Unidentified scratchpad

Trying to formally define CCC units

$c$: 1 times the speed of light in vacuum (such that the speed of light in vacuum is 1 times this unit)
$C_4$: $\frac{2907}{102140353000}$ of the frequency of radiation corresponding to the transition between the two hyperfine levels of the unpertubed ground state of the cesium-133 atom
cal: $\frac{8368\times 10^{40}}{3467157466689}$ of the energy transferred in vacuum when a system absorbs or emits exactly one photon of monochromatic electromagnetic radiation of frequency $C_4$ .