The Andreadakis conjecture compares two filtrations of the automorphism group of a free
group 
.
Write 
for its lower central series, and let 
be the kernel
of the action of 
on 
.
Then 
consists of the automorphisms acting trivially on
the Abelianization. The conjectured equality is
(Andreadakis 1965).
Bartholdi (2013, 2016) gave an earlier counterexample in rank three and degree seven. Kofinas (2026) proved the strict inclusion
 |
for every 
and 
.
Thus the conjectured equality fails throughout these ranks and degrees. The notation
here corresponds to 
in Kofinas (2026).
