  In this article we prove a local implication of boundedness of Fano
varieties. More precisely, we prove that $d$-dimensional $a$-log canonical
singularities, with standard coefficients, which admit an $\epsilon$-plt
blow-up have minimal log discrepancies belonging to a finite set which only
depends on $d,a$ and $\epsilon$. This result gives a natural geometric
stratification of the possible mld's in a fixed dimension by finite sets. As an
application, we prove the ascending chain condition for minimal log
discrepancies of exceptional singularities. We also introduce an invariant for
klt singularities related to the total discrepancy of Koll\'ar components.
