{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:NDSH3SH4UCJPIUOHVJYC5STRAL","short_pith_number":"pith:NDSH3SH4","canonical_record":{"source":{"id":"2406.04530","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.NA","submitted_at":"2024-06-06T22:06:18Z","cross_cats_sorted":["cs.NA","math.OC"],"title_canon_sha256":"d6c79a172049161b2c130c274aa3e96f323e8b734492db492dfd68b3355bbb59","abstract_canon_sha256":"1791da551cd64132d1ac5f0b8be81dabea33a9f8a055e8a3db6daea65bad5e65"},"schema_version":"1.0"},"canonical_sha256":"68e47dc8fca092f451c7aa702eca7102e773a669654f4354d0ae21a205b98e06","source":{"kind":"arxiv","id":"2406.04530","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.04530","created_at":"2026-05-18T03:09:46Z"},{"alias_kind":"arxiv_version","alias_value":"2406.04530v1","created_at":"2026-05-18T03:09:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.04530","created_at":"2026-05-18T03:09:46Z"},{"alias_kind":"pith_short_12","alias_value":"NDSH3SH4UCJP","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"NDSH3SH4UCJPIUOH","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"NDSH3SH4","created_at":"2026-05-18T12:33:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:NDSH3SH4UCJPIUOHVJYC5STRAL","target":"record","payload":{"canonical_record":{"source":{"id":"2406.04530","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.NA","submitted_at":"2024-06-06T22:06:18Z","cross_cats_sorted":["cs.NA","math.OC"],"title_canon_sha256":"d6c79a172049161b2c130c274aa3e96f323e8b734492db492dfd68b3355bbb59","abstract_canon_sha256":"1791da551cd64132d1ac5f0b8be81dabea33a9f8a055e8a3db6daea65bad5e65"},"schema_version":"1.0"},"canonical_sha256":"68e47dc8fca092f451c7aa702eca7102e773a669654f4354d0ae21a205b98e06","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:09:46.935418Z","signature_b64":"rZAuQOuaM/Mi9cRyHTt/GN3z4wEKFFUDjBmAyaaqQB2bA8+dgJSIKTkoJnDsWsG7rg1gnYm0nk3FO4eiU2mGAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"68e47dc8fca092f451c7aa702eca7102e773a669654f4354d0ae21a205b98e06","last_reissued_at":"2026-05-18T03:09:46.934616Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:09:46.934616Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2406.04530","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":"2026-05-18T03:09:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oPr8lm/CuHcRCmWUcUNBmcDZANbagi7mBgHPJql8k93CrsXswgWmIpr8f1/d2+8O0MUD4xQFLu4ToHwaYkdmDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T23:31:01.221016Z"},"content_sha256":"ae3fd77d2cee0474e025974132f89e2e50e91ce07dfed939617b01c8e7bc9c85","schema_version":"1.0","event_id":"sha256:ae3fd77d2cee0474e025974132f89e2e50e91ce07dfed939617b01c8e7bc9c85"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:NDSH3SH4UCJPIUOHVJYC5STRAL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A general framework for floating point error analysis of simplex derivatives","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.NA","math.OC"],"primary_cat":"math.NA","authors_text":"Amy Wiebe, Warren Hare, Yiwen Chen","submitted_at":"2024-06-06T22:06:18Z","abstract_excerpt":"Gradient approximations are a class of numerical approximation techniques that are of central importance in numerical optimization. In derivative-free optimization, most of the gradient approximations, including the simplex gradient, centred simplex gradient, and adapted centred simplex gradient, are in the form of simplex derivatives. Owing to machine precision, the approximation accuracy of any numerical approximation technique is subject to the influence of floating point errors. In this paper, we provide a general framework for floating point error analysis of simplex derivatives. Our fram"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.04530","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":""},"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":"2026-05-18T03:09:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4tmK/SEFiYcBDiDHPIyRurdWtwE108MKXe5crurF6VI+BZQAnb0vc5ELhVs4dtMLK0TTL61OaNCBQUBTvCdOCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T23:31:01.221724Z"},"content_sha256":"503053970afd28ae3b8abe5e3d15e078ff76ade1cdad5f211452e2088f7f96ec","schema_version":"1.0","event_id":"sha256:503053970afd28ae3b8abe5e3d15e078ff76ade1cdad5f211452e2088f7f96ec"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NDSH3SH4UCJPIUOHVJYC5STRAL/bundle.json","state_url":"https