Dear Saul,
very simple and elegant idea, very convincingly expressed. For me, the text has appealed to visual intuition even more than the pictures. Another strong plus is that your essay is one of the few that hits the central question of the Contest right on the head.
One observation. You stress in various ways (e.g. with your first image) that your approach is opposite to Tegmark's. In my opinion, they can still coexist. If reality is ultimately a complex mathematical structure (let's not worry about the multiverse aspects), what's wrong with imagining homo-sapiens building the knowledge network for describing that external reality just as you indicated? Your meta-theory works independent of the origin or status of that reality.
Another point. I notice your prudence in envisaging the eventual formation of a final, mega-hub at the top. Indeed, there are phenomena and driving forces in nature, as found in our evolving biosphere, that seem to escape a precise mathematical formulation, and to resist the math-based game of regularity finding/aggregation/abstraction. Hence, the scenario implied by your meta-theory is one in which multiple separate disciplines - physics being one - will keep existing and developing, forever separated from one another by their degree of math-friendliness.
Is some stronger unification possible/desirable?
Perhaps it is, by looking not only at the top of knowledge but also at the bottom of reality. Let me explain. Your essay is extremely effective in covering the evolution of human knowledge (the observer side), and suggests a unification process going upwards, looking at the top of knowledge, while the observed object - the universe - remains passive and static. But if we viewed it as dynamic, and managed to find the seed at the bottom of reality, and that seed turned out to be a simple algorithm (as some crazy people dare suggesting), from which everything would emerge - fields, matter, but also biospheres - then we would have a more unified scenario: that seed would certainly deserve a very special place in the network of human knowledge. Perhaps the top, although it seems to me that it would not be a hub exactly as you conceive them...
Best regards
Tommaso