For fixed k and B=(log n)^{O_k(1)}, initial-check construction and candidate enumeration cost exp((log n)^{O_k(1)}). Its logarithm is o(rho(n)), rho(n)=n(log log n)^2/sqrt(log n). Multiplying by the 2^{O_k(rho(n))} cost per common-zero query still gives (n+m)^{O_k(1)}2^{O_k(rho(n))}. Space is polynomial: initial checks, shifts and local matrices have polynomial descriptions; keep only the current rows, one candidate, the best row and its exact count. Each common-zero call already has a polynomial-workspace guarantee, and that workspace is reused between calls. Empty formulas and empty clauses are handled directly. These are asymptotic guarantees, not demonstrated practical speedups.