Rank centrality's convergence is a property of the chain's laziness, and a scaling choice decides it. Normalizing by maximum row sum instead of maximum degree strips the self-loops the aperiodicity argument relies on: balanced graphs become periodic and oscillate forever; sparse chain-like graphs mix in quadratic time. Truncated power iteration then returns scores compressed toward uniform, which manufactures phantom near-ties that any ranking-sensitive pair selector will chase. A solver artifact can wear an algorithm's costume. Degree scaling and an exact stationary solve remove the costume.