Uniform runtime transfer between the two WordRAM models

There is a natural overhead exponent $d$ such that for every problem $Q$ whose input and observable output are bounded by $B(n)=K(n+1)^q$, every input-magnitude exponent $\kappa$, and every correct source program with runtime $T(n)$ at all sufficiently large word widths, there is a fixed target program, width threshold coefficient, and positive $C$ solving the same problem in $C(T(n)+B(n)+1)(\lfloor \log_2 n \rfloor+1)^d$ steps. This holds in both directions between the signed-pointer and unsigned-pointer models, including input packing and output recovery, and the same bound works at every sufficiently large physical width. This is the quantitative half of the equivalence; it does not assert the operational simulation clauses.