The following eight posts were put on Usenet sci.physics on 8/08/08 as a tribute to Octonion
Algebra and the number 8. They contain a bit more explanation and justification of claims than
found in the PDF above.
Why Octonions 3: Octonion Algebraic Variance and Invariance
Why Octonions 1: Introduction
Why Octonions 2: A Full Description of the Algebra
Why Octonions 4: The Octonion Ensemble Derivative
Why Octonions 5: Octonion Fields and 8-Current Density
Why Octonions 6: Octonion Work-Force and Conservation Equations
Why Octonions 7: The Full Form of Conservation
Why Octonions 8: Concluding Remarks
Octonion Algebra and its Connection to Physics.pdf
Variance Sieve on the Associator
The following are links to PDF files you may find interesting.

This PDF is a good place to start.
This PDF shows the results from running the associator through the Octonion Variance Sieve
Algorithm. The invariant portion is identically zero. This is not to say algebraic invariant forms are
associative, they are not. The concept of algebraic invariance itself does seem to be associative.
I have had discussions on my claim that Left Octonion Algebra is not isomorphic to Right
Octonion Algebra. Grab this PDF for a full disclosure of my position and its relevance.
On Isomorphism Within Octonion Algebra
This PDF discusses how 3D Euler Angles can be represented as an Octonion automorphism
Octonion Euler Angles for Physical 3D Space