://pith.science/pith/NDSH3SH4UCJPIUOHVJYC5STRAL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NDSH3SH4UCJPIUOHVJYC5STRAL/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":"2026-05-22T23:31:01Z","links":{"resolver":"https://pith.science/pith/NDSH3SH4UCJPIUOHVJYC5STRAL","bundle":"https://pith.science/pith/NDSH3SH4UCJPIUOHVJYC5STRAL/bundle.json","state":"https://pith.science/pith/NDSH3SH4UCJPIUOHVJYC5STRAL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NDSH3SH4UCJPIUOHVJYC5STRAL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:NDSH3SH4UCJPIUOHVJYC5STRAL","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":"1791da551cd64132d1ac5f0b8be81dabea33a9f8a055e8a3db6daea65bad5e65","cross_cats_sorted":["cs.NA","math.OC"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.NA","submitted_at":"2024-06-06T22:06:18Z","title_canon_sha256":"d6c79a172049161b2c130c274aa3e96f323e8b734492db492dfd68b3355bbb59"},"schema_version":"1.0","source":{"id":"2406.04530","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.04530","created_at":"2026-05-18T03:09:46Z"},{"alias_kind":"arxiv_version","alias_value":"2406.04530v1","created_at":"2026-05-18T03:09:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.04530","created_at":"2026-05-18T03:09:46Z"},{"alias_kind":"pith_short_12","alias_value":"NDSH3SH4UCJP","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"NDSH3SH4UCJPIUOH","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"NDSH3SH4","created_at":"2026-05-18T12:33:37Z"}],"graph_snapshots":[{"event_id":"sha256:503053970afd28ae3b8abe5e3d15e078ff76ade1cdad5f211452e2088f7f96ec","target":"graph","created_at":"2026-05-18T03:09:46Z","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":"Gradient approximations are a class of numerical approximation techniques that are of central importance in numerical optimization. In derivative-free optimization, most of the gradient approximations, including the simplex gradient, centred simplex gradient, and adapted centred simplex gradient, are in the form of simplex derivatives. Owing to machine precision, the approximation accuracy of any numerical approximation technique is subject to the influence of floating point errors. In this paper, we provide a general framework for floating point error analysis of simplex derivatives. Our fram","authors_text":"Amy Wiebe, Warren Hare, Yiwen Chen","cross_cats":["cs.NA","math.OC"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.NA","submitted_at":"2024-06-06T22:06:18Z","title":"A general framework for floating point error analysis of simplex derivatives"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.04530","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:ae3fd77d2cee0474e025974132f89e2e50e91ce07dfed939617b01c8e7bc9c85","target":"record","created_at":"2026-05-18T03:09:46Z","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":"1791da551cd64132d1ac5f0b8be81dabea33a9f8a055e8a3db6daea65bad5e65","cross_cats_sorted":["cs.NA","math.OC"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.NA","submitted_at":"2024-06-06T22:06:18Z","title_canon_sha256":"d6c79a172049161b2c130c274aa3e96f323e8b734492db492dfd68b3355bbb59"},"schema_version":"1.0","source":{"id":"2406.04530","kind":"arxiv","version":1}},"canonical_sha256":"68e47dc8fca092f451c7aa702eca7102e773a669654f4354d0ae21a205b98e06","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"68e47dc8fca092f451c7aa702eca7102e773a669654f4354d0ae21a205b98e06","first_computed_at":"2026-05-18T03:09:46.934616Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:09:46.934616Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rZAuQOuaM/Mi9cRyHTt/GN3z4wEKFFUDjBmAyaaqQB2bA8+dgJSIKTkoJnDsWsG7rg1gnYm0nk3FO4eiU2mGAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:09:46.935418Z","signed_message":"canonical_sha256_bytes"},"source_id":"2406.04530","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ae3fd77d2cee0474e025974132f89e2e50e91ce07dfed939617b01c8e7bc9c85","sha256:503053970afd28ae3b8abe5e3d15e078ff76ade1cdad5f211452e2088f7f96ec"],"state_sha256":"f66a3a433def7bbec86c4613d0e3dfac3a3332237b5a66c09cf64d2f4bdc879d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6g4051DCRmKtw6cWJjS9Re2YAECnlrnXyCynMQg81rjVrXw7wmareVXXF7Avf7q7Hew6s7KaPhXHe9rjRIJvDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T23:31:01.224863Z","bundle_sha256":"1c0d61e0978704d535ac0c947bb57f4c405b9ad9fdaf80e7b7972b9db35cf985"}}