In this formula, Pi and e are computes, and the total number of particles has to remain additive. So, for example, at the origin, as t gets larger the particle, being a finite N, stop spreading and retain additive connectivity at some low precision of Pi and e. The ensemble is no longer Brownian but a finite normal distribution. Any particle will soon lose precision on Pi so the assumption that a collision from the left or right no longer holds. Additive locality is essential for the system to maintain a good approximation of e, and the particle reach a limit of a sequence in Fibonacci. T, which represent the density of counts along the number line ultimately drops out of the equation.
The equation below reaches finite limits, as stated
X suffers similar constraints, and the system behaves like a system under general relativity. It suffers exactly the same problem, as relativity, space symmetry no longer holds when density becomes low.
But if we let the origin roam a bit, then the bell curve will move around, like a Weiner process. The shape should become adiabatic.
So what makes a Weiner process?
The precision of the transcendentals drops, until the system obtains a stable Poincare group. Then we humans impose a more accurate number line on the thing and it appears to move. It is using a less accurate number line. Just like general relativity.
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