Information Dynamical System (IDS): Structural Attractors and the Geometric Birth of Time

This paper proposes a dual-attractor framework for information dynamical sys- tems (IDS), identifying two universal entropy stability points: K = 1 in the tem- poral domain, and ℜ(s) = 1 2 in the spectral domain of the Riemann zeta function. These points correspond to minimal entropy curvature basins and serve as struc- turally protected attractors under small perturbations. We formalize this through a curvature-based entropy model and support it with numerical and theoretical analysis. This framework offers a new foundation for entropy modeling in AI, time theory, and zero-point physics.