The Coherence Evolution Model

This paper introduces the Coherence Evolution Model (CEM), a novel framework positing that prime numbers and their arithmetic correlations govern universal coherence across scales. Empirical validation of the CEM is presented through fractal analysis of the Cosmic Microwave Background (CMB), revealing a fractal dimension matching the golden ratio and excess power at prime-indexed multipoles. These findings challenge the standard inflationary paradigm. The paper addresses critiques, outlines falsifiable predictions across cosmology, biophysics, and materials science, and invites independent verification of this unifying paradigm. * Prime Basis: The paper proposes that physical systems occupy orthogonal states indexed by primes, minimizing entropic interference. This suggests a fundamental connection between prime numbers and the building blocks of reality. * Zeta-Regulated Dynamics: The Riemann zeta function, which is closely related to prime numbers, governs long-range order via arithmetic quantum chaos. * Empirical Validation through CMB Fractality: The paper claims that the fractal dimension of the Cosmic Microwave Background (CMB) is related to the golden ratio, which arises from entanglement entropy calculated based on the distribution of prime numbers. * Prime-Indexed Coherence and the Horizon Problem: The uniformity of the CMB across causally disconnected regions is explained by "prime-indexed coherence," where primes carry non-local correlations. * Excess Power at Prime Multipoles: The paper also claims to find excess power in the CMB's harmonic spectrum at multipole moments that correspond to prime numbers. * Prime-Energy Correspondence: The paper explores the relationship E_p = \log p, linking prime numbers to energy scales in physical systems. * Mathematical Necessity: Primes are linked to the zeros of the Riemann zeta function, and the von Mangoldt function, \Lambda(n) = \log p for n = p^k, encodes the density of primes. * Physical Justification: The logarithm converts multiplicative primes into additive energy scales, mirroring how entropy converts multiplicative microstate counts into additive quantities. * Holographic Scaling: Primes are posited to label Planck-scale "atoms" of spacetime, with their spacing in energy reflecting holographic discreteness. In essence, the paper proposes a model where prime numbers are not just mathematical abstractions but are fundamental to the structure and behavior of the universe at various scales.本文介绍了相干演化模型（Coherence Evolution Model, CEM），这是一种全新的理论框架，其核心假设为质数及其算术关联支配着所有尺度下的宇宙相干性。通过对宇宙微波背景（Cosmic Microwave Background, CMB）的分形分析完成了对CEM的实证验证，研究发现其分形维度与黄金比例吻合，且在质数索引多极矩处存在额外功率。上述发现对标准暴胀范式构成了挑战。本文回应了相关质疑，梳理了宇宙学、生物物理学与材料科学领域中可证伪的预测，并呼吁学界对这一统一范式开展独立验证。 * 质数基底（Prime Basis）：本文提出物理系统占据由质数索引的正交态，从而最大限度降低熵干涉。这一假设暗示质数与现实基本构成单元之间存在本质关联。 * ζ函数调控的动力学（Zeta-Regulated Dynamics）：与质数密切相关的黎曼ζ函数（Riemann zeta function）通过算术量子混沌支配长程有序。 * 基于CMB分形特性的实证验证（Empirical Validation through CMB Fractality）：本文宣称宇宙微波背景（CMB）的分形维度与黄金比例相关，而该比例源自基于质数分布计算的纠缠熵。 * 质数索引相干性与视界问题（Prime-Indexed Coherence and the Horizon Problem）：宇宙微波背景在因果分离区域内的均匀性可通过“质数索引相干性”解释，即质数承载着非局域关联。 * 质数多极矩处的额外功率（Excess Power at Prime Multipoles）：本文还宣称在宇宙微波背景的谐波谱中，与质数对应的多极矩处存在额外功率。 * 质数-能量对应关系（Prime-Energy Correspondence）：本文探讨了E_p = log p的关联，将质数与物理系统中的能量尺度联系起来。 * 数学必然性（Mathematical Necessity）：质数与黎曼ζ函数的零点存在关联，而冯·曼戈尔特函数（von Mangoldt function）Λ(n) = log p（当n = p^k时）则编码了质数的密度。 * 物理解释（Physical Justification）：对数运算将乘法形式的质数转化为加法形式的能量尺度，这与熵将乘法形式的微观态数目转化为加法形式的物理量的过程相呼应。 * 全息标度（Holographic Scaling）：本文假设质数用于标记时空的普朗克尺度“原子”，其能量间距反映了全息离散性。 简言之，本文提出的模型认为，质数绝非仅为数学抽象，而是宇宙各尺度下结构与运行规律的基础。