Solution (source code)

= Solution

The production rate is $\sigma_{c\rm Th}\phi N_{\rm Th}$, while depletion includes both capture and fission of the fissile population, $\sigma_{a\rm U}\phi N_{\rm U}$. Thus the <conversion ratio> in this stipulated model is
$$
CR(t)=\frac{\sigma_{c\rm Th}N_{\rm Th}(t)}{\sigma_{a\rm U}N_{\rm U}(t)}.
$$
At zero instantaneous flux this expression describes the limiting ratio of the two reaction rates. The total absorption coefficients are $a=3.08+0.02=3.10\,\mathrm b$ and $b=7.10+57.10=64.20\,\mathrm b$, so
$$
\boxed{CR(0)=\frac{3.08}{64.20(0.05)}=0.9595.}
$$
It is below one: fissile nuclei are initially removed slightly faster than this simplified chain replaces them. Consequently this model is not initially self-replacing in fissile inventory. Inventory replacement is distinct from the instantaneous <neutron> balance that determines criticality.