Forgotten $T_\rho$, Thermal Particle

From the post "One Plus One Plus One",

$T_\rho=\sqrt { 2{ mc^{ 2 } } }\,G$

where $T$ is considered inertia along the $t_T$ time axis, such that

$T=AT_\rho$

$T_{ \rho  }=\cfrac { 1 }{ 2Ac^{ 2 }G^{ 2 } }$

$T_{ \rho  }=\cfrac { 1 }{ 2\pi c^{ 2 }a^{ 2}G^{ 2 } }$

$a$ is the radius of the disc that defines $T$.  And $T_\rho=0$ is a valid solution too.

The two types of temperature particles are shown above.