  Based on energy conservation in a Friedmann-Lemaitre-Robertson-Walker (FLRW)
Universe, on the Legendre transformation between energy density and pressure,
and on nonperturbative asymptotic freedom at high temperatures we derive the
coefficient $\nu_{\rm CMB}$ in the high-temperature ($T$) -- redshift ($z$)
relation, $T/T_0=\nu_{\rm CMB}(z+1)$, of the Cosmic Microwave Background (CMB).
Theoretically, our calculation relies on a deconfining SU(2) rather than a U(1)
photon gas. We prove that $\nu_{\rm CMB}=\left(1/4\right)^{1/3}=0.629960(5)$,
representing a topological invariant. Interestingly, the relative deviation of
$\nu_{\rm CMB}$ from the critical exponent associated with the correlation
length $l$ of the 3D Ising model, $\nu_{\rm Ising}=0.629971(4)$, is less than
$2\times 10^{-5}$. We are not yet in a position to establish a rigorous
theoretical link between $\nu_{\rm CMB}$ and $\nu_{\rm Ising}$ as suggested by
the topological nature of $\nu_{\rm CMB}$ and the fact that both theories share
a universality class. We do, however, line out a somewhat speculative map from
the physical Ising temperature $\theta$ to a fictitious SU(2) Yang-Mills
temperature $T$, the latter continuing the asymptotic behavior of the scale
factor $a$ on $T/T_0$ for $T/T_0\gg 1$ down to $T=0$, and an exponential map
from $a$ to $l$ to reproduce critical Ising behavior.
