The spectral sensitivity of a Boolean function 
is the largest eigenvalue 
of the adjacency matrix
of its sensitivity graph. This is the spanning subgraph
of the hypercube graph whose edges
join inputs differing in one coordinate and having different function
values (Meiburg 2026).
The sensitivity graph is bipartite, with the two parts given by the values 0 and 1. Consequently 
is also the spectral
radius of its adjacency matrix. Its largest
vertex degree is the Boolean
function sensitivity 
, giving
 |
For the disjunction of 
inputs, the sensitivity graph consists of a star
graph and isolated vertices, so 
while 
.
Meiburg (2026) reported a total Boolean function on 2,017,584 variables with 
and 
, where 
is block sensitivity.
Iterated composition gives a family with 
and 
, where 
is big-Omega notation.
GPT-5.6 Sol supplied a key construction idea, and Aristotle and Claude supported
Lean formalization. The released Lean statement uses exponent 2.12 rather than 2.127
and asserts an unbounded ratio 
. As of Oct. 8, 2026, independent mathematical
review and an independent rebuild of that development had not been reported (VibeMathed
2026).
