The block sensitivity of a Boolean function 
at an input 
is the largest number of pairwise disjoint sets of coordinates 
, each nonempty, such that 
for every 
, where 
reverses the coordinates in 
. The block sensitivity of 
is 
(Virza 2010).
Blocks consisting of singleton sets show that 
, where 
is Boolean function
sensitivity. For example, the disjunction of
inputs has both quantities equal to 
at the all-zero input. The sensitivity
conjecture concerns a bound on block sensitivity that is polynomial in 
.
The analogous quadratic bound in terms of spectral sensitivity also has a reported counterexample. Meiburg (2026) constructed a
total Boolean function on 2,017,584 variables
with 
and 
,
where 
is spectral sensitivity. Iterated composition
yields superquadratic growth with exponent 2.127. GPT-5.6 Sol supplied a key construction
idea. The accompanying Lean statement proves exponent 2.12 and an unbounded ratio
,
but an independent rebuild and independent mathematical review had not been reported
as of Oct. 8, 2026 (VibeMathed 2026).
