A Dynamical Stability Framework for the Riemann Hypothesis

This paper proposes a novel physics-inspired approach to prove the Riemann Hypothesis (RH), arguing that the observed behavior of prime numbers forces all nontrivial zeros of the Riemann zeta function to lie on the critical line Re(s) = 1/2. Core Argument: The explicit formula connecting primes to zeta zeros shows eternal, undamped oscillations in prime-counting functions Any dynamical system reproducing these oscillations must follow a universal template:ȯ(t) = -jkMo(t) + S(t)where M is self-adjoint and S(t) is bounded For stable, bounded evolution across all time, the spectrum of M must lie exactly on Re(s) = 1/2 Any deviation would cause exponential growth/decay, contradicting observed prime behavior Key Insight:The Riemann Hypothesis emerges as a necessary condition for dynamical stability - the primes' persistent oscillatory pattern can only exist if all zeta zeros are perfectly aligned on the critical line. Significance:This framework bridges number theory and dynamical systems, offering a physical interpretation of RH as a stability requirement rather than purely a mathematical conjecture.