Mathematical Model Shows Smooth Flow Converging to Discrete Integer Values

Researchers present an exactly solvable gradient flow model with a periodic potential. At every finite time, the flow is a smooth, strictly increasing bijection of the real line. As time tends to infinity, the flow collapses intervals onto integers, which are its stable fixed points. The model provides a continuous, exactly composable process whose endpoint is a discrete, integer-based system. Full details and code are available in a linked GitHub repository.