The Krzyż conjecture asserts that every analytic function 
from the unit disk to the punctured unit
disk satisfies 
for every positive integer 
. The proposed extremal functions are
 |
where 
.
Wikström (2026) proved the conjecture, including the equality characterization, for 
.
The proof combines an analytic reduction with rigorous computer-assisted exclusion
of extremals with fewer than six atoms in their integral representation. The general
conjecture remains open.
Wikström (2026) reports using Claude for numerical exploration and verification-code development, with a separate GPT-6 Astra code review. The author checked the arguments and code.
