4D?

x4 + y4 + z4 = w4

Conjectured incorrectly by Euler to have no nontrivial solutions. Proved by Elkies to have infinitely many nontrivial solutions, with a computer search by Frye determining the smallest nontrivial solution.[4]

This equation does not factor, I thnik.

This equation counts the queue of updates needed in a 5D system to maintain N at maximum 5D accuracy. It is not counting quantity, it is a count the count of error updates, absolute positive integers.

The error matrix need to hold at least for each of x,y,z in its pending error packing.  If the condition is met, ther there will be an emission of the selected count queue and the w queue, where w will be the 4D equivalent of monopolarism needed to balance N.  This think will generate error updates as long as any axis gets an update, with the exception of these three collapses. I have four dimensions.

Note, any scale increase of those arrivale queues and I get the same partition accuracy,. Unstable, it seems to me.

It does not seem to factor. I dunno, just ow looking.

Otherwise, Chinese remainder theorem, look it up. It is about keeping the error term updated from a small finite set of choices..

That is the problem, this 4D system is flait. If this was a coloring rule it simply says, place red/yellow, blue/Yellow,,green/yellow.   His N is endless, his Plank perfect, violates rule two way back =many blog posts.

So, I am a five coloring, I need 'spots' for he new new update.  I have:

5uvxyz =

I have set the counts reserves for these in the error packer.  My sysem hais assigning cloks, actually.

Then there is a bunch of square terms, how many counts need for those still unampled twice?, these square terms define that space but are subtracted by all counts reserved for interaction twice, and so on up to the fourth power.   Then along the maximum entropy path, I must continually shrink that tree that have collapses which are partition interactions.  That processing of the error tree is Boltzman. I always get that, then N gets me Plank and that gets me a spot on the Tree, and the fermion and boson (wosun, gohin,m etc etc)  split in the soup. My soup always has a convenient ruler to place colors.

Good stuff, we can take a whole class of problems and put them onto a graph, generator, and find proofs by node manipulation as long as we are maximizing entropy.