  We report on a direct connection between quasi-periodic topology and the
Almost Mathieu (Andre-Aubry) metal insulator transition (MIT). By constructing
quasi-periodic transfer matrix equations from the limit of rational approximate
projected Green's functions, we relate results from $\text{SL}(2,\mathbb{R})$
co-cycle theory (transfer matrix eigenvalue scaling) to consequences of
rational band theory. This reduction links the eigenfunction localization of
the MIT to the chiral edge modes of the Hofstadter Hamiltonian, implying the
localized phase roots in a topological "bulk-bulk" correspondence, a
bulk-boundary correspondence between the 1D AAH system (boundary) and its 2D
parent Hamiltonian (bulk). This differentiates quasi-periodic localization from
Anderson localization in disordered systems. Our results are widely applicable
to systems beyond this paradigmatic model.
