mitchell porter, if it's not too much of a digression from the main topic at hand here, could you elaborate on this statement? Does the Higgs mass play nicely into theories of asymptotically safe gravity (which I assume is the "agravity" mentioned later in your post)?

The special feature of the Higgs and top masses is that they place the standard model at the edge of metastability. One interpretation of this (see section 5.1 here) is that the Higgs quartic and its beta function both go to zero at the Planck scale. A 2009 paper showed how to obtain this under the assumption of asymptotic safety of gravity.

Agravity is short for adimensional gravity, gravity with only dimensionless couplings. It resembles conformal gravity. See "Agravity" and "Agravity up to infinite energy". The idea seems to be, embed the standard model in a nongravitational field theory in which all couplings are asymptotically safe (Francisco Sannino's group works on this), then couple that field theory to dimensionless gravity so as to preserve those special Planck-scale boundary conditions without finetuning (see figure 1, page 15 of the second agravity paper).