Goldbach's Conjecture: Placeholder, Proof Retracted

This paper, originally uploaded December 2025, claimed a structural proof of Goldbach's conjecture via a "Goldbach-Jacobsthal bound" asserting that gaps between consecutive Goldbach sieve survivors in [3, n/2] are O((log n)²). On review in May 2026, the proof claim is retracted on five grounds: (a) the parity barrier — Selberg's obstruction to sieve methods — was not engaged at any point in v1.0, despite being the precise obstruction the field has known since the 1950s and the reason no Goldbach proof by pure sieve methods exists despite seventy years of effort by Iwaniec, Friedlander, Maynard, Tao and others; (b) the central Goldbach-Jacobsthal "theorem" of v1.0 Section 3.2 is asserted via an average-count argument with O(p_k) error terms, not proven as a pointwise lower bound — the error term is precisely where the parity obstruction reappears; (c) v1.0's own Section 3.4 empirical table self-refutes the headline claim — the ratio max_gap/(log n)² reads 0.75, 2.33, 2.49, 3.96 across four decades of n, with decade-on-decade ratios of 3.1×, 1.07×, 1.59× (uneven but with no return to bounded behaviour), falsifying bounded O((log n)²); (d) the structural threshold N₀ in v1.0 Section 4.4 is undefined — the bridge to Oliveira e Silva's 4×10¹⁸ computational verification requires N₀ to be effectively bounded and explicitly below that figure, but N₀ is not computed in v1.0; (e) the generalised-method implication is not engaged — v1.0 invokes the same machinery for Goldbach, Twin Primes, and Cramér without addressing the consequence that, if such machinery worked, it would dissolve the parity barrier (a headline result more significant than any of the three). What survives is nothing original. The Goldbach sieve definition (two classes per prime) is standard; the link between the sieve's survival structure and the twin prime constant C₂ is folklore in sieve theory (properly stated via the normalised Hardy–Littlewood singular series, not v1.0's loose ∏(q−2)/q shorthand); the empirical Goldbach-pair counts are correct but unremarkable; the computational verification to 4×10¹⁸ stands in the published record (Oliveira e Silva, Herzog, Pardi 2014). v1.0's Section 3.4 table is preserved here as documented counter-evidence to the headline claim. This v2.1 is a placeholder marking the retraction honestly; the slot is held in case future work in the 2I Universe Programme produces a structural Goldbach argument that explicitly engages the parity barrier, but this placeholder makes no commitment that it will be filled.