The Big G Formula: A Geometric Scale of Gravity and Entropy

Abstract: In standard physics, gravity is conventionally conceptualized as spacetime curvature parameterized by empirical mass. In this Letter, we demonstrate that gravitational tension is not a fundamental interaction, but a macroscopic topological residual arising from a pure geometric T (1, 2) vacuum manifold. Governed by the Law of Spontaneous Doubling, the underlying manifold exhibits a strict 2⁴: (2⁴-1) dynamic asymmetry between its conjugate temporal and spatial axes. We introduce the Big G Formula, redefining gravity strictly as the logarithmic (entropic) evaluation of overlapping temporal degrees of freedom. Normalized by the inverse base quantum rigidity, the formula reveals that the gravitational constant is fundamentally an intrinsic geometric scaling factor required to maintain topological consistency. This dimensionless framework establishes gravity as an absolute geometric veto mechanism against temporal divergence, completely independent of physical mass. The manuscript features a rigorous mathematical expansion of the topological action, including the asymmetric geometric metric tensor and explicit Euler-Lagrange derivations, alongside a quantitative alignment with CODATA empirical values.