The Anstee-Sali conjecture predicts the asymptotic number of columns in a simple (0,1)-matrix avoiding a fixed submatrix 
, where simple means that no two columns are equal and avoidance
allows permutation of rows and columns. Write this maximum for 
rows as 
. For the column product 
, each column of 
is stacked above each column of 
. Let 
be the least number 
such that every 
-fold product of sufficiently large identity
matrices, their binary complements, or upper triangular all-ones matrices
contains 
.
The conjectured estimate is 
.
Anstee et al. (2026) refuted the conjecture. If 
is the incidence matrix
of the cycle graph 
and 
is a column of 
ones, then, for 
,
 |
For this forbidden matrix, 
, so the exponent is larger than the conjectured 
.
The forbidden pattern is detected by restricting columns to selected rows, not merely
by finding an ordinary hypergraph subgraph.
Anstee et al. (2026) attribute discovery of the lower-bound example to GPT-5.6 Sol assistance in the underlying work. The mathematical claims were reviewed by the authors.
-Extension
of 
-A
Counterexample of the Anstee-Sali Conjecture." 26 Sep 2026.