The trick to TOEing

The concept isw simple long division. If one constructs a compact generator that produces the typical sequence for packing a channel, and the channel error is bound, then long division between two generators co-packing a channel works.

The tree is an example. All things being equal, the tree root and tree branch system ate optimally queued, there is n transient built up or shortages along th root system up and branch system out.  No branches are dying, the trunk is round. In that situation, one can integrate all the root nutrients on their wayup, and inegrate all the waste products queued for exit; a ratio of those two should be linear.

We get a quotient ring when we introduce the pit boss which keeps the flow error bound, and the trunk round.  This is a big assumption, the hidden hand so to speak.  In markets we have the market maker, in physics the gluon (in a three color).  When we have a two color packer and bound error, then both the ratio and its derivative are valid.  The delta is valid because the pit boss gets equal access and will be index synchronous in assigning yield swaps. The assumption is the market maker is fast enough to keep up, deltas are within bandlimit and can be measured without too much alias.  The market maker makes the inputs sample the outputs sufficiently to be just congested, just outside the Shannon bandwith requirement and the aliasing is managed. The idea is to abe a slightly imperfect sampler such that price variation is allowed within the bound bit error.

Under those conditions, hyperbolics apply, the queues are structured, balanced and their is suffiecient flow to maintain quantizatiuon, the Huffman tree. The optimum condition for s/l and delta s/l follows the tanh differential equation, and the optimal point, the ratio of savings to loans is known, a mathematical constant of sphere packers.  Sphere packers will always move toward that ratio, one can derive it, it is when the second derivative is maximum.

hen savings and loan ratio migrates toward the optimum, always, then the price variation has maximum extent, it can count out the greatest number of variations without overlap.  The economy heads toward maximum complexity, always, in a sphere packing assumption.

The market maker is really using the WalMart checkout stand algorithm, the maker is moving up an down the aisles changing the 'items per basket' to keep queues stable. He is maintaining, in the absract, two balanced Huffman tree sin an adaptive mode.