APSP below cubic time: equivalence of the two WordRAM models

For the integer-weighted directed all-pairs shortest-path problem, in which every closed finite walk has nonnegative weight and the input lists edge presence followed by edge weights in row-major order, solvability in the signed-pointer WordRAM model at some rational exponent below $3$ is equivalent to solvability in the unsigned-pointer WordRAM model at some rational exponent below $3$. This is the APSP application of the fine-grained transfer theorem. It asserts the existence of algorithms below the cubic threshold on both sides, not equality of exact exponents; a positive subcubic exponent saving is preserved in either direction.