I've been perusing finiteness theorems limit cycles and could really use Archimedean Equivalence Classes to solve Hilbert's 16th problem from first principles. However, I am repulsed by germ theory, and that is where Archimedean Equivalence Classes are derived from. Attached are the limit cycles I'd like to equate in a Milky Way Equivalence Class of sorts because their relative positions are easily discernible in observational cyclic cohomology.

So as not to be accused of tossing word salad, my sources are Volume 50 & 94 of the American Mathematical Society's Proceedings.