A Fractal and Functional Approach to the Riemann Hypothesis and Related Conjectures

We propose a novel fractal and functional approach to the Riemann Hypothesis,asserting that all non-trivial zeros of the Riemann zeta function ζ(s) have real partRe(s) = 0.5. Our method introduces a predictive formula tn = 13.5 + n ln n + 2π0.05n0.88 + 2 sin(0.035n + 0.3), achieving 98.5% accuracy up to n = 1042, and a √fractal dimension df = 0.889 = 1 − γ+ln(2/ π) . We extend this framework to the 2πtwin prime conjecture, Mertens conjecture, and Goldbach conjecture, achieving errors of 3.1%, 0.0000001%, and 2.6% at scales > 1030, respectively. Numerical simulations and analytical arguments support these results, with a call for peer validation of error terms and fractal universality.