Formula

Value (10⁸⁶ m)

Remarks

$R_e^2/2l_P$

9.07577

1D-2D Holographic Principle with $R_e$ [5]

${ƛ}_e\exp \left(\exp \left(\exp \left(\exp \left(\exp \left(-g_2\right)\right)\right)\right)\right)$

9.07577

The final log of $R_c/{ƛ}_e$ is a SU(2) coupling: $g_2\approx W/\left({495}^2+{\left(\tau /\mu \right)}^2\right)$

${\left({ƛ}_W{ƛ}_Z\right)}^{1/2}{e}^{1/\left(a-9\right)}\mathrm{<mi>\; </mi>}\exp \left(\exp \left(\exp \left(\exp \left(\exp \left(-g_0\right)\right)\right)\right)\right)$

9.07579

from the connections $g_0\approx g_2$ and $a-9\approx 2^7$

$e^{210}R{\left(f\left(16\right)e^{e^6}9\mu /n_t\right)}^{-1/6}$

9.07577

confirms the role of the central topologic term $f\left(16\right)=e^{16}$

$e^{210}\mathrm{<mi>\; </mi>}{l}_{Wien}\beta {\left(\sin {\theta }_1\right)}^4$

9.07577

confirms the Holic Principle and the CMB invariant temperature

$2^{128}{l}_P{\left(g_{0}R/{ƛ}_H\right)}^2$

9.07577

confirms $1/g_0=1+g_1^2+g_2^2=1+{\left(Z/H^{\left(0\right)}\right)}^2$

$R{p}_t{\left(6d_e{P}^{\sqrt{a}-4}/\pi \right)}^{1/3}$

9.07574

from the cosmic atomic mass $M_c/m_H\approx P^{\sqrt{a}}$

$l_P{R}_C/{ƛ}_e^{g_3}{\left(p_G/2a\right)}^{1/2}$

9.07574

confirms the SU(3) coupling $g_3$ and $p_G$

$l_P{\tau }_0^{{\left(a\beta \right)}^2/4\times 137}$

9.07540

confirms the base ${\tau }_0=\left(2+3+5+7\right)\left(2\times 3\times 5\times 7\right)=3570$

${ƛ}_{e}14p_t^2/p_W{n}_t{\left(a/4\right)}^{64}$

9.07579

with $p_W=6{\pi }^5$

$2{ƛ}_e{\left({\sin }_Z{\theta }_{eff}\right)}^{-4}{\left(4a_s\right)}^{64}$

9.07777

implying a relation between a and $a_s$

$l_P\left({\Pi }_{+}/18\right)3^{256}$

9.07586

confirms the cosmic base 3

$R{a}^6{\left({12}^{32}/P\right)}^{4}1839/4H$

9.07587

base 12

${ƛ}_e\left(n_t/a^2{g}_0\right){\left(3\right)}^{210}$

9.07567

base 3

$g_2{ƛ}_e\left(60H/61p_t\right){\left(1/q\right)}^{2^6}$

9.07548

confirms the electric charge q; $61/60\approx {\left(n_t/p_t\right)}^{12}$

$l_P\left(2/\sqrt{5}\right){\left(80\right)}^{64}$

9.07510

implies the musical property (16 ppb): ${\left({\left(3/2\right)}^4/5\right)}^{256}\approx 24{\left(a/137\right)}^{32}{\left(p_t/p_W\right)}^{1/2}$

$e^{\mu }{ƛ}_{CMB}{\left(R_e/R\right)}^2{\left(p_t/p_{t0}\right)}^4$

9.07584

confirms the CMB invariant temperature, with $p_{t0}=1836$

$e^{\mu }{\lambda }_{Wien}e/2{\beta }^2\sqrt{d}{ƛ}_e$

9.07575

confirms the CMB invariant temperature, through the Wien wavelength

$e^{\mu }{l}_{phCMB}{\left(\left(a-136\right)p_t/p_{t0}\right)}^2$

9.07573

confirms the CMB invariant temperature, through its photon length $l_{phCMB}$

$e^{\mu }{ƛ}_e{\beta }^{1/2}{\left(p_t/n_t\right)}^{1/4}$

9.07576

confirms the CMB invariant temperature

$2{\left(a/137\beta \right)}^2{l}_{nl}^4{ƛ}_{bc}^{\left(0\right)}/R_e{ƛ}_e{l}_P^2$

9.07580

Holic Principle, with the reduced wavelength of the DNA bi-codon

$l_P{\left(\sqrt{a_w}{\left(a\right)}^2\right)}^{16}$

9.07568

bases $a_w$ and $a_s$ , the nuclear couplings

$l_P\sqrt{1+{\left(\sin {\theta }_1\right)}^2}{a}^{j/2}$

9.07566

base a the electric coupling, with j the scale factor [5]