Within the meta-theoretical framework of the three Zhu-Liang Truth Theorems (Functor Theorem, Metabolic Theorem, and Prime Mover Theorem), this paper proposes and proves the Zhu-Liang Cognitive Projection Theorem. Cognitive projection is defined as the projection mapping of the truth functor onto the internal categories of a cognitive subject, uniquely determined jointly by the subject's innate cognitive structure and the principle of entropy reduction. We prove the existence of a unique sequence of cognitive projection functors \Pₙ\₍=₀^, projecting the truth functor sequence \Tₙ\ onto the subject's cognitive category sequence \Cₙ\, such that the projections satisfy a recursive relation compatible with the truth metabolic equation. This theorem completes the rigorous mathematical transition from objective truth to subjective cognition, revealing that the essence of cognition is the recursive manifestation of truth within finite consciousness, and proving that cognition can never exhaust truth but can approach it infinitely through hierarchical ascent. Furthermore, we demonstrate the isomorphism between cognitive projection and truth metabolism, showing that the cognitive lifting functors and truth lifting functors form a commutative "twin-tower structure, " providing a solid meta-mathematical foundation for epistemology, cognitive science, and artificial intelligence. The conclusion is absolute and immutable.
Jianbing zhu (Mon,) studied this question.