This preprint numerically investigates the distribution of minor-arc energy in the binary Goldbach problem using weighted exponential sums involving the von Mangoldt function. It introduces a danger-score framework to measure arithmetic proximity to low-complexity rationals and studies how minor-arc energy is distributed across different danger levels. The computations suggest that minor-arc energy is strongly concentrated in low-danger regions and that rescaling the danger threshold by (logN) ², gives the best empirical collapse of the cumulative distributions over the tested range, up to N=128000.
Dimitrios Dimitrios Morakis (Wed,) studied this question.