A Proof of the Riemann Hypothesis via the Golden Ratio Numeral System

While investigating the mathematical foundations of Qi theory in The Mathematical Essence of the Universe, the author systematically examined the relationship between the golden ratio and recursive algorithms. Following the "-ary system + recursive algorithm" approach, new proofs of Fermat's Last Theorem and Goldbach's conjecture were completed. These two works share the same methodological core: represent integers in the golden ratio numeral system (the -ary system), thereby exposing the deep recursive structure of integers, and then analyze them using recursive algorithms — which is, in essence, the modern mathematical expression of "Fibonacci numbers + infinite descent. " Encouraged by this, the present paper applies the same approach to the Riemann hypothesis. The Riemann hypothesis concerns the global distribution of prime numbers, which may appear different from the additive decomposition problem of Goldbach's conjecture, but within the -ary framework, the two share the same prime number sieve automaton. The core of the proof is the Uniformity-Symmetry Golden Law: in the -ary system, the most uniform distribution of primes in the space of legal strings directly implies the spectral symmetry of the zero distribution of the prime generating function, forcing all non-trivial zeros onto the critical line (s) =1/2. This extremality is jointly enforced by the optimal coverage and optimal robustness properties of. The entire proof avoids the complicated analytic continuations and exponential sum estimates of traditional analytic number theory, relying instead on the intrinsic mathematical structure of the -ary system. Note: The complete Chinese version of this paper is also provided as a supplementary file.