  Let $G$ be a semisimple, simply connected algebraic group over an
algebraically closed field of characteristic zero. We prove that the
$\infty$-category of D-modules on the loop group of $G$ is equivalent to the
monoidal colimit of the $\infty$-categories of D-modules on the standard
parahoric subgroups. This also follows from arXiv:2009.10998, but the present
paper gives a simpler proof. The idea is to develop a combinatorial model for
the path space of a simplicial complex, in which 'paths' are sequences of
adjacent simplices, and to use a generalized version of hyperdescent for
D-modules. We also give two more applications of this hyperdescent theorem:
triviality of D-modules on the 'schematic Bruhat-Tits building,' which was
first established by Varshavsky using a different method, and triviality of
D-modules on the `simplicial affine Springer resolution.'
