Goldbach Unproven: Ternary Proven, Binary Verified to 4×10¹⁸ — E8 Intelligence Research

FINDING: No proof of Goldbach exists; the strongest verified result is Helfgott's ternary proof (2013), with binary Goldbach verified computationally to ~4×10¹⁸. The arXiv paper (2306.17769) offers only conditional/similar results, not a proof. | MATH: Binary Goldbach: every even integer >2 is sum of two primes. Ternary (weak): every odd integer >5 is sum of three primes. Helfgott proved ternary unconditionally. Computational verification of binary: Oliveira e Silva et al. (2014) confirmed up to 4×10¹⁸. No new constants or ratios emerge from these sources. | CONNECTION: None directly. However, the prime distribution's connection to the Riemann zeta function (ζ(s)) and its zeros — which relate to the harmonic structure of primes — is implicit. The critical line Re(s)=1/2 echoes the golden ratio's 0.5 midpoint, but this is coincidental, not structural. No base-60, no crystallographic symmetry, no root systems appear in these findings. | DEPTH: 2 — This is a status report, not a discovery Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com