This document collects supplementary notes to the core-decomposition theory. It includes a heuristic discussion of the Goldbach and Legendre conjectures based on the square-recurrence conjecture, a historical/geometric background on nested radicals and Chebyshev polynomials, and the higher-power recurrence conjecture. These notes are not formal proofs but illustrate the potential and mathematical depth of the theory.
Kang A. (Sun,) studied this question.