{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:V7YNLWPR4CRMCO5GCCERE7APAS","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":"217ac8496d66e40d25f03c9d53fb27646041399a5df4b707975518e0c2b9d713","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-11-26T19:22:42Z","title_canon_sha256":"e6f850e430b9393484f0c5c1e3ca32ae589eddb77ea4b5f6a1f402b03fb5298c"},"schema_version":"1.0","source":{"id":"1311.6779","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.6779","created_at":"2026-05-18T02:51:48Z"},{"alias_kind":"arxiv_version","alias_value":"1311.6779v2","created_at":"2026-05-18T02:51:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.6779","created_at":"2026-05-18T02:51:48Z"},{"alias_kind":"pith_short_12","alias_value":"V7YNLWPR4CRM","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"V7YNLWPR4CRMCO5G","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"V7YNLWPR","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:ef12e5b66db7dbda0e0a665dd5358e385fa9a2f8e8dba122032b8001837f5a90","target":"graph","created_at":"2026-05-18T02:51:48Z","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":"We consider the probability of failure for components made of brittle mate- rials under one time application of a load as introduced by Weibull and Batdorf - Crosse and more recently studied by NASA and the STAU cooperation as an objective functional in shape optimization and prove the existence of optimal shapes in the class of shapes with a uniform cone property. The corresponding integrand of the objective functional has convexity properties that allow to derive lower-semicontinuity according to Fujii (Opt. Th. Appl. 1988). These properties require less restrictive regularity assumptions fo","authors_text":"Hanno Gottschalk, Matthias Bolten, Sebastian Schmitz","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-11-26T19:22:42Z","title":"Minimal failure probability for ceramic design via shape control"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.6779","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:ba1ece0a97580d99a81c521d1021f82b64de8ea8cfa664b2fc6a524ce3670695","target":"record","created_at":"2026-05-18T02:51:48Z","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":"217ac8496d66e40d25f03c9d53fb27646041399a5df4b707975518e0c2b9d713","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-11-26T19:22:42Z","title_canon_sha256":"e6f850e430b9393484f0c5c1e3ca32ae589eddb77ea4b5f6a1f402b03fb5298c"},"schema_version":"1.0","source":{"id":"1311.6779","kind":"arxiv","version":2}},"canonical_sha256":"aff0d5d9f1e0a2c13ba61089127c0f048efc6397f13b364377093c9ccbc64438","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aff0d5d9f1e0a2c13ba61089127c0f048efc6397f13b364377093c9ccbc64438","first_computed_at":"2026-05-18T02:51:48.482409Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:51:48.482409Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"87riuYmeAj2vTG18MGMgppOSOP7asTZPkpa4CfeXhiG6+cxgEQ/2/eBogzgchHXiWGfQWq0UGFwrswex1jRVDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:51:48.482844Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.6779","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba1ece0a97580d99a81c521d1021f82b64de8ea8cfa664b2fc6a524ce3670695","sha256:ef12e5b66db7dbda0e0a665dd5358e385fa9a2f8e8dba122032b8001837f5a90"],"state_sha256":"27b51e0363bfcf5a28f932e156d099734e058a9a4a54e7090cc84eb93833545d"}