Bounds for dynamic identifying codes in the king grid

Let M_n count all visits, including repetitions, in a shortest walk whose visited vertices form an identifying code in the n by n king grid. The limit of M_n/n^2 exists and lies between 28/113 and 1/4. For n at least 6, 28n^2/113 - 7n <= M_n <= n^2/4 + 36n. Three exact integer discharging certificates, a walk-cost inequality, and an explicit family of finite walks give the bounds. Connected-set size and repeated-visit walk cost are kept distinct.