Rick - you wrote: "I am a bit puzzled by both you and Michael Goodband talking Octonion Algebra, S7 and a split signature (as in Minkowski metric spaces) all in the same breath." - I've double-checked the little note I left on Michael Goodband's discussion. All I am doing is refer him to the work of others that I believe is related ... so I don't know what of my writings you're referring to.
Then you wrote: "You do not get S7 with split Octonions that are not even a division algebra." - Sure you can "get S7 with split Octonions", e.g. when supplying Lorentz boosts as in Gogberashvili http://arxiv.org/abs/0808.2496 . So when Goodman proposes that he's working with some decomposition of S7 into S3xS4 or S3x(S3xS1), then that's not a problem to me a priori, on this high level at least. Whether he can actually make it to work is a whole different story, and I'm not competent to comment on that.
You conclude that same paragraph with a statement about me: "I can see where you are coming from since it is good politics [...]" - I'm lost, what are you driving at?
Overall, I am confused how you are - on one side - advertising your approach to recover Maxwell electromagnetism (amongst other claims, of course) from octonions, but - on the other side - criticize others for "talking Octonion Algebra, S7 and a split signature (as in Minkowski metric spaces) all in the same breath". In my analysis of your octonion variance sieve I remained on the mathematical side, without going into physics. The physics part is yours to defend, though I did have a peek. I do understand that you are defining an octonionic action
W = invariant F * j
(i.e., from a generalized octonionic force and flux) where W is built from an octonion differential operator
Del := { d/dx0, ..., d/dx7 }
and an octonion potential
V := { V_0, ..., V_7 }
such that (if I got it right) you define W as:
W = Del ( Del V V Del ) ( Del V V Del )
Here, the notation V Del means applying Del on V but using the commuted octonion multiplication rule. It is a product of three terms, but since the 2nd and 3rd term are the same we don't have to worry about nonassociativity. In turn, this almost instantly proves that it is an algebraic invariant under your octonion variance sieve.
Your notation of this is different, with lots of indices; but I think my notation is faithful (or at least essentially right). Your achievement then follows from recovering Maxwell electromagnetism (and more; again, which is for you to defend) from that. This alone is a notable achievement! What confuses me is your criticism of others attempting to recover Maxwell electromagnetism, algebraic split-signatures, or Minkowski metric through other means. Just like yourself, some of these other approaches also start with octonions, and just as you are proposing an ad-hoc action W as I sketched above, these other approaches propose ad-hoc constructions as well.