  We introduce a supercooled liquid model and obtain parameter-free
quantitative predictions that are in excellent agreement with numerical
simulations, notably in the hard low-temperature region characterized by strong
deviations from Mode-Coupling-Theory behavior. The model is the
Fredrickson-Andersen Kinetically-Constrained-Model on the three-dimensional
$M$-layer lattice. The agreement has implications beyond the specific model
considered because the theory is potentially valid for many more systems,
including realistic models and actual supercooled liquids.
