Newtonian Spacetime Structure in Light of the Equivalence Principle

I argue that the best spacetime setting for Newtonian gravitation (NG) is
the curved spacetime setting associated with geometrized Newtonian gravitation
(GNG). Appreciation of the ‘Newtonian equivalence principle’ leads
us to conclude that the gravitational field in NG itself is a gauge quantity,
and that the freely falling frames are naturally identified with inertial frames.
In this context, the spacetime structure of NG is represented not by the flat
neo-Newtonian connection usually made explicit in formulations, but by the
sum of the flat connection and the gravitational field.