  The theory of DAHA-Jones polynomials is extended from torus knots to their
arbitrary iterations (for any reduced root systems and weights), which incudes
the polynomiality, duality and other properties of the DAHA superpolynomials.
Presumably they coincide with the reduced stable Khovanov-Rozansky polynomials
in the case of non-negative coefficients. The new theory matches well the
classical theory of algebraic knots and (unibranch) plane curve singularities;
the Puiseux expansion naturally emerges. The corresponding DAHA
superpolynomials are expected to coincide with the reduced ones in the
Oblomkov-Shende-Rasmussen Conjecture upon its generalization to arbitrary
dominant weights. For instance, the DAHA uncolored superpolynomials at a=0, q=1
are conjectured to provide the Betti numbers of the Jacobian factors of the
corresponding singularities.
