Operational simulation between the two WordRAM models

There is a natural overhead exponent $d$ such that every program of the unsigned-pointer WordRAM with multiplication has a fixed signed-pointer simulator, and conversely every signed-pointer program has a fixed unsigned-pointer simulator. The simulators preserve successful halting, accept/reject verdicts, and every mapped source memory cell, at target width $w+4$, within $C(t+w+1)(w+1)^d$ steps for a positive constant $C$ fixed before the width and input. This is the operational half of the equivalence; it says nothing about transferring a runtime bound for a whole problem.