A Hidden Geometric Order in Goldbach Pairs:Sunflower Helices and Predictive Deviation Clustering

We introduce a new geometric and algorithmic framework for the search of Goldbach pairs based on the organization of admissible deviations around the midpoint of an even integer. By embedding admissible deviations into a sunflower phase space and a normalized helical geometry, we observe a robust concentration of Goldbach-successful deviations along narrow geometric lanes. This structure persists across multiple scales, from 10^9 up to at least 10^26, and leads naturally to a phase-guided algorithm that reduces the number of primality tests required to find a Goldbach pair. Extensive numerical experiments demonstrate a stable efficiency gain relative to random search strategies. The results suggest the presence of a universal geometric organization underlying the Goldbach conjecture and provide a new perspective on additive problems involving prime numbers.