The hierarchy conjecture for products of irreducible polynomials in PRACs

Let $n_1,n_2,r_1,r_2,k,\ell$ be positive integers with $n_1<r_1<2n_1$, and let $f_1(x),\ldots,f_\ell(x)$ be irreducible polynomials of degree $n_1n_2$ and exponent $r_1r_2$. Suppose that the set of sequences generated by each $f_i(x)$ forms an $(r_1,r_2;n_1,n_2)$-PRAC. Product-folding claim. For every integer $k$ satisfying $1\leq k\leq\ell$, folding the sequences generated by $\prod_{i=1}^k f_i(x)$ yields an $(r_1,r_2;n_1,kn_2)$-PRAC. This gives a proposed hierarchy of PRACs obtained by multiplying irreducible polynomials; the supplied text does not establish whether the claim is proved or remains open.