Figure 6.

A probability density is generated by level sets of the constraint function. Here, it is shown that level sets of p are generated from lifts of level sets of J. When flat, the gauge field descends to a vector field (properly a covector field) on the base whose integral curves are level sets J(x) = c. Horizontal paths are lifts of these integral curves. They can be defined identically by the parallel transport through the bundle of a lifted point, and yield rings making up p(x).