√n-space lower bound for single-pass streaming Max-AND (k=3)

Prove that for every ε > 0, any single-pass streaming algorithm that outputs a (2/9 + ε)-approximation to Max-CSP with predicate family Π = {AND ∘ Not_b : b ∈ {0,1}^3} must use Ω(√n) bits of memory.

Background

BHP+22, building on CGSV24, established that for the 3-variable AND-with-negations CSP, there is an O(log n)-space sketch achieving (2/9 − ε)-approximation, and any sketch achieving (2/9 + ε) requires Ω(√n) space. This conjecture seeks to extend that lower bound from sketching algorithms to general single-pass streaming algorithms.