Reflection lower bound for harmonic hull capacity ($\mathrm{cap}(K)\ge (1+y)/2$)

For a connected slit joining $0$ to $x+iy$ with $x^2+y^2=1$, reflect across the vertical line through $x$. The two slits separate the vertical segment below the common tip and the intervening real boundary from infinity. Brownian reflection symmetry bounds the corresponding model hitting probability by twice the original hull-hitting probability. Mapping out the vertical segment gives total boundary-image length $1+y$ for its two banks together with the real interval between $0$ and $x$. The harmonic-measure asymptotic at infinity gives the displayed bound. This argument requires a separating connected barrier; radius gives no positive lower bound for disconnected harmonic hull capacity.