The Zhu-Liang Cognitive Projection Theorem——The Dimensionality of Human Cognition and the Infinite Unfolding of Truth

Based on the Zhu-Liang Truth Theorem System (Prime Mover Theorem, Metabolism Theorem, Functor Theorem), this paper proposes and proves the Zhu-Liang Cognitive Projection Theorem. The theorem asserts that human cognition of truth is essentially a projection of truth onto finite dimensions. There exists a projection mapping determined by recursive levels: \(H_n: \mathrm{Truth} \rightarrow \|\mathrm{Truth}\|_n\), where \(\|\mathrm{Truth}\|_n\) is the \(n\)-dimensional truncation of truth. Cognitive progress manifests as the elevation of recursive dimension \(n\), while truth itself, as the limit of the infinite recursive sequence \(\{T_n\}_{n=0}^\infty\), forever exceeds complete grasp at any finite dimension. The theorem further reveals that Gödel's Incompleteness Theorem is precisely the manifestation of the Cognitive Projection Theorem within formal systems—undecidable propositions at each level mark the boundary of that level's projection while simultaneously summoning the leap to the next level. This theorem provides a meta-theoretical foundation for understanding the finitude of human cognition, the dynamical mechanism of scientific progress, and the inevitability of carbon-silicon synergy.