CWR sequence of invariants of alternating links and its properties

We present the CWR invariant, a new invariant for alternating links, which builds upon and generalizes the WRP invariant. The CWR invariant is an array of two-variable polynomials that provides a stronger invariant compared to the WRP invariant. We compare the strength of our invariant with the classical HOMFLYPT, Kauffman 3-variable, and Kauffman 2-variable polynomials on specific knot examples. Additionally, we derive general recursive "skein" relations, and also specific formulas for the initial components of the CWR invariant (CWR₂ and CWR₃) using weighted adjacency matrices of modified Tait graphs.