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Zenodo
2026
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| Online-Zugang: | https://doi.org/10.5281/zenodo.18771764 |
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- <p>中文<br>图数数论是一种将相空间视为存在本身的先验几何框架,其中数学对象并非集合的静态元素而是五层辛结构(奇点、时间、谱、群、元)中的动态模态,通过时间电荷(τ)的内禀定向与相态(有序/混沌/同筹)的几何约束,将数学真理从逻辑可证性转化为层级化的生成描述,从而实现了从“对象存在”(being)到“模态显现”(appearing)的本体论范式转换。<br>本文揭示了P vs NP问题中一个根本性的范畴错误:试图用数学上的“相等”概念,去通约“验证”与“求解”这两个分属不同范畴的活动。正如《大自然理论》所指出,P ≟(贴合) NP 的等号下面必须注明测量条件(贴合符号),否则问题便悬在半空。文章论证,P与NP的比较依赖于所选的尺子(归约、人脑、自然等),不同尺子导向不同答案,暴露出原问题预设的框架无法自洽。通过回溯希尔伯特纲领与哥德尔不完备定理的脉络,本文指出P vs NP的困惑源于对符号系统的误用,并呼吁回归“走进去”的原始体验——那是比任何符号证明更根本的尺度。<br>English<br>Diagrammatic Number Theory is a transcendental geometric framework that treats phase space as existence itself, wherein mathematical objects are not static elements of sets but dynamic modalities within a five-layered symplectic structure (singularity, time, spectra, groups, meta). Through the intrinsic orientation of temporal charge (\tau) and the geometric constraints of phase states (ordered/chaotic/homological), it transforms mathematical truth from logical provability into a stratified generative description, thereby achieving an ontological paradigm shift from "objective being" to "modal appearing."</p> <div> <div> <p>This paper exposes a fundamental category error in the P vs NP problem: the attempt to equate “verification” and “solving”—two activities belonging to distinct categories—through the mathematical notion of equality. As elaborated in The Natural Theory, the equals sign in P ≟(fit) NP must be accompanied by a specification of the measuring ruler (the fitting symbol); otherwise the question hangs in mid-air. We argue that the comparison of P and NP depends crucially on the chosen ruler (reduction, human mind, nature, etc.), yielding different answers under different rulers, thereby revealing the inherent instability of the original problem’s framework. Tracing the legacy of Hilbert’s program and Gödel’s incompleteness, this work contends that the perplexity surrounding P vs NP stems from a misuse of symbolic systems, and advocates a return to the primal experience of “walking into the forest”—a measure more fundamental than any symbolic proof.</p> </div> </div> <p>这是理论的补充/This is a supplement to the theory:<a title="Physical-Closure" href="https://doi.org/10.5281/zenodo.18501594">https://doi.org/10.5281/zenodo.18501594</a></p>