Function pou_as_product 

pub fn pou_as_product(n: usize) -> Poly

The closed form of the partition of unity: the product Π_{v<n} ((1+x_v) + x_v) of the per-coordinate atoms. By distributivity Σ_a Π_i f_{i,a_i} = Π_i (f_{i,0} + f_{i,1}), this equals partition_of_unity — a sum of 2ⁿ products rewritten as a product of n sums. Since every atom is 1 (pou_atom), the product is 1 for every n. This is the ratchet to n = ∞: not 2ⁿ terms checked one cube at a time, but n identical unit factors.