Generality of potential to support

[SamDuffield]

What generality non-Markovian SSM to support?

$G(x_k)$?
$G(x_{k-1:k})$?
$G(x_{1:k})$?

@AdrienCorenflos says
$G(x_{k-1:k})$ for cuthbert
$G(x_{1:k})$ for cuthbertlib

This is mainly for SMC but we might want to think about if it makes sense for Gaussian filters too