John,
I am surprised and pleased that you've read the book so quickly.
You say I like eigenvalue functions. Not so much. I simply find them necessary to treat when addressing physicists. And you say that they require nature to be made of linear relationships, and ask how we know the universe is everywhere linear. My belief is that reality is essentially nonlinear and I've treated this elsewhere. Including the QSLR reference [2] in my current essay. This is a much later treatment than that of the book. For example, see [link:www.vixra.org/abs/1408.0005]Quantum Spin and Local Reality:A Quantum Theory of Events[/link] (page 105 to 111) for a more up-to-date view of eigenvalues.
Additionally in my 2013 essay Gravity and the Nature of Information on page 4, I show the key nonlinear relation for which I've developed an iterative scheme. You can't quite tell from the finite diagram, but things head for infinity amazingly fast. So I disagree that linearity is a significant constraint on my theory.
The robot was of course a vehicle to simply show how an algorithmic-based system, not itself conscious, could arrive at a theory of physics. I wanted to remove the 'magic' or 'mystery' from the process of math and physics. You mention the robot doing something "new". Without going back to check I suspect I meant through simple application of a random number generator to shuffle previous algorithms. I can check this if it's important.
You mention fractal math and trees. My goal in the 1970s (this book was 1979 with a few chapters appended in 2009) was to show how numbers arise from physical reality, thus how numbers can be generated from measurements, based on number generating measurement apparatus, and how from these numbers one can arrive at features, and even a "best" feature set, or eigenvector. Several of the topics you mention are outside of this goal, and were not considered.
You say I assume the ability to digitize the universe. That's clear. Thus reducing, not the universe, but the representation of the universe, i.e., the 'map', to numbers. Recall that Kronecker said "God made the integers; all the rest is the work of man." On this basis my main problem was to show how integers arise from the physical world, which I believe I've done. I do believe "All the rest is the work of man", and as such it's already in the books, I did not feel the need to derive it all, up to and including continuity as limit cases. In short the goal was very specific, so it did not cover the waterfront.
You say "it seems you have no place for the continuous as one of the major components of the universe." If you look again at diagram on the first page of my current essay, you will see that what's being measured (at the far left) is undefined. It could be continuous, it could be discrete. John, it looks like you might wish to read Gene Man's World available from the same source. That one is focused on continuity and consciousness (as of 2008). Specifically, Automatic Theory was intended to show how an automata (the robot), based on actual math, could derive the theory of physics without consciousness. [link:www.amazon.com/s/ref=nb_sb_noss?url=search-alias%3Daps&field-keywords=klingman+Gene+Man%27s+World] Gene Man's World[/link] is the basis of my theory of consciousness.
From your remark about free will, I suspect you will enjoy that one better.
Thank you for the effort you put into this, and for your very thoughtful feedback.
Edwin Eugene Klingman