  In homogeneous glasses, values of the important dimensionless
stretched-exponential shape parameter beta are shown to be determined by magic
(not adjusted) simple fractions derived from fractal configuration spaces of
effective dimension d* by applying different topological axioms (rules) in the
presence (absence) of a forcing electric field. The rules are based on a new
central principle for defining glassy states: equal a priori distributions of
fractal residual configurational entropy. Our approach and its beta estimates
are fully supported by the results of relaxation measurements involving many
different glassy materials and probe methods. The present unique topological
predictions for beta typically agree with observed values to ~ 1% and indicate
that for field-forced conditions beta should be constant for appreciable ranges
of such exogenous variables as temperature and ionic concentration, as indeed
observed using appropriate data analysis. The present approach can also be
inverted and used to test sample homogeneity and quality.
