In other words, if you project the ten-dimensional space of string theory onto a four-dimensional space-time, is the resulting space-time, which will have an uncertainty principle in the coordinates at the Planck scale, accurately represented by a spin foam?
I don't enjoy the aggressive tone used by many contributors to blogs on RG. I believe that people who know me do not blame me to be arrogant; and I don't think that I am particularly stubborn. I actually only try to sometimes comment on questions. People who do not like my comments are not obliged to study them! I am retired, and I do not have to make a career, anymore. But sometimes I am still thinking about science, and I am interested in upholding intellectual honesty. (There are no benefits to be gained from kidding oneself into believing that certain problems are understood or, at least, promise to be understood, soon, when they are very poorly understood.)
This question contains too many ill-defined expressions to admit a clear answer. Generally speaking, the answer is: NO! Dimensional reduction of superstring theories can pass from ten to six or to four or to two dimensions. Usually, the noncompact dimensions that remain need not be noncommutative. (It is actually more likely that the "internal space" becomes noncommutative.) There is no obvious connection with "spin foam".
But, as I have said already, the problem with your question is that you are using too many expressions whose meaning is vague or unclear.
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