A Geometric Construction for the Goldbach Conjecture: Sphere Helix Identity and Gauss Partition Method

This version (V2) reverses the reading of the Goldbach conjecture: the reflection symmetry p↔D−p is not a property prime pairs happen to satisfy, but their cause. The causal chain is: the functional equation ξ(s)=ξ(1−s) is an intrinsic reflection symmetry of ζ; the Euler product ζ=∏(1−p⁻ˢ)⁻¹ makes ζ identical with the primes; the Equivalence Theorem (V13) makes ζ identical with the sphere helix; on the even-diameter sphere the reflection is realized as the equatorial map ρ:p↔D−p. The conjugate chord product equals p·q — a single term of the Euler product — and is the invariant of ρ. Holding this multiplicative invariant fixed under reflection is what carries primality across the equator, pairing each prime position with its conjugate; a single conjugate prime pair is a Goldbach decomposition. The reflection's fixed point is the equator D/2, the same 1/2 that fixes the critical line of RH and the construction's vertex — the third appearance of one self-conjugate locus. The argument rests entirely on the geometric rigidity of the sphere helix (V13, S1) and the intrinsic symmetry of ζ; no analytic lower bound and no numerical fit is used. V2 replaces V1's balance identity cos(t_p)+cos(t_q)=1/R and its approximate modulus formula with the exact conjugate-chord invariant p·q and the causal role of the symmetry. Bilingual: Chinese and English PDFs.