Existence of Goldbach Partitions for Large Even Numbers under the 1/6 N Strong Constraint and a Rigorous Proof of the Order of Magnitude of the Goldbach Counting Function

This paper studies the counting function of even numbers expressed as sums of two primes. Using the 1/6N constraint and symmetric sieve method, we prove the discrete monotonicity of the counting function, which provides a new proof idea for Goldbach's Conjecture.