Goldbach’s Conjecture as a Resolution Condition Under Entropy Geometry

This letter presents a structural derivation of the Goldbach Conjecture (GC) from the Total Entropic Quantity (TEQ) framework, assuming the Riemann Hypothesis (RH) as an emergent property of entropy geometry. Within TEQ, the spectrum of primes corresponds to entropy-stable modes arising from curvature in distinguishability space. We show that the additive closure condition expressed by GC is structurally required for entropy resolution to remain complete, and thus follows necessarily from TEQ and RH. This argument is not statistical or empirical—it is geometric. Though compact, it rests on a profound shift in the conception of mathematical truth: from formal derivation to structural necessity.