A graph tensor of positive integer bond dimension 
over 
is the tensor associated with a
finite graph by placing 
on each graph
edge and grouping all tensor factors incident to the same graph
vertex into a single factor. Here 
is the standard basis of 
(Christandl et al. 2019). This construction is distinct
from the graph tensor product.
The asymptotic tensor rank of a tensor 
is
 |
where 
is tensor rank and corresponding vertex factors are
grouped together in each tensor power. For the bond-dimension-2 tensor 
of the complete graph
with 
, Zhou (2026) proved
 |
Here 
is the floor function. In particular, equality
holds for even 
.
Zhou (2026) attributes the central construction to an AI-generated argument developed
under human mathematical direction.
