  We present a first-principles implementation of spatial scale invariance as a
local gauge symmetry in geometry dynamics using the method of best matching .
In addition to the 3-metric, the proposed scale invariant theory also contains
a 3-vector potential $A_k$ as a dynamical variable. Although some of the
mathematics is similar to Weyl's ingenious but physically questionable theory,
the equations of motion of this new theory are second order in
time-derivatives. Thereby we avoid the problems associated with fourth order
time derivatives that plague Weyl's original theory. It is tempting to try to
interpret the vector potential $A_k$ as the electromagnetic field. We exhibit
four independent reasons for not giving into this temptation. A more likely
possibility is that it can play the role of "dark matter". Indeed, as noted in
scale invariance seems to play a role in the MOND phenomenology. Spatial
boundary conditions are derived from the free-endpoint variation method and a
preliminary analysis of the constraints and their propagation in the
Hamiltonian formulation is presented.
