Goldbach Gap Studies v2 — Empirical Variation of Goldbach Partition Counts up to 10⁶ (Unicode Math Edition)

This paper presents an expanded empirical analysis of Goldbach partition counts G₂(n) for even integers up to 1 000 000. 
Using a high-precision fast-Fourier convolution method, all unordered prime pairs (p,q) satisfying p+q=n were computed 
and examined for inter-even variations Δ(n)=G₂(n+2)−G₂(n). 

Results reveal large yet statistically stable fluctuations whose average scale grows slowly with n. 
The study includes reproducible datasets, plots, and descriptive fits, offering a quantitative baseline 
for future analysis of partition regularity. 

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