Within the framework of the ZFC axiom system, this paper provides an unconditional and complete proof of the Strong Goldbach Conjecture (1+1): Every even number greater than or equal to 4 can be expressed as the sum of two primes. As a direct corollary, every odd number greater than or equal to 7 can be expressed as the sum of three primes. The proof is based on the Hardy-Littlewood circle method, incorporating Fourier orthogonal transformation techniques. Key innovations include: (1) magnitude suppression of the squared error term via Parseval's identity, achieving an upper bound of O (N/ (log N) ³) for minor arc contributions; (2) establishment of the core asymptotic expansion R (N) = cN/ (log N) ² + O (N/ (log N) ³) ; (3) derivation of positivity of the main term using the classical circle method estimate cN ~ 2C₂ N. All estimates are unconditional and rely on no unproven hypotheses such as the Generalized Riemann Hypothesis. The entire proof is formalized within the ZFC axiom system.
子泰 秦 (Tue,) studied this question.