The recent work [Devadas-Hopkins-Kalai-Kothari-Lombardi-Mathialagan, STOC 2026] proposed a low-norm Nullstellensatz hypothesis for the "AND code": every polynomial vanishing on the "AND-code ideal'' should admit a Nullstellensatz decomposition over the local AND constraints whose total coefficient (\ell_1)-norm is only polynomially larger than the (\ell_1)-norm of .
We give a counterexample to this conjecture by proving an exponential lower bound on the total coefficient (\ell_1)-n