{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:G7SXWQTGJXL2IIU5T45VLGR3SO","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":"ac94188f76999c5fcacfff88b4d36d20443de829f973cbd6a6265f3fa35a5913","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-03-20T11:38:06Z","title_canon_sha256":"563e8d1b14d4cbd3cccfde0fe3a71aec5eb53dcf94e03a2b4667eafdf67210d6"},"schema_version":"1.0","source":{"id":"1703.06690","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.06690","created_at":"2026-05-18T00:48:22Z"},{"alias_kind":"arxiv_version","alias_value":"1703.06690v1","created_at":"2026-05-18T00:48:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.06690","created_at":"2026-05-18T00:48:22Z"},{"alias_kind":"pith_short_12","alias_value":"G7SXWQTGJXL2","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"G7SXWQTGJXL2IIU5","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"G7SXWQTG","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:306997633982f1bcbcf5d386ba73d83e7e89d69ddbc8ab5935efc0ae4ef95391","target":"graph","created_at":"2026-05-18T00:48:22Z","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":"The popular BFGS quasi-Newton minimization algorithm under reasonable conditions converges globally on smooth convex functions. This result was proved by Powell in 1976: we consider its implications for functions that are not smooth. In particular, an analogous convergence result holds for functions, like the Euclidean norm, that are nonsmooth at the minimizer.","authors_text":"Adrian Lewis, Jiayi Guo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-03-20T11:38:06Z","title":"BFGS convergence to nonsmooth minimizers of convex functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.06690","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":"sha256:2eb06510185c521990ebc7d07f5891c88572601e26a2007eee96701594e9df0e","target":"record","created_at":"2026-05-18T00:48:22Z","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":"ac94188f76999c5fcacfff88b4d36d20443de829f973cbd6a6265f3fa35a5913","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-03-20T11:38:06Z","title_canon_sha256":"563e8d1b14d4cbd3cccfde0fe3a71aec5eb53dcf94e03a2b4667eafdf67210d6"},"schema_version":"1.0","source":{"id":"1703.06690","kind":"arxiv","version":1}},"canonical_sha256":"37e57b42664dd7a4229d9f3b559a3b938411fe84349d336830a790d726cec1c7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"37e57b42664dd7a4229d9f3b559a3b938411fe84349d336830a790d726cec1c7","first_computed_at":"2026-05-18T00:48:22.023063Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:22.023063Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"d9rO25YfmU8yVwAut9NxUSJzqNE+odSlzQiEwHL1YaA5U//15qnuEvdTCXk7oMRLi561z0Vohx63Ay62WakvCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:22.023689Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.06690","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2eb06510185c521990ebc7d07f5891c88572601e26a2007eee96701594e9df0e","sha256:306997633982f1bcbcf5d386ba73d83e7e89d69ddbc8ab5935efc0ae4ef95391"],"state_sha256":"4a4d05226f493b7153a19991e5e98c98985a65805e008570f5a18cd85f517dfa"}