The grid S={-L,...,L-1}, L=2^a, is a complete residue system modulo 2^(a+1). Write C_prime(t)=product_{q in S,q!=t}(t-q). For fixed t, nonzero differences t-q have valuation at most a. Exactly 2^(a-j) of them have valuation j, for 0<=j<=a. Therefore v_2(C_prime(t)) is the same sum of these levels for every t, including zero. This is equality of valuations, not equality of the products themselves. The uniform counts permit cancellation of powers of two when using local coordinates t+alpha z with alpha=2^(a+1).