The exponent-pair conjecture for weak Carmichael numbers

Let $e,f,e',f'$ be integers with $1\le e\le f$, $e+f\ge 3$, and likewise $1\le e'\le f'$ and $e'+f'\ge 3$. Let ${\mathcal P}_w(e,f)$ denote the set of pairs $(p,q)$ of distinct primes such that $p^e q^f\in {\mathcal C}_w(e,f)$, where ${\mathcal C}_w(e,f)$ is the corresponding set of weak Carmichael numbers. Exponent-pair conjecture. If

$${\mathcal P}_w(e',f')={\mathcal P}_w(e,f),$$

then $f=f'$ and $e\mid e'$, or $e=e'$ and $f\mid f'$. This conjecture describes when two exponent pairs determine the same prime-pair set; the source provides the inclusion in one direction and conjectures this converse, with no resolution stated.