Separation exponent at least $2.119$ from a periodic profile invariant

For every real $\varepsilon>0$ and every integer $S\ge2$, there exist a natural number $n$ and a total Boolean function $f:\{0,1\}^n\to\{0,1\}$ satisfying

Here sensitivity $s(f)$ and block sensitivity $bs(f)$ are maximized over all inputs, and sensitive blocks must be nonempty and pairwise disjoint. The dimension and function may depend on $\varepsilon$ and $S$. The exact exponent is $2119/1000$. This establishes an exponent bound strictly above $2.1$, with arbitrarily large sensitivity.