Essays on Gravitation contest
The essay, "Quaternion space-times-time invariance as gravity" was submitted to the 2015 Essays on Gravitation contest run by the Gravity Research Foundation.
By comparison with typical technical physics papers, an effort was made to make the math simpler and have less jargon. It is seven pages long. It has five equations in the body of the paper, and five more in the appendix. There are eleven references.
The results are in... The winner was an essay by Gerard 't Hooft, a Nobel Prize winner and all around smart guy. My essay did not win second, or third, or forth, or fifth, or honorable mention. The contest gets plenty of submissions from fringe physicists. I suspect the word "quaternion" in the title and my non-academic address meant the paper was quickly dismissed.
Hard core stuff
I did learn something about my own efforts from reading the paper. His paper was about conformal symmetry breaking. Roughly speaking, that has to do with the scale of measurements in time and space. Maxwell's theory for how light works has conformal symmetry. If we use light to measure things, then the absolute size of anything cannot be known. Cool. We can figure out relative sizes and times.
This cannot be the entire story since we can figure out the absolute sizes of things. He writes that something about quantum gravity is going to break conformal symmetry. You would have to read the paper to struggle to see his point.
In my own effort, there are two numbers that enter in to make measurements different. One is the relativistic velocity of an observer. That is plain old special relativity. The other is the dimensionless gravitational length of a graviational source. It would be this value that breaks conformal symmetry in quaternion gravity.