Kalai's conjecture (Frankl and Füredi 1987) states that, for 
, 
, and every tight tree 
with 
hyperedges,
 |
where 
is the maximum number of hyperedges
in an 
-vertex
-uniform
hypergraph containing no copy of 
. When 
, the statement is the Erdős-Sós conjecture.
Mubayi and Verstraëte (2026) proved the stronger hypergraph shadow bound
 |
The bound is attained for infinitely many 
. The authors report that GPT-6 Astra found the proof and that
they checked and rewrote it. Independent external review had not been reported as
of Sep. 23, 2026.
