Goldbach Reimagined The First Complete AI-Augmented Structure of Proof

This work undertakes a systematic verification of the Goldbach Conjecture for all even integers n≤1012n \leq 10^{12}n≤1012. The approach combines exhaustive numerical decomposition into sums of two primes with the generation of detailed statistical data, including distribution patterns, decomposition distances, and decomposition counts. Formal proof assistants and AI-guided heuristics were employed to explore intermediate conjectures and structure potential formalizations. The repository includes cleaned datasets, computational summaries, and the complete research manuscript associated with the project. All computations are reproducible and follow a rigorous methodology grounded in computational number theory.