Standard Model scales from warped extra dimensions

If in the Randall and Sundrum RS1 model the inverse of the compactification radius, the AdS curvature scale, and the five and four-dimensional Planck scales are equal in size, as is natural, then the warp factor at the location of the low energy brane is of value 1/pi. So that all scales derive from locations in the space, we identify the extra dimension with the infinite covering space of the S1/Z2 orbifold. The extra dimension is then essentially a series of connected line intervals, punctuated by branes. Scales on successive branes in the extra dimension descend from Planck scale in a geometric sequence of common ratio 1/pi. Evidence is provided for such a sequence within the spectrum of particle masses, and of a second geometric sequence, of common ratio 2/pi, which suggests that the AdS spacetime is six-dimensional and doubly warped. The scales of the Standard Model lie at coincident levels within the two sequences. A third sequence, of common ratio 1/e, provides a symmetrical framework for the Standard Model and points to a warped product spacetime.