An 
-universal
permutation is a permutation containing every permutation of length 
as a permutation pattern
(Chen and Wang 2026). Thus each length-
permutation occurs as the
relative order of some subsequence, not necessarily
in consecutive positions.
Chen and Wang (2026) proved that, for all sufficiently large 
, a uniformly random permutation
of length 
is 
-universal
with failure probability at most 
for an absolute constant 
. The sharp threshold constant conjectured
to be 
remains open. Chen and Wang (2026) state that GPT-6 Pro found the proof,
which the authors verified and digested.
