{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:FP5Y6QZ2BBJOVYG4WZVYVDKTK6","short_pith_number":"pith:FP5Y6QZ2","canonical_record":{"source":{"id":"2102.09762","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2021-02-19T06:38:04Z","cross_cats_sorted":[],"title_canon_sha256":"352d1da32220e66e214893bf2aceaadd2ef8e92216e37de16f730781da626d25","abstract_canon_sha256":"98c193f83e16a49c796cdb01caa9f2ea614d088e9cf15ac212c581a58ade18cc"},"schema_version":"1.0"},"canonical_sha256":"2bfb8f433a0852eae0dcb66b8a8d535786112ffcd05b29e17f5de66b882325c0","source":{"kind":"arxiv","id":"2102.09762","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2102.09762","created_at":"2026-07-05T02:16:30Z"},{"alias_kind":"arxiv_version","alias_value":"2102.09762v1","created_at":"2026-07-05T02:16:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2102.09762","created_at":"2026-07-05T02:16:30Z"},{"alias_kind":"pith_short_12","alias_value":"FP5Y6QZ2BBJO","created_at":"2026-07-05T02:16:30Z"},{"alias_kind":"pith_short_16","alias_value":"FP5Y6QZ2BBJOVYG4","created_at":"2026-07-05T02:16:30Z"},{"alias_kind":"pith_short_8","alias_value":"FP5Y6QZ2","created_at":"2026-07-05T02:16:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:FP5Y6QZ2BBJOVYG4WZVYVDKTK6","target":"record","payload":{"canonical_record":{"source":{"id":"2102.09762","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2021-02-19T06:38:04Z","cross_cats_sorted":[],"title_canon_sha256":"352d1da32220e66e214893bf2aceaadd2ef8e92216e37de16f730781da626d25","abstract_canon_sha256":"98c193f83e16a49c796cdb01caa9f2ea614d088e9cf15ac212c581a58ade18cc"},"schema_version":"1.0"},"canonical_sha256":"2bfb8f433a0852eae0dcb66b8a8d535786112ffcd05b29e17f5de66b882325c0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:16:30.619617Z","signature_b64":"SHnobjzGvLIPoLuugTjEKHvOuk7U52CVHsJ/IwJMkBYL7F8ixpc6acK30GN1MPkCxn7KDXkvwVXlSsq04IjACQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2bfb8f433a0852eae0dcb66b8a8d535786112ffcd05b29e17f5de66b882325c0","last_reissued_at":"2026-07-05T02:16:30.619224Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:16:30.619224Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2102.09762","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T02:16:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OBtvWv9uIgLcXBhnug6LdBmrwwGbyhMnRxbkxxzIJ8bqAjZLDmZx1qZFdqyNOj4ipbWQunutlxl+oWKN4JbUBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T10:36:13.768418Z"},"content_sha256":"71b33ad2194425480c2e4206d1ff6203ffb38319a02ebcfbcbc76dff8e28fd06","schema_version":"1.0","event_id":"sha256:71b33ad2194425480c2e4206d1ff6203ffb38319a02ebcfbcbc76dff8e28fd06"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:FP5Y6QZ2BBJOVYG4WZVYVDKTK6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Numerical Performance of Derivative-Free Optimization Methods Based on Finite-Difference Approximations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Figen Oztoprak, Hao-Jun Michael Shi, Jorge Nocedal, Melody Qiming Xuan","submitted_at":"2021-02-19T06:38:04Z","abstract_excerpt":"The goal of this paper is to investigate an approach for derivative-free optimization that has not received sufficient attention in the literature and is yet one of the simplest to implement and parallelize. It consists of computing gradients of a smoothed approximation of the objective function (and constraints), and employing them within established codes. These gradient approximations are calculated by finite differences, with a differencing interval determined by the noise level in the functions and a bound on the second or third derivatives. It is assumed that noise level is known or can "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.09762","kind":"arxiv","version":1},"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/2102.09762/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":"2026-07-05T02:16:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3ATnAjHrju9gtDJNw1DXFrNIHx7frx0HzWVIxVoGnO/U9qAU+SazyZI/zciv9AmNp3Qj/AoB9EhaBFp2Ci+iBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T10:36:13.768784Z"},"content_sha256":"84473127d939a2142d9c46a57995b216a811cecafd8794d272b1019a132e95e1","schema_version":"1.0","event_id":"sha256:84473127d939a2142d9c46a57995b216a811cecafd8794d272b1019a132e95e1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FP5Y6QZ2BBJOVYG4WZVYVDKTK6/bundle.json","state_url":"https://pith.science