The universal integral means spectrum is the supremum of the growth exponents of derivative integral means over univalent functions
on the unit disk. For a univalent
function 
, define
 |
(1)
|
and
 |
(2)
|
The universal spectrum 
allows all univalent
functions, whereas 
restricts to bounded univalent
functions. They obey 
(Binder et al. 2026).
Binder et al. (2026) proved
 |
(3)
|
for 
,
implying Brennan's conjecture. They additionally
announce strict inequality for 
with 
, but defer the details of that strengthening to a separate
paper. Binder et al. (2026) derived their shorter argument while validating
earlier AI-generated proofs. Some authors used AI to understand
those arguments, while the write-up of their own proof
was prepared without AI assistance.
