A blocking set in a finite projective plane is a set of points meeting every line. It is minimal if deleting any point
destroys this property. In 
it is small when its size is less than 
(Sziklai 2026).
The linearity conjecture asserts that every small minimal blocking set consists of the 
-projective points represented by the
nonzero vectors of a subspace 
over a subfield.
Write 
,
where 
is prime, and let 
be the largest exponent for which every line
meets the blocking set in 
points. Sziklai (2026) reports a proof
of linearity over 
when 
or 
. The general cases 
and 4 are not covered. The smallness hypothesis is essential
to the stated result, and the complete argument requires further independent verification.
Sziklai (2026) reports AI assistance with mathematical exploration and computations.
