The 2 ∆ contains the first instance of statistically non-independent behavior and is both size-extensive and mappable uniquely to the many-body wavefunction. By setting 2 ∆ to zero, one obtains the usual idempotency requirement. The cumulant is a measure of the statistical dependence of particles; large values of the trace or square norm of ∆ is what we would like to associate with the term, "strong correlation".