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For a distribution $\\nu$ supported over $\\{x\\in \\{0,1\\}^k:\\sum_{i=1}^k x_i=0 \\text{ (mod 2)} \\}$, with marginal distribution $\\mu_p$ in each coordinate, the corresponding $k$-query linearity test $\\text{Lin}(\\nu)$ proceeds as follows: Given query access to a function $f:\\{0,1\\}^n\\to \\{-1,1\\}$, sample $(x_1,\\dots,x_k)\\sim \\nu^{\\otimes n}$, query $f$ on $x_1,\\dots,x_k$, and accept if and only if $\\prod_{i\\in [k]}f(x_i)=1$.\n  Building on the work of Bhangale, Khot, and Minzer (STOC '23), we"},"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":"2502.01900","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2025-02-04T00:16:23Z","cross_cats_sorted":[],"title_canon_sha256":"8209ff9b4cb3cb67ccac729ce66828ded0d8385081dfdecea49973c3217d98c5","abstract_canon_sha256":"a65017a2b31e2c9a221e106d5c23d0de502012d348d405683359a6c58e0bb907"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:09:20.899720Z","signature_b64":"fIJcPTT3j9xhMFjzf4NbG8VkuzH+xbtEd/Msb9l45U8QYCjWgYTt1VQTYPq9pxdyrrIZeero6wSRncVknnMSAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"531d22cabd91797f6b3a853262e578fc5b07ffa4cccde4d413f625691abe9e3e","last_reissued_at":"2026-07-05T10:09:20.899264Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:09:20.899264Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Biased Linearity Testing in the 1% Regime","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Kunal Mittal, Subhash Khot","submitted_at":"2025-02-04T00:16:23Z","abstract_excerpt":"We study linearity testing over the $p$-biased hypercube $(\\{0,1\\}^n, \\mu_p^{\\otimes n})$ in the 1% regime. 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