{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:WF3FU5ZRAZK75A2DEEAYTYSDOJ","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":"d02d150fe41d30716013376a2c926c12195b9220ea6b1f3db18c1309201c0863","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-07-15T20:21:43Z","title_canon_sha256":"62c3a94589385f1c15a66c22732d525c0b14a7bc93e0fea8de6f023fbd6f2c1f"},"schema_version":"1.0","source":{"id":"1307.4097","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.4097","created_at":"2026-05-18T03:18:19Z"},{"alias_kind":"arxiv_version","alias_value":"1307.4097v1","created_at":"2026-05-18T03:18:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.4097","created_at":"2026-05-18T03:18:19Z"},{"alias_kind":"pith_short_12","alias_value":"WF3FU5ZRAZK7","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"WF3FU5ZRAZK75A2D","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"WF3FU5ZR","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:2756676483e18d2a38d727ced5c9842df38aa84edb08c92640b284d1a4ad0978","target":"graph","created_at":"2026-05-18T03:18:19Z","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 problem of accurate computation of the finite difference $f(\\x+\\s)-f(\\x)$ when $\\Vert\\s\\Vert$ is very small. Direct evaluation of this difference in floating point arithmetic succumbs to cancellation error and yields 0 when $\\s$ is sufficiently small. Nonetheless, accurate computation of this finite difference is required by many optimization algorithms for a \"sufficient decrease\" test. Reps and Rall proposed a programmatic transformation called \"computational divided differencing\" reminiscent of automatic differentiation to compute these differences with high accuracy. The run","authors_text":"Stephen Vavasis","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-07-15T20:21:43Z","title":"Some notes on applying computational divided differencing in optimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.4097","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:d865cb5c597f431d323337718fcab6229c1f3290eed33161849a72884962dbe5","target":"record","created_at":"2026-05-18T03:18:19Z","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":"d02d150fe41d30716013376a2c926c12195b9220ea6b1f3db18c1309201c0863","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-07-15T20:21:43Z","title_canon_sha256":"62c3a94589385f1c15a66c22732d525c0b14a7bc93e0fea8de6f023fbd6f2c1f"},"schema_version":"1.0","source":{"id":"1307.4097","kind":"arxiv","version":1}},"canonical_sha256":"b1765a77310655fe8343210189e2437279a3e404f2939ec47a520833d87992ca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b1765a77310655fe8343210189e2437279a3e404f2939ec47a520833d87992ca","first_computed_at":"2026-05-18T03:18:19.680394Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:18:19.680394Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EQPbxk2fpb0iXe/+6C6pOITmDemW13qKXWmmbUYIqrTFfuRvc0hP2RzmrhXs4kiTU5YFnNOp5tluANhO1vkoAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:18:19.681218Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.4097","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d865cb5c597f431d323337718fcab6229c1f3290eed33161849a72884962dbe5","sha256:2756676483e18d2a38d727ced5c9842df38aa84edb08c92640b284d1a4ad0978"],"state_sha256":"b342fde4ffa6b98da2de1776bd2aa8fc18ce82e4ea77db4474e494087f9ba200"}