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% deviation from the experimentally measured value is quantitatively linked to the predicted vacuum zero-point thermal softening. Crucially, by incorporating the independently measured vacuum yield energy g ≈ 31 meV from the proton radius puzzle, this geometric foundation leads to a falsifiable prediction: the vacuum exhibits a characteristic zero-point temperature of T_zp ≈ 2.61 K. This temperature scale invites direct experimental verification, particularly through a predicted "quantum plateau" in the low-temperature dependence of zero-bias chiral conduction anomalies (CISS effect). Context: This paper constitutes the second theoretical demonstration of the Space-Vacuum Granular Dynamics (SV-TGD) framework, building upon the vacuum yield energy derived in our previous work on the proton radius puzzle.