Numerically Evaluate: $c = 1 / \sqrt{\epsilon_0 \rho_0}$

c is the speed of light in vacuum, a fundamental physical constant representing the maximum speed at which electromagnetic radiation and information can travel in space. Its value is exactly 299792458 m/s by definition in the SI system.

$\epsilon_0$ is the vacuum compressibility in the context of the Super Golden TOE, a measure of how much the superfluid aether vacuum can be compressed under pressure. It has units of s²/kg (or m²/N) and is derived as $\epsilon_0 = 1 / (\rho_0 c^2) \approx 2.16 \times 10^{-114} s²/kg$, ensuring the phonon speed matches c.

$\rho_0$ is the vacuum superfluid density in the Super Golden TOE, representing the effective mass density of the aether medium. It is approximately $5.15 \times 10^{96} kg/m³$, derived from Planck units as $\rho_0 = M_{\rm Pl} / l_{\rm Pl}^3$, where $M_{\rm Pl}$ is the Planck mass and $l_{\rm Pl}$ is the Planck length.

The expression evaluates numerically to 299792458 m/s, matching the value of c exactly by construction in the TOE.