Vik,
Great essay, unique in its approach to the difficult theme given us by the organizers. Toungue-in-cheek funny, a few good serious pokes at the orthodoxy, and your own view of deity dancing around in the background.
To build your approach around the Munchausen Trilemma is brilliant. Would like to see MT used in an attempt to undermine MUH as well as support it.
Your arguments regarding the applicability of the first two lemmas of MT seem reasonable.
Regarding the third lemma, your 'rudimentary equality' seems to me to lack a good definition. My impression is you found it necessary to introduce this idea and its associated proof (which I find at least a little questionable) to support your view that "...physics was not designed to be a circular argument in the first place."
However, the last sentence of your essay reads
"Suppose we choose to believe that this Grand Mathematical Superposition is intelligent. What could it be? Hmm."
To my mind this suggests the opposite, that in your allusion to the possibility of a 'creator' and a 'creation' one can perhaps consider that physics was indeed a circular argument to begin with.
It is a characteristic of viable networks that they are in some sense self-supporting, an emergent property. A consequence of the interactions that sustain the network. There is a closure, a circularity, a circulation in that web of interactions, both in the networks of ideas that comprise our physical models and the physical reality they seek to describe. To me this suggests the possibility that the circular argument lemma is satisfied without the need for your questionable proof.
I like the bit of a sidestep in the way you bring in emergence, tying it to the rather ambiguous 'rudimentary equality'. I'm surprised that Tegmark seems to ignore it in his MUH paper. I don't see how he can make his argument tenable without addressing emergence.
Many thanks for this essay. It is clever, very funny, and horribly twisted. Unique and powerful its own special way.
And given that a google search for rudimentary equality gave only reference to a legal technicality, can see where you get the notion that being a lawyer is appropriate when considering the absurdity of the universe.