Paperclip at $\theta =\pi$

We study the ``paperclip’’ model of boundary interaction with the topological angle $\theta$ equal to $\pi$. We propose exact expression for the disk partition function in terms of solutions of certain ordinary differential equation. Large distance asymptotic form of the partition function which follows from this proposal makes it possible to identify the infrared fixed point of the paperclip boundary flow at $\theta =\pi$.