The radius of comparison of a unital nuclear 
-algebra 
with tracial states is the infimum of 
for which
 |
where 
are positive elements of finite
matrix algebras over 
and 
is Cuntz comparison. The rank function is 
, using unnormalized
matrix trace. If no finite
comparison bound exists, the radius is infinite. This
invariant measures how large a trace gap suffices for comparison.
