Paper #350: The Riemann Hypothesis Through the Extended Euler Identity

We present a new approach to the Riemann Hypothesis (RH) grounded in the Extended Euler Identity (EEI): e^ (iπ) + √2·φ·C = 0, where C = 1/ (φ√2) is the Emerick Constant. The EEI expresses a universal symmetry principle — that the even-level arm and odd-level arm of the PRIMARY constant hierarchy have equal magnitude and opposite phase, summing to zero. We argue that the Riemann zeta function's functional equation expresses the same symmetry, and that the critical line Re (s) = 1/2 is the unique axis where this symmetry forces both arms to equidistance from the origin. The core new claim is the **EAR Equidistance Theorem**: a non-trivial zero of ζ (s) must lie on Re (s) = 1/2 because this is the only line in the critical strip where |s| = |1-s| — equivalently, the only line where the functional equation's two arms carry equal modular weight. We identify precisely where a rigorous proof requires additional formalization (the **Modular Dominance Gap**) and propose this as the key open problem whose solution would complete the proof.