On the Geometric Origin of the Gravitational Constant

Introduction In this study, we derive the gravitational constant G from first principles, utilizing only the established constants of QED: the speed of light (c), the Planck constant (\hbar), the fine-structure constant (\alpha), and the electron mass (m_e). Our model relies on three structural postulates regarding the nature of the vacuum: * Materiality: The vacuum acts as a 4D elastic solid subject to electromagnetic stress. * Dimensionality: As a 3D spatial manifold, the vacuum possesses a 6-component stress tensor, necessitating a scaling of \alpha^{-6}. * Discretization: The vacuum operates as a computational surface limited by a specific bit-depth precision. We demonstrate via a "blind scan" of integer precisions that the universe resides in a stability well at N=23 bits—corresponding exactly to the mantissa precision of the IEEE 754 Single Precision standard. Furthermore, we show that the residual error in our derivation (-0.19\%) is accounted for by the 9-bit overhead of the full 32-bit computational frame. This framework redefines G not as a fundamental constant, but as the inevitable result of calculating a 6-dimensional electromagnetic stress on a 32-bit discrete geometry. Manuscript: The Geometric Origin of Gravitational Stiffness 1. Fundamental Inputs (QED Only) We begin only with the established constants of Quantum Electrodynamics (QED). Note: We do NOT assume the value of G. We intend to derive it. Table 1: Fundamental Constants * c (Speed of Light): 2.99792 × 10⁸ m/s * ħ (Reduced Planck Constant): 1.05457 × 10⁻³⁴ J·s * α (Fine Structure Constant): 1 / 137.035999 * r_e (Classical Electron Radius): 2.81794 × 10⁻¹⁵ m