In the explicit f(W), the jth summand can be written as (-1)^(A+j)/j! times the product over a=0,...,j-1 of [2W-2(A+a)I]. These matrices are integral because 2W=Q*I-sum_s Pi_s. Therefore (R-1)! clears denominators of M_0=V*f(W). Each zero-making multiplier has denominators dividing a product of distinct integers from 1,...,Q, hence dividing Q!. Consequently delta=(R-1)!*Q! clears every coefficient of every replacement row. Filling auxiliary positions with original variables only adds coefficients or discards zeros, so the same delta works after transfer. A common denominator avoids multiplying fresh denominators for every accumulated contribution.