We apply the Wästlund reflection r -> 1/r on the real projective line RP¹ to the arithmetic of Goldbach's conjecture, obtaining three proved results and one conditional chain. (i) We introduce the von Mangoldt weighted Goldbach ratio distribution: for fixed even n, weight each prime pair (p, q) with p+q=n by log (p) log (q) and study the CDF of r=p/q. The Cramér model for this distribution is FCr (r) = r/ (1+r), the unique CDF satisfying the Wästlund reflection symmetry F (r) +F (1/r) =1 in the continuous setting. (ii) We prove three Cramér-Lambda golden identities: FLambda (phi^-1) = 2phi^-2 and the Goldbach partition of unity 2phi^-2 + phi^-3 = 1, together with the universal identity FC (phi^-1) = Cphi^-2 for any Cramér-type distribution FC (r) = C*r/ (1+r). All three proofs are one line from phi² = phi+1. (iii) We prove the Goldbach-Wästlund duality theorem: over all pairs (p, q) with p+q=n, the von Mangoldt weighted CDF satisfies F (r) +F (1/r^-) = 1, making F (r) = r/ (1+r) the unique CDF consistent with the Wästlund reflection. (iv) We establish a scope theorem: the Pythagorean-Golden duality for consecutive prime gaps does not extend to Goldbach pairs. (v) Conditionally on the equivalence of Form (13) with the Riemann Hypothesis, we derive the chain Form (13) iff kappa=0 iff RH implies G (n) > 0 for all sufficiently large n.
Paul Buchanan (Sun,) studied this question.