A Geometric Axiom System in Which the Riemann Hypothesis Follows from a Positive K-Channel Obstruction (V8)

We do not claim a proof of the Riemann Hypothesis (RH) within classical complex analysis. We establish a geometric axiom system — the Wang 2026 Geometric Identity Principle — under which RH follows immediately from a positive-definite K-channel obstruction. The axiom system replaces the two-dimensional complex-plane representation of zeta(s) with a three-dimensional spherical-helical topology Xi_geo(s), in which the non-trivial zeros of zeta are equivalent to the absolute closure of the full three-dimensional structure. The third channel, denoted K_ob(sigma), encodes the K-parity radial imbalance and depends only on sigma, not on t. Its positivity for sigma != 1/2 provides the obstruction. Under Axiom 1, the proof reduces to a five-step contradiction chain: zeta(s_0) = 0 (assumption) => Xi_geo(s_0) = 0 (Axiom 1: Wang 2026 Geometric Identity) => K_ob(sigma_0) = 0 (three-channel decomposition) => D_n(sigma_0) = 0 for all n >= 2 (K_ob positive-definite) => sigma_0 = 1/2 (unique algebraic solution) => Re(s_0) = 1/2 Axiom 1 holds the same logical position as Euclid's parallel postulate: an independent geometric premise whose acceptance generates a coherent and rigid structure. If Axiom 1 is rejected, the present framework collapses but classical analysis is unaffected. If Axiom 1 is accepted, RH follows in five steps. This work is part of the RHR (Resonant Helix Reductionism) framework, developed independently by the author over twenty years. Author: Dirk Wang (王立鑫) Email: [email protected]