The monte carlo version of stokes theorem

The classical Kelvin–Stokes theorem relates the surface integral of the curl of a vector field over a surface Σ in Euclidean

Consider generalized stokes.  We construct an N dimensional hologram from an N-1 quantixing channel with momentum. The channel is the refleftion plane of a transformation.  Instead of summing flux we consider momentum instead.  N-1 dimensional circle plus momentum -> N dimensional sphere, for example.

What is we only had a probabilistic model?  The N and N-1 forms and momentum are only known to a bound uncertainty?

Then we make a monte carlo generators, and we quantize values to fit the channel within a bound. Then we get a set of proofs about deterministic systems. We can show changes to our generator, in graph terms, as the uncertainty bounds go to very small.   Determine when the hologram has jumps or changes adiabaticaly. We can say something about the round off error, if it is a repeating fraction we consider that an error, the original system is leaking.

And so on.  That is the handwave version of auto pricing. I presumes a pit boss process that can carry round off error in probabilistic system, so we are originally using a monte carlo generator that accepts fixed uniformly distributed values.

A related idea is the centrality graph of a transform, it come with a kind of generator.