On Goldbach Conjecture

This paper presents a proof of Goldbach's Conjecture by modeling the problem as a connectivity theorem in an additive graph constructed from the prime number set. Using a contradiction-based strategy and leveraging modern prime gap bounds, we demonstrate that every even integer must be the sum of two primes. The argument is supported by computational verification and analytic number theory, culminating in a contradiction that no such gap-based counterexample can exist.