In the paper "Playing pool with $\pi$ (the number $\pi$ from a billiard point of view)" http://www.maths.tcd.ie/~lebed/Galperin.%20Playing%20pool%20with%20pi.pdf George Galperin provides the following interesting "experimental" method to find out digits of $\pi$:

Take two billiard balls with the ratio of their masses $M/m=100^N$.

Put the small ball, $m$, between the wall at the origin and the big ball, $M$.

Push the big ball towards the small ball.

Calculate the total number of hits in the system: the number of collisions between the balls plus the number of reflections of the small ball from the wall.

It turns out that this number of hits gives the first $N+1$ digits of $\pi$ ignoring the decimal point. The proof of this result involves a conjecture that $$\left [\frac{\pi}{\arctan{(10^{-N})}}\right]=\left [\frac{\pi}{10^{-N}}\right]$$ is true for any big enough natural number $N$. Galperin writes that the modern mathematics is far from proving this conjecture. Galperin's article was in 2003. Has anything changed as far as the proof of this conjecture is concerned?