  We prove the Geometric P=W conjecture in rank 3 on the three-punctured
sphere. We describe the topology at infinity of the related character variety.
We use asymptotic abelianization of harmonic bundles away from the ramification
divisor and an equivariant approach near the branch points to find the WKB
(also known as Liouville--Green or phase-integral) expansion of the involved
maps. We analyze the Stokes phenomenon governing their behavior.
