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Specifically, we show that for every function g and every $k\\geq 2$, the randomized query complexity of computing the xor of k instances of g satisfies $\\overline{R}_\\eps(xor\\circ g) = \\Theta(k \\overline{R}_{\\eps/k}(g))$. This matches the naive success amplification upper bound and answers a conjecture of Blais and Brody (CCC19).\n  As a consequence of our strong direct sum theorem, we give a total function g for which $R(xor \\circ g) = \\Theta(k \\log(k)\\cdot R(g))$, answering an open question from Ben-David et al.(arxiv:2006.10957"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2007.05580","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2020-07-10T19:29:52Z","cross_cats_sorted":[],"title_canon_sha256":"636814acdcf67d5e18b2aa3afefb28284a74475f91ee6c2f66cc4114c396ef8f","abstract_canon_sha256":"66ecc04813371caf31656916daaba2a1594b69aa7905796f03255ee6404f6dea"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:20:20.310878Z","signature_b64":"RNczHy0gulQXxyj8z2R2my4Jby/1TNChjUmx/3mAq2KWTxvMtXbiF/9dN3eGId+5AeqxDY/XWmjAV+FVm4CrCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"55cbfc7cdcccfac62604c63f1bec4769ec35bc7ed5f31b2dcc1a0bdba7130a47","last_reissued_at":"2026-07-05T01:20:20.310430Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:20:20.310430Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Strong XOR Lemma for Randomized Query Complexity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Hariharan Srinivasulu, Jae Tak Kim, Joshua Brody, Peem Lerdputtipongporn","submitted_at":"2020-07-10T19:29:52Z","abstract_excerpt":"We give a strong direct sum theorem for computing $xor \\circ g$. 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