P vs NP 問題的圖層維度視角：複雜性作為維度錯位的顯現

This paper proposes a novel structural explanation for the P vs NP problem by introducing a dimensional-layer framework. Rather than treating the difficulty of NP problems as an algorithmic inefficiency within a flat computational space, we argue that the true complexity arises from a dimensional misalignment between the solution space (Lₚ) and the verification space (Lᵥ). We formalize this mismatch as a non-reversible projection function P: Lₚ → Lᵥ, wherein solutions exist in a higher-dimensional layer inaccessible to polynomial-time algorithms operating within lower-dimensional structures. Through the metaphor of a multi-layered maze, we show that the apparent intractability of NP problems stems from the attempt to resolve high-dimensional structures using tools native to reduced dimensions. The proposed model reframes NP ≠ P not as a failure of algorithm design, but as a structural dislocation in the space where problems are rendered and verified. This perspective opens new theoretical paths for complexity theory, connecting it with dimensional cognition, visualization logic, and layered syntax emergence. Future work will extend this framework into the domain of temporal layers and observer-dependent logic systems. 本文提出一種全新的結構性解釋模型，重新探討 P vs NP 問題之本質。我們主張，NP 問題之所以難解，並非源自演算法效率的缺陷，而是問題圖層（Lₚ）與驗證圖層（Lᵥ）之間的維度錯位所致。透過一個不可逆的投影函數 P: Lₚ → Lᵥ，我們建構出一個跨維度的顯像模型，指出高維解空間無法於低維圖層中有效搜尋，進而導致複雜性鴻溝。本文以迷宮層級結構為比喻，展示當前演算法所處的觀測維度與問題本身所需解構的維度並不一致，NP ≠ P 的難題因此轉化為圖層語法與顯像邊界的問題，而非純演算效率的瓶頸。本文觀點可拓展至更廣泛的複雜性研究與意識觀測理論，未來將延伸至時間圖層與主觀顯像邏輯之探討。