Peter, I watched your Vimeo video of 38 minutes (in your bibliography) and then read your essay. Listening to you speak in the video helped me to read your voice on the page.
It seems you advocate a "language translation" between models: the model used in your video to the current Standard Models for example. I wonder if the translation might be done formally following the diagram of the "infomorphism" on page 73 of "Information Flow: The Logic of Distributed Systems" by Barwise and Seligman.
My own belief is that we will never understand the Universe-- there will always be mysteries. And then there is the old story about the blind men encountering an elephant for the first time. One grabs the tail, and the tail becomes the model in support of his statements about the elephant.
Much like your sphere in various situations becomes the models supporting your statements in the paper. Much like experiments become the models supporting statements in the Standard Models.
Of course in the old story about the elephant, each blind man has a different model, each model supporting their differing statements. Although there would be no infomorphism between some statements-- such as the elephant being like the branch of a tree for the man holding the tail, while for the man feeling the leg, the elephant is like a tree trunk-- there may be other statements which translate exactly. For example, the smell of the elephant would be largely the same for each man.
My own approach In this contest is to translate from the probable experiential knowledge of particular pre-socratics (Thales, Xenophanes, Parmenides, and then Socrates himself)-- specifically about their probable experiential knowledge of "the self"-- into possible scientific knowledge for a community of researchers, for example, those who have the know-how to use non-wellfounded sets, co-algebras and streams. Especially when the likes of string theory seems beyond verification by experiment.
As for the blind men feeling the elephant, for each domain of mathematics such as field theory, co-algebras etc., there may be infomorphisms between each language, including yours.
Thank you for making me aware of your work!