$m_G$

$m_{\hslash }$

$r_1={\hslash }^2/G{m}_G{m}_{\hslash }^2$

Precision

Arithmetic Property

$m_e$

$m_P$

${ƛ}_e$ : Electron reduced wavelength

exact

$m_e^{\left(red\right)}$

$m_P/\sqrt{a}$

$r_H$ : Bohr’s radius

exact

$r_H/{ƛ}_e\approx {\mathrm{137\; <mo>\; =\; </mo>2}}^7+2^3+2^0$

$m_N$

$m_N$

$R_e/2$ : half cosmos reduced holographic radius

exact

$R_e/{ƛ}_e\approx {\left(3^3\right)}^{3^3}$

$m_{bc}^{\left(0\right)}$

$m_{bc}^{\left(0\right)}$

$2l_{cc}$ : double non-local length

$-6.3\times {10}^{-3}$

$l_{cc}/{ƛ}_e\approx {\pi }^{50}$

$m_P{a}^3$

$\sqrt{m_p{m}_H}$

${\lambda }_{Wn}$ : Wien CMB wavelength (thermal background)

$-3.2\times {10}^{-4}$

${\lambda }_{Wn}/l_P\approx {\pi }^{64}$

$m_e$

$\sqrt{m_p{m}_H}$

$R/2$ : half Universe radius

exact

$R/{ƛ}_e\approx g\left(6\right)\approx 2^{2^7}\approx {\left(2R/R_e\right)}^{210}$

$m_{bc}^{\left(0\right)}{R}_e/R$

$\sqrt{m_{ph}{m}_{gr}}$

$R_C$ : Cosmos radius = $R_C/c=\left(R/2\right)m_N^3/m_{bc}{m}_{ph}{m}_{gr}$

$4.7\times {10}^{-4}$

$R_C/{ƛ}_e\approx e^{e^{2e}}\approx 6^{2^7}\approx {\left(2R/R_e\right)}^{64a_s}$