= Locality of a chord law under conformal changes of neighborhoods
A scale-invariant law of unparameterized chords from zero to infinity in the <complex upper half-plane> is local when a boundary-preserving <conformal map> between neighborhoods of zero, fixing zero, transports its curve stopped on leaving the first neighborhood to the same-law curve stopped on leaving the second. Equality concerns the stopped curves up to increasing reparameterization. For <SLE> with parameter six, the <transformed SLE driving function> is a <continuous local martingale> with bracket six times the image capacity clock. The <Lévy characterization of Brownian motion> makes that driver Brownian in the new clock, proving the local stopped-curve invariance.
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