Target-change locality of SLE6 ($\kappa =6$)

Changing the target boundary point by a conformal automorphism of the upper half-plane preserves the local chordal SLE law at parameter six, up to a capacity time change and until the relevant boundary point is swallowed. The transformed SLE driving function has zero drift at six; the Dambis-Dubins-Schwarz theorem makes it Brownian in image capacity time.

At parameter six, changing a boundary target preserves the initial unparameterized SLE law until the growing hull separates the two possible targets. After separation, each curve continues in the complementary component whose boundary contains its own target. A curve targeted at infinity follows the unbounded component, whereas a finite separated target lies on a different component. The target-change locality of SLE6 proof no longer applies: its conformal automorphism of the upper half-plane conjugates corresponding surviving domains only before this separation. A zero drift before contact does not give equality of complete curve laws afterwards.