That x thing in Brownian motion

See it? That x^2 thing? What is it? It is the solvent. Einstein and company are, yet again, assuming the vacant space in which Newton's Grammar can be written. That is not so, the X thing are particles, just like the thing that is doing the D, for diffusion.  There are two, and X^2/D is a power ratio, otherwise known as a spectrum ratio.

What we are looking at is more than likely e^[-(tanh)^2].  You can't get completely there by assuming the solving is a flat property, there is a covariant viscosity between the two materials. This is a power spectral distribution between to adapted systems. T is just Ito's calculus counter which tells you the order in which things must fit into the differential. It is really a sequential quant number.  N is the additive number which generates the rational approximation to Pi and e.  It will look like, ak/aj; where the k and j go as: a1 +2*a2 or a1+a2, depending upon the Lagrange.

I checked this out, that hyperbolic angle 3/2*ln(Phi) comes out as something like log(Phi+2), so at that half angle the second Lagrange is taking over, and Phi will be something like F16/F17, making it the log of (F16+2*F17)/F17. The silver ratio takes over at the barrier where probability his highest and the first Lagrange cannot get any more accurate. So that N and the Pi thing will cancel, e becomes a rational ratio and p(x,t) will end up being -tanh*log(tanh) or tanh*tanh', one of those, I am sure.

Hyperbolics does this with the Horwitz rational approximation and additive sequence. I mean, the graph guys are using a similar scheme to make 'greedy' links and nodes which work just like the rational approximation sequence. It is time to dump the Greek letters. Newton is the limit as Ito's index gets large, nothing more than that. When the index gets larger, the sequential Ito counter's,t, become dense, that is all that is happening.