My hhree axis model

I have N squish things which set three variable, one of these thing can have a be about the proper center in any of the three axis.

So a thing is a bit up on one axis, a bit forward on the on the and a bit left on the third. In any exchange, two parties can agree on the position of an axis orr disagree. On a disagreement the discussion is passed on to the next party for a bet on the second axis.   Each of the tree axis has obtaining a cluster of bets.

Agreement happen when two parties see theri positions within a known precision. The number N is unknwon but the axis clusters are not optimum until N is represented. When two parties continually agree along  one is, a second may drift off until one party disagrees.

Undr sampling.  Let X,Y,Z be e numer od undersampled.
X^2 is he number undersampled twice.

x^2 + y^2+ z^2  = 3xyy. This relationship tells us the uncersampling for missing one sample and missing two asmple.  No there is no case of missing three sample.,

At  any given tie we have a collection of missed one and missed trice.

My undesampled must be    3 *  xyz  +  xyz The number undersampled twice and he number once.   My smallest error bit must be 2/3.  , this error is 8/3. I have gone throu two comrpessions, thtis is greater than one half.        The numbers xyz are queu length, as integer.

Introdsuce N and get probabilities. The smaller error erm is 1/N of the larger. If opur xyz are poisson then wecall them the average queue length and N gvs us a goussian arival rate.

Three Markov queue distributing error. Every bet passes tci through a three way selector.  .

Three queues, each structure on log3 with a specified number of empty spots.  It is sampled ythe pi boss, a twos complement sampler.

Shannon is one color, hypberbolic two colro, andthose are the bottom rung and themarkov idenifies thethree color sysmetsm

They partition N into one tw orthree groups The basic system error is xyz/N^3.

5*13*183/Avagogros^3 = Plank? Plank should be a probbiliy. But this number need squart to make it binry. the exponent become -34.

So we have methods to expression optimumpacking in any two9 adjacent dimensions.

xyz/216 = 6? This is the smallest error for a system organized by error mode. This or 1/3 of it. We shoud have an N hat takes the square root of this and makes it binary and the planks uncertainty.

Anyway

The markov gives you your error shape, the pit bas. Tell it the nume of error modes in N-1 dimension and it give the error modes in N+1.  The error modes must be distributed among the generatro which will have ran x,y,z; integers.   X,Y is Dimension = two, it tells you the error modes needed in Z. The error generators operatedas Log3.  We etthe gernreal N dimensional packing system.

Runnub a finv dmesnional meand finding he zeroeth, fis, second and so on, error mode undersa,pling, each one ive times the oter.