Spacetime Substantivalism V:The Cui Constant and the Constitutive Response of Spacetime: A Mechanical Unification of Galaxies, Black Holes, and Cosmic Voids

Abstract
We introduce the Cui constant (Cc) as a universal constitutive amplification factor governing how spacetime converts geometric curvature into effective gravitational response. Defining the geometric load parameter η = log10(A/M), where A denotes the effective enclosing area and M the baryonic mass, we demonstrate that cosmic voids, solar systems, galaxies, and black hole horizons occupy distinct operating points on a single constitutive spectrum Cc(η). Empirical evidence spanning over twenty orders of magnitude reveals a complete constitutive spectrum: (i) a null-response state (Cc = 0.000) in cosmic voids, (ii) a linear elastic phase (Cc = 1.000) in solar-scale systems, (iii) a nonlinear amplification plateau (Cc ≃ 5.0) characteristic of galaxies, and (iv) a saturation limit (Cc = 6.670) at black hole horizons. This framework provides a unified mechanical ontology of gravitation without invoking dark matter or modifying the Einstein field equations, and yields falsifiable predictions in void lensing,
black hole formation thresholds, and large-scale structure dynamics.

中文摘要:时空实体论 V】

本文引入了**“崔常数”(Cui constant, Cc)**作为普适的本构放大因子,用以统御时空如何将几何曲率转化为有效的引力响应。

通过定义几何负荷参数 eta = log10(A/M)(其中 A 代表有效包围面积,M 代表重子质量),我们证明了宇宙空洞、太阳系、星系以及黑洞视界,实际上都处于同一个本构光谱 Cc(eta) 上不同的运作点。

跨越二十个数量级的实证证据揭示了一个完整的本构光谱:

1. 零响应状态(Cc = 0.000):对应宇宙空洞;

2. 线性弹性阶段(Cc = 1.000):对应太阳系尺度系统;

3. 非线性放大平台(Cc 约等于 5.0):星系的典型特征;

4. 饱和极限(Cc = 6.670):对应黑洞视界。

该框架在无需引入暗物质或修改爱因斯坦场方程的情况下,提供了一种统一的引力力学本体论,并在空洞透镜效应、黑洞形成阈值以及大尺度结构动力学方面,给出了可证伪的科学预测。