Algebraic Fractal Structure, the Principle of Least Effort, and the Strong Goldbach Conjecture

We present a conditional framework that combines two complementary ideas: (i) a "gearbox" identity that chains ternary representations from the Weak Goldbach Conjecture to produce Goldbach pairs, and (ii) a Principle of Least Additive Effort which heuristically favors partitions into two primes for n ≥ 8. We clarify the two analytical bottlenecks that remain open—the density of odd ternas and the simultaneous level of distribution—and prove that, under either of these two density hypotheses, the framework implies the Strong Conjecture. We include numerical verification up to n ≤ 1010 and discuss lines of attack to close the gaps.