{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:5Y5UVXGF2VFXY4MG7HV73OFTP2","short_pith_number":"pith:5Y5UVXGF","canonical_record":{"source":{"id":"2209.13555","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2022-09-27T17:09:54Z","cross_cats_sorted":[],"title_canon_sha256":"1c7dd55f5ddad4e3ac349f46642969f5ba7ecab10cadee27cc9d8731a595dfc9","abstract_canon_sha256":"f7c8ab2871a36470c171727863ccbfafd976fcc2334e5f9a6bfc1f8a6a430c7e"},"schema_version":"1.0"},"canonical_sha256":"ee3b4adcc5d54b7c7186f9ebfdb8b37ead17659bcb63066b0274e25dc0e19293","source":{"kind":"arxiv","id":"2209.13555","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2209.13555","created_at":"2026-07-05T06:08:09Z"},{"alias_kind":"arxiv_version","alias_value":"2209.13555v3","created_at":"2026-07-05T06:08:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.13555","created_at":"2026-07-05T06:08:09Z"},{"alias_kind":"pith_short_12","alias_value":"5Y5UVXGF2VFX","created_at":"2026-07-05T06:08:09Z"},{"alias_kind":"pith_short_16","alias_value":"5Y5UVXGF2VFXY4MG","created_at":"2026-07-05T06:08:09Z"},{"alias_kind":"pith_short_8","alias_value":"5Y5UVXGF","created_at":"2026-07-05T06:08:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:5Y5UVXGF2VFXY4MG7HV73OFTP2","target":"record","payload":{"canonical_record":{"source":{"id":"2209.13555","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2022-09-27T17:09:54Z","cross_cats_sorted":[],"title_canon_sha256":"1c7dd55f5ddad4e3ac349f46642969f5ba7ecab10cadee27cc9d8731a595dfc9","abstract_canon_sha256":"f7c8ab2871a36470c171727863ccbfafd976fcc2334e5f9a6bfc1f8a6a430c7e"},"schema_version":"1.0"},"canonical_sha256":"ee3b4adcc5d54b7c7186f9ebfdb8b37ead17659bcb63066b0274e25dc0e19293","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:08:09.352865Z","signature_b64":"59ACJf0/4gDBStHt+cf4pIiSILJ+dbPLT7NH1J/Sdpq9MFbX6LvbHXLV1dz5CrAJ8GIXk1SQJ3lsiOAHpuX+Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ee3b4adcc5d54b7c7186f9ebfdb8b37ead17659bcb63066b0274e25dc0e19293","last_reissued_at":"2026-07-05T06:08:09.352373Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:08:09.352373Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2209.13555","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":"2026-07-05T06:08:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cix+2Mou3ewDoOMbs2VfVJBFJyPJIPayKTzE2oR3iLb0a8aed+Co2Oy+z9+GQuqj9WsnP0nrlvqzaym4bXZcBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T04:27:00.853116Z"},"content_sha256":"c67818d576b3d7046feaec36c2bf800cf612a7b79f911740c89677abc09a97f6","schema_version":"1.0","event_id":"sha256:c67818d576b3d7046feaec36c2bf800cf612a7b79f911740c89677abc09a97f6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:5Y5UVXGF2VFXY4MG7HV73OFTP2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Escaping saddle points in zeroth-order optimization: the power of two-point estimators","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Na Li, Yujie Tang, Zhaolin Ren","submitted_at":"2022-09-27T17:09:54Z","abstract_excerpt":"Two-point zeroth order methods are important in many applications of zeroth-order optimization, such as robotics, wind farms, power systems, online optimization, and adversarial robustness to black-box attacks in deep neural networks, where the problem may be high-dimensional and/or time-varying. Most problems in these applications are nonconvex and contain saddle points. While existing works have shown that zeroth-order methods utilizing $\\Omega(d)$ function valuations per iteration (with $d$ denoting the problem dimension) can escape saddle points efficiently, it remains an open question if "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.13555","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/2209.13555/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":"2026-07-05T06:08:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NqkFdJJGa85C0DUp/Em1qtTEkgObl4tp9L2N09ZmvugViPkXoIH2HE1exwl0yq9j2IBjPgWJ5LQy3LeoucjeCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T04:27:00.853612Z"},"content_sha256":"4a0c3410f93c3a7ae4c9f6b51d3c5f47ba43286d0e9f3f681985595b204b9a51","schema_version":"1.0","event_id":"sha256:4a0c3410f93c3a7ae4c9f6b51d3c5f47ba43286d0e9f3f681985595b204b9a51"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5Y5UVXGF2VFXY4MG7HV73OFTP2/bundle.json","state_url":"https://pith.science/pith/5Y5UVXGF2VFXY4MG7HV73OFTP2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5Y5UVXGF2VFXY4MG7HV73OFTP2/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":"2026-08-21T04:27:00Z","links":{"resolver":"https://pith.science/pith/5Y5UVXGF2VFXY4MG7HV73OFTP2","bundle":"https://pith.science/pith/5Y5UVXGF2VFXY4MG7HV73OFTP2/bundle.json","state":"https://pith.science/pith/5Y5UVXGF2VFXY4MG7HV73OFTP2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5Y5UVXGF2VFXY4MG7HV73OFTP2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:5Y5UVXGF2VFXY4MG7HV73OFTP2","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":"f7c8ab2871a36470c171727863ccbfafd976fcc2334e5f9a6bfc1f8a6a430c7e","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2022-09-27T17:09:54Z","title_canon_sha256":"1c7dd55f5ddad4e3ac349f46642969f5ba7ecab10cadee27cc9d8731a595dfc9"},"schema_version":"1.0","source":{"id":"2209.13555","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2209.13555","created_at":"2026-07-05T06:08:09Z"},{"alias_kind":"arxiv_version","alias_value":"2209.13555v3","created_at":"2026-07-05T06:08:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.13555","created_at":"2026-07-05T06:08:09Z"},{"alias_kind":"pith_short_12","alias_value":"5Y5UVXGF2VFX","created_at":"2026-07-05T06:08:09Z"},{"alias_kind":"pith_short_16","alias_value":"5Y5UVXGF2VFXY4MG","created_at":"2026-07-05T06:08:09Z"},{"alias_kind":"pith_short_8","alias_value":"5Y5UVXGF","created_at":"2026-07-05T06:08:09Z"}],"graph_snapshots":[{"event_id":"sha256:4a0c3410f93c3a7ae4c9f6b51d3c5f47ba43286d0e9f3f681985595b204b9a51","target":"graph","created_at":"2026-07-05T06:08:09Z","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/2209.13555/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Two-point zeroth order methods are important in many applications of zeroth-order optimization, such as robotics, wind farms, power systems, online optimization, and adversarial robustness to black-box attacks in deep neural networks, where the problem may be high-dimensional and/or time-varying. Most problems in these applications are nonconvex and contain saddle points. While existing works have shown that zeroth-order methods utilizing $\\Omega(d)$ function valuations per iteration (with $d$ denoting the problem dimension) can escape saddle points efficiently, it remains an open question if ","authors_text":"Na Li, Yujie Tang, Zhaolin Ren","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2022-09-27T17:09:54Z","title":"Escaping saddle points in zeroth-order optimization: the power of two-point estimators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.13555","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:c67818d576b3d7046feaec36c2bf800cf612a7b79f911740c89677abc09a97f6","target":"record","created_at":"2026-07-05T06:08:09Z","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":"f7c8ab2871a36470c171727863ccbfafd976fcc2334e5f9a6bfc1f8a6a430c7e","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2022-09-27T17:09:54Z","title_canon_sha256":"1c7dd55f5ddad4e3ac349f46642969f5ba7ecab10cadee27cc9d8731a595dfc9"},"schema_version":"1.0","source":{"id":"2209.13555","kind":"arxiv","version":3}},"canonical_sha256":"ee3b4adcc5d54b7c7186f9ebfdb8b37ead17659bcb63066b0274e25dc0e19293","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ee3b4adcc5d54b7c7186f9ebfdb8b37ead17659bcb63066b0274e25dc0e19293","first_computed_at":"2026-07-05T06:08:09.352373Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:08:09.352373Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"59ACJf0/4gDBStHt+cf4pIiSILJ+dbPLT7NH1J/Sdpq9MFbX6LvbHXLV1dz5CrAJ8GIXk1SQJ3lsiOAHpuX+Aw==","signature_status":"signed_v1","signed_at":"2026-07-05T06:08:09.352865Z","signed_message":"canonical_sha256_bytes"},"source_id":"2209.13555","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c67818d576b3d7046feaec36c2bf800cf612a7b79f911740c89677abc09a97f6","sha256:4a0c3410f93c3a7ae4c9f6b51d3c5f47ba43286d0e9f3f681985595b204b9a51"],"state_sha256":"220610107b4bd6084d8d76473d92086fe42f682a083cc72b02ab90f5932dfc15"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oJa4qD8qzAsZry9lZYoJZuwEnCBBSURYogx+WKB7fSJUgtZgRWEyeM7rFDuAGdj9fgSNnGV3zB9ddegqfrjxCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-21T04:27:00.858069Z","bundle_sha256":"0e3b00a79316d66d58eaaef4fca3be8c40e43da8ac39bd7aab533f6e18b6c077"}}