Bending the Riemann Critical Strip to a Lunula: No Zeroes in 1/2 < Re(z) < 1

The critical strip of the Riemann \(\zeta(z)\) is transformed into a crescent-like lunula and the critical line into the unit circle by a conformal transformation. In the new extended complex plane, the argument principle is used to show that there are no zeroes outside of the unit circle, thus proving that there are no zeroes in the right half of the strip, \(1/2 < Re(z) < 1\). This constitutes a truly elementary proof of the Riemann Hypothesis.