The Zhu-Liang Theorem of Recursive Nested Functions: Reconstructing the Prime Mover

The Prime Mover is a central concept in Western philosophy and theology, introduced by Aristotle to explain the ultimate cause of motion in the universe and later identified with God by medieval theology. However, this concept has long faced the tension between external transcendence and internal immanence: if the Mover is external to the universe, how is its connection to the world established? If it is internal to the universe, how can it remain unmoved while participating in motion? Based on the Zhu-Liang Theorem of Recursive Nested Functions, this paper reconstructs the Prime Mover as the self-causing structure of the terminal coalgebra $\Omega$. It proves that $\Omega$ remains invariant under the double negation functor $G$ ($\omega:\Omega\to G(\Omega)$ is an isomorphism), thus being the ``Unmoved Mover''; all cognitive objects unfold recursively toward $\Omega$ via the truth function $h_A$, and their motion originates from the terminality of $\Omega$ rather than external impetus. This reconstruction dissolves the dichotomy between external transcendence and internal immanence, resonates with the Eastern wisdom of ``one flower, one world,'' and provides a recursive ontological foundation for the problem of cosmic origin.