Hybrid Sequence:
The starting point is $\lib{sym-ratch-real}$.
First, modify the library to sample $R$ lazily at the last possible moment.
Rewrite the logic of $\ratchadvance$, putting the computation of $G$ into two branches of an if-statement.
Apply the PRG security of $G$ (three-hop maneuver not shown).
The if-branch of $\ratchadvance$ samples $R$ uniformly but doesn't actually use its value. So just as before, we can leave $R$ undefined in this case; it will be sampled uniformly later when it is needed.
We can add a boolean flag ``$\textsf{compromised}$'' that is $\mytrue$ if and only if $\ratchadvance$ has been called, if and only if $R$ is defined. The result is $\lib{sym-ratch-rand}$.
$\lib{sym-ratch-real}$
$R \gets \bits^\secpar$
$\ratchadvance$( ):
$R \| \key := G(R)$
return $\key$
$\ratchcompromise$( ):
return $R$