  Any positive word comprised of random sequence of tokens form a finite
alphabet can be reduced (without change of length) using an appropriate size
Braid group relationships. Surprisingly the Braid relations dramatically reduce
the Kolmogorov Complexity of the original random word and do so in distinct
bands of (rate of change) values with gaps in between. Distribution of these
bands are estimated and empirical statistics collected by actually coding
approximations to the Kolmogorov Complexity (in Mathematica 9.0).
Lempel-Ziv-Welch lossless compression algorithm techniques used to estimate the
distribution for gaped bands. Evidence provided that such distributions of
reduction in Kolmogorov Complexity based upon Braid groups are universal i.e.
they can model more general algebraic structures other than Braid groups.
