Suppose a physical system admits a 1-form of Action. That is, the functional
form of the coefficients of the 1-form of Action are subsumed to be adequate to
describe the physical system. (Note that many primitive unconstrained Lagrange
systems start with a 1-form of Action, A = L(x,v,t)dt on a space N (=3n+3n+1)
dimensions.

Now ask the question: Are all the independent variables necessary, or is there a
minimal set of functions that can be used to describe the same problem.? Can
functional combinations be constructed that yield the same topological
information?

It is remarkable that there is a simple answer to such a question. The minimum
number of functions required to adequately describe the 1-form is equal to its
Pfaff dimension ( or class ).

Presume the orignal functional form of the 1-form has been constructed over some
model space of variables, and presume the coefficient functions are c1
differentiable. Then construct the sequece of differential forms

{A, dA, A^dA, dA^dA, A^dA^dA,....}

At some integer M, the sequence terminates.

M is the Pfaff dimension of the 1-form.

Only M independent functions and there differentials are required to describe
the system.

Topological Torsion appears at Pfaff dimension 3 and above. Thermodynamic
irreversibility appears at Pfaff dimension 4.

If the Pfaff dimension is 2 or less, then A^dA =0, which is the Frobenious
unique integrability condition. The direction field represented by the "normal"
to the surface A=0 can be put into correspondence with the gradient of a
"unique" function. Uniqueness in this sense is lost in domains where the Pfaff
dimension is 3 or greater.