Toward a Dynamical Reconstruction of the Riemann Critical Line

We introduce a recursive multiplicative framework aimed at reconstructing the spectral structure associated with the non-trivial zeros of the Riemann zeta function directly from the prime decomposition of the integers. Starting from the Euler product and the logarithmic derivative of the zeta function, we define a regularized multiplicative detector whose spectral components are generated by logarithmic prime frequencies of the form mlog⁡pm pmlogp. A recursive memory dynamics is then introduced in order to stabilize coherent multiplicative resonances while dispersing decorrelated oscillatory contributions. Within this framework, the critical line Re (s) =1/2Re (s) =1/2Re (s) =1/2 appears as an asymptotically stable equilibrium configuration of the recursive dynamics rather than as an externally imposed analytic symmetry. Persistent spectral structures are characterized through a stability criterion and associated with an asymptotic atomic spectral measure μ∞_μ∞. Using the explicit formula connecting prime distributions and non-trivial zeros of the zeta function, we propose a conjectural identification between this stable measure and the spectral measure generated by the Riemann zeros. The work combines recursive dynamics, spectral stabilization, weak distributional convergence, and numerical experiments investigating the emergence of persistent resonances near known Riemann zero frequencies. Although the present framework does not constitute a proof of the Riemann Hypothesis, it proposes a new dynamical and spectral perspective in which the critical line emerges from the intrinsic multiplicative organization of the integers themselves.