Geometric Origin of the Fine-Structure Constant and the Prediction of Vacuum Zero-Point Temperature within a Granular Medium Framework

We propose a paradigm in which the quantum vacuum is modeled not as an empty geometric arena but as a discrete, jammed granular medium. Its ground state is hypothesized to be a Face-Centered Cubic (FCC) lattice of fundamental mechanical constituents—Discrete Vacuum Quanta (DVQs). Within this Space-Vacuum Granular Dynamics (SV-TGD) framework, we perform a first-principles geometric analysis. The key finding is that the minimal cooperative rearrangement region in the FCC lattice, defined by a characteristic radius of R = 2a, possesses an effective coordination number of N_eff = 138. This invariant geometric constant provides a direct, parameter-free origin for the fine-structure constant: α ≈ 1/138. The 0.7%…