The property $(\mathcal P)$ conjecture for the digits of Pi and the Euler constant

Let $m\ge 2$ be an integer, and consider the digits in basis $m$ of the fractional part of either Pi or the Euler constant. Denote by $(\mathcal P)$ the large-deviation property defined earlier in the paper for such digit sequences. The property $(\mathcal P)$ conjecture. For every integer $m\ge 2$, the digits of the fractional part of either Pi or the Euler constant in basis $m$ satisfy $(\mathcal P)$. This would provide a concrete large-deviation property for the digit sequences of these important constants and contribute to understanding their randomness in arbitrary integer bases. The source does not give a resolution of the conjecture.