“…, u r ) ∈ K r with |u i | ∞ ≤ q s i q q−1 for each 1 ≤ i ≤ r − 1 and |u r | ∞ < q sr q q−1 . Following [CM19a], we explicitly construct a t-module G s,u and an algebraic point v s,u ∈ G s,u (K) in (3.3.3) and (3.3.4) using s and u, and note that the logarithm of the t-module G s,u , denoted by Log Gs,u , converges ∞-adically at v s,u . We then establish the following explicit formula for this logarithmic vector Log Gs,u (v s,u ) (stated as Theorem 3.3.7 via Proposition 3.2.3 using hyperderivatives).…”