If we apply epistemological quantum path integrals to a sequence of characters, the "sum" is the result of the path of least resistance across the information field. Isopsephy essentially "flattens" the bipartite tensor product of characters into a finite stable state probability distribution. Two words sharing a sum are essentially entangled states within the 5th-dimensional dissipative system you described. They occupy the same phase space coordinates despite having different internal "spin" (letter arrangements).