  Colored knot polynomials possess a peculiar Z-expansion in certain
combinations of differentials, which depends on the representation. The
coefficients of this expansion are functions of the three variables (A,q,t) and
can be considered as new distinguished coordinates on the space of knot
polynomials, analogous to the coefficients of alternative character expansion.
These new variables are decomposed in an especially simple way, when the
representation is embedded into a product of the fundamental ones. The fourth
grading recently proposed in arXiv:1304.3481, seems to be just a simple
redefinition of these new coordinates, elegant but in no way distinguished. If
so, it does not provide any new independent knot invariants, instead it can be
considered as one more testimony of the hidden differential hierarchy
(Z-expansion) structure behind the knot polynomials.
