I think that is what we are doing, completing that spectral theory. It is the calculus of Bayes, measuring the effect of inconsistent N on closure of set combinatorials. The model has operations closure over transitions from one Markov node to another. And transitions from one dimensional tree to another. It really does ell you the tick size along a centroid that best matches sets M on a scale, in N. It is a resolution, the the continued fraction is a refinement of one resolution within another. I think this useful, having our own Bayesian calculus.
When you let dimension M go as far as it needs, then you pick two geodesic points on a planar complex plane. You are finding the best irrational partition of N between set partitions. You are assuming all the resolutions are centered, but there is variation in even odd N always. That is because the center is N=0 or N=1. The Shannon-Markov-Boltzman-Einstein-Avagadro condition tells us how big N must be to stay within the current set partitions (maintain consistent compression)
It does not use the complex plan because there is no zero; deviations are all positive definite. They really go as 1/N. or really M/N, dimensionality reduces the uncertainty of the center. The quantum mechanic solution are the integer sets implied by the Markov tree over a descent to ground state. But light still seems to be 3D, according to my simple searches. Any other condition imposed seems to be resolvable with a trip up the Markov triples. That is, and other N-tuple Markov tree offers a cross link to a tree of lower dimensionality prior to breaching one. Except for M=3, the condition implied by the triple tree.
The system starts at one, which for a 4 tuple is (1,1,1,1) but that connects at (1,1,2) a valid 3 tuple and a a connected Markov tree. The Markov 2-tuples have no tree. Sort of the theory of Markov trees but it means something in connected sets. In each dimension there is a thickening of the topology by another layer, but the rule of topology holes are obeyed. And we prove queueing (information, set, combinatorial, etc) theory by showing there is always a 4D representation of the finite 3D system that is accurate to a nearest 3D Markov node. The system with inconsistent N can be compressed and expanded to geodesic in the circular domain. The theory of counting jelly beans in a bottle. What is the layering needed to keep the colors mostly consistent to the area/volume of three colored jelly beans. But the bottom layer can be one of the three colors only, and the second bottom layer has tow of the same color.
Time is a freebie. When the model adds M+1 to make a center, it gets a unitary expansion of the fourth set, into time. The circular assumption of time is that the resolution of R is the same as the resolution of time. When you select a 4 Tuple node, you are selecting the best approximation to N, according to your measured kinetic motion in Euclidean space. You have already inserted Heisenburg without knowing it. The 4D solution is compressed to cover variation in N. You are simply asking Markov to give you a more precise version of the closed colored surface, already demanded integer solution and already accepted the minimum value of one. You really do not have a time = 0.
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