lossy open stub of \$ \frac{1}{32} \lambda \$ is equivalent to?
Completely ignoring the exact question and the proper way of doing this...

It is useful to remember that a 1/4 wave line transforms the impedance to its complex conjugate. 

Which is to say, mirrors it across the centre of the smith chart.

Shorts become opens
Opens become shorts
Zin = Z0/Zout
capacitance becomes inductance 

at 1/2wave it is undone: 1/2waves are transparent Zin = Zout

Very short transmission lines will be just what they are: a couple of bits of wire near each other