The Spacetime Uniqueness Law (STM) of Yuanxian Theory asserts that the ontological topology of the universe is a sixty-four-dimensional compact torus (T64), whereas the four-dimensional spacetime (R4) perceived and scientifically described by human observers is merely its low-dimensional projection. However, the explicit construction of the projection operator (P) from T64 to R4, the quantification of the information loss incurred during this projection, and the question of whether discarded high-dimensional information can be recovered or indirectly observed remain foundational issues that the theory must rigorously address. This paper aims to fill this gap. First, we explicitly construct the projection operator P: L2 (T64) to L2 (R4), which is strictly defined as an integral operator averaging over sixty compact dimensions. In the Fourier domain, this operator is equivalent to an ideal low-pass filter: it retains exclusively those modes with a winding number of zero along the compact directions (nₚerp = 0) while entirely discarding all non-zero winding modes (nₚerp != 0). Second, we introduce the concept of projection entropy (Sₚroj) to quantify this information loss, proving that under typical physical power spectra decaying by a power law, the amount of lost information is massive and non-negligible, meaning that observable 4D physics captures less than one-fifth of the total informational content of the ontological universe. Third, we analyze the observational effect boundaries of the discarded information, demonstrating that through the non-linear self-interactions of the self-referential mind field (PsiSR), a portion of the high-dimensional topological effects can leak into the low-dimensional projection as "residual anomalies" (e. g. , higher-dimensional effective operators, primordial gravitational wave background modifications, and quantum computing correlations). Finally, we propose two information recovery strategies for this ill-posed inverse problem: regularized reconstruction based on the Moore-Penrose pseudoinverse, and iterative physical inversion constrained by True-Circle Self-Consistency (TCSC) dynamics. This work establishes a rigorous mathematical foundation for the high-dimensional projection hypothesis in Yuanxian Theory and delineates concrete directions for its future experimental and computational verification. 元宪理论的时空唯一性律 (STM) 断言: 宇宙的本体拓扑为一个六十四维紧致环面 (T64), 而人类所感知并科学描述的四维时空 (R4) 仅仅是其低维投影。然而, 从 T64 到 R4 的投影算子 (P) 的显式构造、投影过程造成的信息损失及其量化, 以及丢失的高维信息能否通过某种方式被恢复或间接观测, 是该理论必须回答的基础性问题。本文旨在填补这一空白。 首先, 我们显式构造了投影算子 P: L2 (T64) 到 L2 (R4), 将其严格定义为对60个紧致维度取平均的积分算子。在傅里叶域中, 该算子等价于一个理想的低通滤波器: 它仅保留紧致方向上环绕数 nₚerp = 0 的长波模式, 而将其余非零环绕数 (nₚerp != 0) 的高维信息全部丢弃。其次, 我们引入了“投影熵” (Sₚroj) 的概念来量化这一信息损失, 并证明在典型的物理幂律功率谱下, 丢失的信息量是巨大且不可忽略的——人类观测到的四维物理仅仅触及了宇宙本体不到五分之一的信息含量。再次, 我们分析了丢失信息的可观测效应边界, 指出高维信息并非绝对不可见: 通过自指心场 (PsiSR) 的非线性相互作用, 部分高维拓扑效应可作为“残留反常” (如非标准有效算符、原初引力波谱周期性鼓包及量子计算模拟关联) 渗入低维投影, 在特定能标留下可探测的痕迹。最后, 针对该逆问题的病态性, 我们提出了两种信息恢复策略: 基于 Moore-Penrose 伪逆的数学正则化重建, 以及基于真圆自洽律 (TCSC) 动力学约束的物理迭代反演。本文为元宪理论中“高维投影”这一核心假说提供了严格的数学基础, 并为其未来的实验与数字模拟检验指明了方向。
Zhenyuan Acharya (Thu,) studied this question.