Diophantine imaging reveals the broken symmetry of sums of integer cubes

Origin and purpose

We call “Diophantine Imaging” a method of arithmetic geometry by which solutions of diophantine equations are represented over the unit circle based on their prefixes in certain bases. The purpose of this method is to keep the representation contained for arbitrarily large numbers and maintain an intuitive metric based on converging series of angular distances, which in itself is borrowed from p-adic arithmetic. Since we intend to make this method accessible to the widest possible audience in both mathematics and computer science, we will be adding here even the most…