:10.904318Z"},"content_sha256":"c2b02168bd99b5f18aa2a0a219f6367be1e571ac272c99a7d4781cd3dc87dabc","schema_version":"1.0","event_id":"sha256:c2b02168bd99b5f18aa2a0a219f6367be1e571ac272c99a7d4781cd3dc87dabc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:7VW42PS4CU6M2KCFK4NS5K6ERC","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T08:13:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wwGtaCs7sAULF3g6C8tTthBJy5s92a4lBcjM5abrU9GKh7vn9szh1rJbJgBBHPAgcC2ndJ22rM4gHEIuShn8BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T05:20:10.905063Z"},"content_sha256":"e831b296adb2c0f56197102c1c3eab3f695923c0aed16eb94a0e93810743fa34","schema_version":"1.0","event_id":"sha256:e831b296adb2c0f56197102c1c3eab3f695923c0aed16eb94a0e93810743fa34"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7VW42PS4CU6M2KCFK4NS5K6ERC/bundle.json","state_url":"https://pith.science/pith/7VW42PS4CU6M2KCFK4NS5K6ERC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7VW42PS4CU6M2KCFK4NS5K6ERC/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":"2026-08-21T05:20:10Z","links":{"resolver":"https://pith.science/pith/7VW42PS4CU6M2KCFK4NS5K6ERC","bundle":"https://pith.science/pith/7VW42PS4CU6M2KCFK4NS5K6ERC/bundle.json","state":"https://pith.science/pith/7VW42PS4CU6M2KCFK4NS5K6ERC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7VW42PS4CU6M2KCFK4NS5K6ERC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:7VW42PS4CU6M2KCFK4NS5K6ERC","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":"e89b04ff5effedd9bd980b0b01e3b378b8a96b06e52c1d9f8607e1c36573d376","cross_cats_sorted":["cs.NA","math-ph","math.MP","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2022-09-09T21:58:44Z","title_canon_sha256":"abc85aa294cce7d75817318ec50aa2badf8dba7b605d2bd9d82a2aa29bd5c1ce"},"schema_version":"1.0","source":{"id":"2209.04538","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2209.04538","created_at":"2026-07-05T08:13:24Z"},{"alias_kind":"arxiv_version","alias_value":"2209.04538v3","created_at":"2026-07-05T08:13:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.04538","created_at":"2026-07-05T08:13:24Z"},{"alias_kind":"pith_short_12","alias_value":"7VW42PS4CU6M","created_at":"2026-07-05T08:13:24Z"},{"alias_kind":"pith_short_16","alias_value":"7VW42PS4CU6M2KCF","created_at":"2026-07-05T08:13:24Z"},{"alias_kind":"pith_short_8","alias_value":"7VW42PS4","created_at":"2026-07-05T08:13:24Z"}],"graph_snapshots":[{"event_id":"sha256:e831b296adb2c0f56197102c1c3eab3f695923c0aed16eb94a0e93810743fa34","target":"graph","created_at":"2026-07-05T08:13:24Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2209.04538/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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 ","authors_text":"Alberto Maione, Patrick Dondl, Steve Wolff-Vorbeck","cross_cats":["cs.NA","math-ph","math.MP","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2022-09-09T21:58:44Z","title":"Phase field model for multi-material shape optimization of inextensible rods"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.04538","kind":"arxiv","version":3},"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:c2b02168bd99b5f18aa2a0a219f6367be1e571ac272c99a7d4781cd3dc87dabc","target":"record","created_at":"2026-07-05T08:13:24Z","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":"e89b04ff5effedd9bd980b0b01e3b378b8a96b06e52c1d9f8607e1c36573d376","cross_cats_sorted":["cs.NA","math-ph","math.MP","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2022-09-09T21:58:44Z","title_canon_sha256":"abc85aa294cce7d75817318ec50aa2badf8dba7b605d2bd9d82a2aa29bd5c1ce"},"schema_version":"1.0","source":{"id":"2209.04538","kind":"arxiv","version":3}},"canonical_sha256":"fd6dcd3e5c153ccd2845571b2eabc488a94648cf7873295a5c25f15c9e4cbc21","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fd6dcd3e5c153ccd2845571b2eabc488a94648cf7873295a5c25f15c9e4cbc21","first_computed_at":"2026-07-05T08:13:24.599772Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:13:24.599772Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"grXaNTzeMxiRuaTZvIIEp8fnUmlq4q8SpIXwxAOYVrS6I42zuX3IlgS0Wl0FKEtEtzgBxvKak/qzDJwZiHm6Bw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:13:24.600175Z","signed_message":"canonical_sha256_bytes"},"source_id":"2209.04538","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c2b02168bd99b5f18aa2a0a219f6367be1e571ac272c99a7d4781cd3dc87dabc","sha256:e831b296adb2c0f56197102c1c3eab3f695923c0aed16eb94a0e93810743fa34"],"state_sha256":"07e81577997ee1677ab709300ccb320a435ef30ebd37b6409ef2b97cdd0e92c1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9wwykB4Sb3f7GjZvTFEVZehy+5Mm0NLVwulE6JZwva6XWUCRRohbDDqK1oBIo1R5/ChEPIvXmWUl1yMJCf0SCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-21T05:20:10.911869Z","bundle_sha256":"d3378c608a03b38351618e1a78d840e243a8ea80c5bbfd11dac54e20defbeb98"}}