/pith/FP5Y6QZ2BBJOVYG4WZVYVDKTK6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FP5Y6QZ2BBJOVYG4WZVYVDKTK6/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":"2026-08-14T10:36:13Z","links":{"resolver":"https://pith.science/pith/FP5Y6QZ2BBJOVYG4WZVYVDKTK6","bundle":"https://pith.science/pith/FP5Y6QZ2BBJOVYG4WZVYVDKTK6/bundle.json","state":"https://pith.science/pith/FP5Y6QZ2BBJOVYG4WZVYVDKTK6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FP5Y6QZ2BBJOVYG4WZVYVDKTK6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:FP5Y6QZ2BBJOVYG4WZVYVDKTK6","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":"98c193f83e16a49c796cdb01caa9f2ea614d088e9cf15ac212c581a58ade18cc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2021-02-19T06:38:04Z","title_canon_sha256":"352d1da32220e66e214893bf2aceaadd2ef8e92216e37de16f730781da626d25"},"schema_version":"1.0","source":{"id":"2102.09762","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2102.09762","created_at":"2026-07-05T02:16:30Z"},{"alias_kind":"arxiv_version","alias_value":"2102.09762v1","created_at":"2026-07-05T02:16:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2102.09762","created_at":"2026-07-05T02:16:30Z"},{"alias_kind":"pith_short_12","alias_value":"FP5Y6QZ2BBJO","created_at":"2026-07-05T02:16:30Z"},{"alias_kind":"pith_short_16","alias_value":"FP5Y6QZ2BBJOVYG4","created_at":"2026-07-05T02:16:30Z"},{"alias_kind":"pith_short_8","alias_value":"FP5Y6QZ2","created_at":"2026-07-05T02:16:30Z"}],"graph_snapshots":[{"event_id":"sha256:84473127d939a2142d9c46a57995b216a811cecafd8794d272b1019a132e95e1","target":"graph","created_at":"2026-07-05T02:16:30Z","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/2102.09762/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The goal of this paper is to investigate an approach for derivative-free optimization that has not received sufficient attention in the literature and is yet one of the simplest to implement and parallelize. It consists of computing gradients of a smoothed approximation of the objective function (and constraints), and employing them within established codes. These gradient approximations are calculated by finite differences, with a differencing interval determined by the noise level in the functions and a bound on the second or third derivatives. It is assumed that noise level is known or can ","authors_text":"Figen Oztoprak, Hao-Jun Michael Shi, Jorge Nocedal, Melody Qiming Xuan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2021-02-19T06:38:04Z","title":"On the Numerical Performance of Derivative-Free Optimization Methods Based on Finite-Difference Approximations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.09762","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":"sha256:71b33ad2194425480c2e4206d1ff6203ffb38319a02ebcfbcbc76dff8e28fd06","target":"record","created_at":"2026-07-05T02:16:30Z","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":"98c193f83e16a49c796cdb01caa9f2ea614d088e9cf15ac212c581a58ade18cc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2021-02-19T06:38:04Z","title_canon_sha256":"352d1da32220e66e214893bf2aceaadd2ef8e92216e37de16f730781da626d25"},"schema_version":"1.0","source":{"id":"2102.09762","kind":"arxiv","version":1}},"canonical_sha256":"2bfb8f433a0852eae0dcb66b8a8d535786112ffcd05b29e17f5de66b882325c0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2bfb8f433a0852eae0dcb66b8a8d535786112ffcd05b29e17f5de66b882325c0","first_computed_at":"2026-07-05T02:16:30.619224Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:16:30.619224Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SHnobjzGvLIPoLuugTjEKHvOuk7U52CVHsJ/IwJMkBYL7F8ixpc6acK30GN1MPkCxn7KDXkvwVXlSsq04IjACQ==","signature_status":"signed_v1","signed_at":"2026-07-05T02:16:30.619617Z","signed_message":"canonical_sha256_bytes"},"source_id":"2102.09762","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:71b33ad2194425480c2e4206d1ff6203ffb38319a02ebcfbcbc76dff8e28fd06","sha256:84473127d939a2142d9c46a57995b216a811cecafd8794d272b1019a132e95e1"],"state_sha256":"8e4820e3e6124f44f2ee435a61a1e510957a12c8a89ba8a7046e8c53b15f625d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u0xxa9h27DEvebacJr60NitkkOjbKzEY5JAzkkgKvMyC2qssmBeLLwuMcJ5FJgrauI0tmB5+wR/nCCBfgM0GBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T10:36:13.772023Z","bundle_sha256":"ffba2ac5c7839cc7fa872e8d5d241067e7da419e0f8c91e739753edab22298b2"}}