On Andr\'e periods of mixed Tate motives

In this note, we show that the p-adic periods of motives introduced recently by Ancona and Fratila (``Andr\'e periods'') reduce to the classically studied notion in the case of Mixed Tate motives. We also connect Andr\'e periods with Coleman integration by observing that the Frobenius-fixed de Rham paths of Besser and Vologodsky come from motivic paths in characteristic p (unconditionally in the mixed Tate setting, conditionally in general). We use this to realize special values of p-adic multiple polylogarithms as Andr\'e periods in a concrete way.