Fix a subset \(I\subseteq \mathbb R_{>0}\) such that \(\gamma=\inf\{ \sum_{i}n_ib_i-1>0 \mid n_i\in \mathbb Z_{\geq 0}, b_i\in I \}>0\). We give a explicit upper bound \(\ell(\gamma)\in O(1/\gamma^2)\) as \(\gamma\to 0\), such that for any smooth surface \(A\) of arbitrary characteristic with a closed point 0 and an \(\mathbb R\)-ideal \(\mathfrak{...

Upper bound of discrepancies of divisors computing minimal log discrepancies on surfaces