Bounding minimal log discrepancies of complexity one T-varieties

The minimal log discrepancy is an invariant that plays an important role in the birational classification of algebraic varieties. Shokurov conjectured that the minimal log discrepancy can always be bounded from above in terms of the dimension of the variety. We prove this conjecture for $T$-varieties of complexity one, adding to previous results on this conjecture which include threefolds, toric varieties, and local complete intersection varieties.