  This paper shows that the motivic BPS invariants associated to a
noncommutative crepant resolution of a compound Du-Val singularity are
controlled by the labelled Dynkin combinatorics appearing in the work of
Iyama--Wemyss. In particular, we show that the invariants vanish for dimension
vectors which are not a multiple of a restricted root obtained from the affine
root system under a natural quotient map. An immediate corollary is a
description of the curve classes for which the Gopakumar--Vafa invariants of
geometric crepant resolutions vanish, generalising a recent result of
Nabijou--Wemyss to the nonisolated setting. We furthermore formulate a method
for finding symmetries among the non-vanishing invariants using derived
equivalences, and show how this can be applied to line bundle twists and
mutation functors in some settings. In particular, we find new wall-crossing
relations among the Gopakumar-Vafa invariants of the different crepant
resolutions of a cDV singularity.
