Conjecture on near-polynomial predicates with a missing zero

Prove or refute the conjecture that there exists δ > 0 such that for the predicate POLY^*_f defined by f(x) = (x_1 + x_2 + x_3)(x_1 + x_2 + x_3 − 1) over F_3 (with the zero vector removed), the non-redundancy satisfies NRD(POLY^*_f, n) = Ω(n^{2+δ}).

Background

The authors consider predicates obtained by removing the all-zero tuple from a low-degree polynomial zero set. For POLY^*_f over F_3 with f(x) = (x_1+x_2+x_3)(x_1+x_2+x_3−1), they show NRD(POLY^*_f, n) = Ω(n^2) and O(n^{2.75}), and they conjecture superquadratic growth.

This conjecture probes whether removing the zero vector from an affine-like structure can significantly increase non-redundancy beyond the obvious quadratic lower bound.