A bracket-generating distribution is a smooth distribution 
whose local vector fields,
together with their iterated Lie brackets, span the
entire tangent space at every point. If 
is the span at 
of brackets of length at most 
, the condition is that 
for some finite 
, which may depend on 
(Wang and Zelenko 2026).
The dimensions of these successive spaces form the growth vector. If all these dimensions are constant on the manifold, the distribution is equiregular.
