“…Local interactions result in so-called "ice rules" that 33 govern the number of moments pointing into and out of each vertex to minimize the 34 local magnetostatic energy. Artificial spin ice structures have proven to be exemplary 35 systems in which to study frustration [5,6] and have been noted for their technological 36 potential as both a reconfigurable metamaterial and as a memory storage medium [7,8,37 9, 10,11,12]. Connected artificial spin ice in particular has been studied extensively in 38 the last decade [13,14,15,16,17,18,19,20,21,22,23,24,25].…”