Dear Alma,
A writer's greatest reward is to be understood. Thank you! I sometimes feel I should apologize for being subtle, and yet I find that one can't apply natural language with the desired precision, without putting a fine point on it. Someday, I expect, we will communicate in a universal language -- if not mathematics as we know it, then something like mathematics -- that smooths the edges of ambiguity and allows a polished thought to reflect its intended glow. (Computer science maverick Lev Goldfarb is making strides in this direction.)
It's remarkable that you caught the irony of Lamport's "Buridan's Principle." There's a story behind that -- several years ago, I was perusing Leslie's publication page and ran across what I considered an important unpublished paper (though it was written over 30 years ago) and I suggested he try Foundations of Physics, where it was reviewed and published in 2012. To Lamport, the paper is not ambitious -- it is simply an acknowledgment of a hard problem (decidability) in computer programming, along with strategies to deal with it. To me, the principle implies deeper fundamental issues. I made the mistake, in referencing Lamport, of calling him a mathematician (he is most certainly educated and highly competent in the art) -- in which he corrected me, "I am not a mathematician; I am a computer scientist." I subsequently corrected the mistake, though it stuck with me, the difference between mitigating a problem in computer science and trying to solve it mathematically. Perhaps all programming is mitigation -- there are hardly any computer scientists who think P = NP. Do you?
That "the donkey still dies" led me to ponder the perfect first question. For if we could actually do the Schrodinger cat experiment with a dead cat as the initial condition, there would be no decidability problem. Dead cat in, dead cat out, with probability 1 in a bounded interval of time. The same principle that keeps a computer-simulated "cat" alive, assures us that dead cats don't spontaneously come to life.
Yet, conventional quantum theory would have us believe the contrary -- all life is a superposition of alive and dead. So you are right on point that I take the view that " ... the path analyticity that you require as a condition ..." is the sum of all Feynman path integrals in every bounded interval, i.e., -- to use the words of Karl Hess and Walter Philipp, every "timelike correlated parameter" (TLCP). This view supports Einstein's finding from special relativity that all physics is local.
Tegmark actually provided his own criterion for falsifiability. If all measured events are random choices between "alive and dead" the MUH is refuted. Probability without randomness, however, falls to cosmology -- the initial condition of the universe. That's why the multiverse hypothesis (an extension of Everett's many worlds interpretation of quantum theory) is inevitable in Max's program. Every free will choice, of what to measure, being a product of local events, implies global continuity; i.e., analytical continuation that I equate to the sum of Feynman path integrals. The multiverse is totally ordered, to satisfy our partially ordered measures of the universe.
Thanks again and all best,
Tom
P.S. -- thanks for the skinny on Ionesco. I didn't know that! LOL!