Goldbach Conjecture: Proposal of a Geometric Approach with Holes and Shadows in Odd Numbers

Goldbach's conjecture has challenged numerous minds throughout the ages. It is a problem at once soelementary and yet so complex that it impinges upon the fundamental roots of numbers in their most primordialform. Various techniques have been attempted; however, the core obstacle remains constant: the tension betweenthe multiplicative relationship that composes natural numbers via primes versus addition, and the 'sink' where allattempts converge—the pseudo-random distribution of prime numbers. This work proposes an alternativeapproach: the construction of a framework that transforms additive analysis into a geometric one through thecreation of a metric, thereby bypassing the distribution of primes by addressing holes and shadows within theodd integers.