  We claim that the recently discovered universal-matrix precursor for the $F$
functions, which define the differential expansion of colored polynomials for
twist and double braid knots, can be extended from rectangular to
non-rectangular representations. This case is far more interesting, because it
involves multiplicities and associated mysterious gauge invariance of
arborescent calculus. In this paper we make the very first step -- reformulate
in this form the previously known formulas for the simplest non-rectangular
representations [r,1] and demonstrate their drastic simplification after this
reformulation.
