When a 3 tuple is minimizing a surface and the vacuum has its own deviations, then add the extra dimension. The surface curves in two dimension, increases the hole size where collisions do not occur. The Markov surface is now under sampling and will compress along another axis. That would be another curvature, or better said, enlarge the current dual curvature to significance. Mass is path cancellations, minimizing the interactions with the vacuum.
So, in a Bayesian sense, the speed of light, c, is a ratio between two arbitrary axis. It is the numer of partitions in x one can make in t. If one combined partitions twice, then one has the number of combinations that measures the number N, the empty vacuum where no collision occurs, all the eliminated paths generated for the operator. Plank, steps of light, Boltzman make the duplicate paths converge into an axis to spread deviations, adding the next estimate to continued fraction measure of deviation.
The (v/c) ^2 is simply stating the Shannon, Markov, etc conditions. So sampling bandwidth is redistributed. The effect is to gain sampling bandwidth for mass and rob it from vacuum. Energy is spatial bandwidth, the space covered in a Markov 4- tuple. For the operators, it is like aliasing the next spin position, sometimes too far, sometimes to close. The extra continued fraction allows it to distinguish and cancel along that axis.
One could pretend to have a toroidal object with a proportion N in a hole relative to an enclosed sphere. Then choose a v/c, a compression ratio, and determine the two spherical curvatures needed to meet the conditions and map that to an enclosing sphere.
A collision is when the vacuum operator and spin object collide and emit a boson, two canceling spins. All these color operators meet the (etc) condition, so they combine, split always as needed, makes physics simple.
The vacuum has an optimum conpression with its neighbors. Exceed is and a photon emitted. The vacuum unit has imprecision, it is the principle that imprecision is balanced at light steps.The physicist is limited, he cannot decompress an axis and get more samples then the (etc.) condition allows.
The breaking point between 3D and 4D systems is when total N exceeds the 3D maximum. There is a point up the 1,y,z, links on the tree that lead to a maximum N, the point where the (etc.) condition cannot be met. There really is a finite, an Avogradro's. The unattended count when N > Avogadro are operators, they will be along an axis. Depending on the unattended count ratio, there are some combinations that will split or combine spin, the curvature null point.
Path merging. The 4 Tuple discards 3/4 of the paths, the 3D only 2/3. That is one more whole in the enclosed volume. It is just the necessity of the vacuum being a color operator, it will adjust 1/3 of the available two steps per light. The other 2/3 show no improvement in deviation count. So vacuum at zero simply recolors itself at light speed. But it is not at zero, it is at 1/2 using traditional quanta. Deviation count never goes to zero.
So, essentially. Specify the partition ration on any two axis. Markov tells you the equivalent N needed to meet the condition, and the second curvature can be significant. But one needs to know Avagoadro, which is the maximum number N that can fit in a 3D model before segmentation. I should boil down to five or six rational fractions.
Prediction:
Avogadro is large, thus deviations in count are very small, the system will form a stable boundary when kinetic energy flow favors quanta. Complexity at the boundary will increase, an evolution. Essentially, the system can hold as a 4 tuple in an energy surplus from the environment. So one gets this fractal effect, up on past the orbitals into biochemistry. Accuracy has energy cost, constantt velocity supplies greater N.
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