For fixed beta, target coefficients factor over packet-group row products. Each substituted source form uses only column bits in its own source group. The remaining original tensor factors also partition by group. Distributivity therefore turns the sum over independent X,Y bits into the product over groups of the child contractions Z_(g,beta). Summing over all feasible beta gives F(t+alpha zeta)=sum_beta product_g Z_(g,beta) modulo 2^p_t. Omitted tuples vanish by their coefficient divisibility. No extra assignment multiplicity or factorial appears; the identity is an equality of ring elements, not just agreement on whether a count is nonzero.