**Problem.** *Does a compact metric space of finite packing dimension admit an equi-Hölder embedding into a Hilbert space?*

A map $f:X\to Y$ between metric spaces $(X,d_X)$, $(Y,d_Y)$ is called *equi-Hölder embedding* if there are positive real constants $c,C,\alpha$ such that
$$c\cdot d_X(x,y)^\alpha\le d_Y(f(x),f(y))\le C\cdot d_X(x,y)^\alpha$$
for all $x,y\in X$.

The *packing dimension* of a compact metric space $(X,d)$ in the (finite or infinite) number
$$Dim(X)=\limsup_{\varepsilon\to 0}\frac{\ln N_\varepsilon(X)}{\ln(1/\varepsilon)},$$
where $N_\varepsilon(X)$ is the cardinality of the smallest cover of $X$ by subsets of diameter $\le\varepsilon$.

**Remark.** By the Assouad Embedding Theorem, a metric space $X$ admits an equi-Hölder embedding in a finite-dimensional Hilbert space if and only if $X$ is doubling. It can be shown that doubling metric spaces have finite packing dimension.