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Our result builds on a new family of random Boolean functions that can be viewed as a two-level extension of Talagrand's random DNFs.\n  Beyond monotonicity, we also prove a lower bound of $\\tilde{\\Omega}(n^{2/3})$ for any two-sided and adaptive algorithm, and ","authors_text":"Erik Waingarten, Jinyu Xie, Xi Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2017-02-22T20:38:35Z","title":"Beyond Talagrand Functions: New Lower Bounds for Testing Monotonicity and Unateness"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.06997","kind":"arxiv","version":2},"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:e050ef4d11cc4592dceab38217c5a8c7510f16626b81c0493c2f0d05816aa485","target":"record","created_at":"2026-05-18T00:37:47Z","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":"8c26f156f3807595f29d25441a2015a14e2b9a27b5bf701d4b57b47be73857e7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2017-02-22T20:38:35Z","title_canon_sha256":"2e63c525968f1662326b338bf36b3d5c3dbe9efc7bf871dad3edb52ef0bdfeef"},"schema_version":"1.0","source":{"id":"1702.06997","kind":"arxiv","version":2}},"canonical_sha256":"ae4c321f8c74415ad8d8839b47db1badc91888e77d37b1142e97068a4bc0d9da","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ae4c321f8c74415ad8d8839b47db1badc91888e77d37b1142e97068a4bc0d9da","first_computed_at":"2026-05-18T00:37:47.888986Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:37:47.888986Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"x2Rb0jOga3lF6QPC/huChrwoEc3d/hSkVggSNMxE0+0B5lXfy8zytil343MLixWIv8SThuGxND4uwzTTH/AGAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:37:47.889641Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.06997","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e050ef4d11cc4592dceab38217c5a8c7510f16626b81c0493c2f0d05816aa485","sha256:64378a678d53d22a69e60b4d49b239c80898f02d0da446355b169f5c42e7ab2e"],"state_sha256":"b541e9922d65ae3b8e72e9b737aa3d3eaea6b757e16c26bdc8202c37bdbf5d20"}