Fine-grained time equivalence above the I/O exponent

For every problem $Q$ whose input length is at most $B(n)=K(n+1)^q$ and whose output predicate depends only on the first $B(n)$ output entries, and for every rational threshold $R>q$, the following are equivalent: $Q$ is solvable in the signed-pointer WordRAM model at some rational exponent $r<R$, and $Q$ is solvable in the unsigned-pointer WordRAM model at some rational exponent $r<R$. Exact exponent bounds are not compared: a solver on one side may be transferred to the other with a polylogarithmic factor, so only existence below the threshold is asserted.