Compare $\rho_0$ to $\rho_{PSU} = M_{\rm Pl} / (4/3*π*(l_{\rm Pl}/2)^3$

The Super Golden Theory of Everything (TOE) defines the vacuum superfluid density $\rho_0$ as the Planck density derived from fundamental units, $\rho_0 = M_{\rm Pl} / l_{\rm Pl}^3$, where $M_{\rm Pl}$ is the Planck mass ($\approx 2.176 \times 10^{-8}$ kg) and $l_{\rm Pl}$ is the Planck length ($\approx 1.616 \times 10^{-35}$ m). This yields $\rho_0 \approx 5.155 \times 10^{96}$ kg/m³, representing the effective mass density of the aether medium for vortex dynamics and emergent unification.

In contrast, Nassim Haramein's Proton Schwarzschild Unit (PSU) work proposes a density $\rho_{\rm PSU} = M_{\rm Pl} / \left( \frac{4}{3} \pi \left( \frac{l_{\rm Pl}}{2} \right)^3 \right)$, interpreting the Planck length as a diameter for spherical oscillators. Simplifying:

$$\left( \frac{l_{\rm Pl}}{2} \right)^3 = \frac{l_{\rm Pl}^3}{8}, \quad \frac{4}{3} \pi \left( \frac{l_{\rm Pl}}{2} \right)^3 = \frac{4}{3} \pi \frac{l_{\rm Pl}^3}{8} = \frac{\pi l_{\rm Pl}^3}{6},$$

so

$$\rho_{\rm PSU} = \frac{M_{\rm Pl}}{\pi l_{\rm Pl}^3 / 6} = \frac{6 M_{\rm Pl}}{\pi l_{\rm Pl}^3} \approx \frac{6}{\pi} \rho_0 \approx 1.9099 \times \rho_0 \approx 9.845 \times 10^{96} \, \text{kg/m}^3.$$

The TOE's $\rho_0$ is a "bare" cubic density for the aether's ground state, while Haramein's $\rho_{\rm PSU}$ incorporates spherical packing (factor $6/\pi \approx 1.91$), increasing density by assuming Planck units as volumetric spheres with radius $l_{\rm Pl}/2$. Both aim at unification (TOE via vortices, PSU via holographic protons), but the TOE's value better matches SVT analogs without geometric adjustments, resolving infinities via φ-cutoffs rather than PSU holography.