Flat, Completely Flat

From the post "One Plus One Plus One",

$m_\rho=\sqrt{m_g}.\sqrt{2}cG$

If the particle $m_g$ is an 2D entity then instead,

$m_g=Am_\rho$

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

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

where $a$ is the radius of the disc that defines $m_g$.  And $m_{ \rho  }=0$ is also valid.

The particle is two dimensional because $\psi$ is oscillating between two space dimensions only.