On the resolution of space-time singularities

In previous articles it has been argued that a differential calculus over a noncommutative algebra uniquely determines a gravitational field in the commutative limit and that there is a unique metric which remains as a classical "shadow". Some examples were given of metrics which resulted from a given algebra and given differential calculus. Here we aboard the inverse problem, that of constructing the algebra and the differential calculus from the classical metric.