Consider a value added chain as a generator producing the typical sequence of total trade events in the chain. Then at maximum entropy we expect that chain to be a two color,the pit boss getting abut six bits of significance from the semi independent buyer and seller queues. The pit boss makes up another two bits, we have an eight bit fixed indexing channel.
Let us rename SNR to bandwidth share. Buyers and sellers work in a noisy channel, each has to accommodate both the potential counter parties and the pit bos. If either trader knows the general ratio, then a log base 2 gives them the number of bits, if this were a canonical twos complement trading system.
But, it is not, at least nit until the pit boss merges streams, collects market error. Hence, following right along, we get a Huffman encoding of the two queues, since the trade bids are not canonical.
So, when we hear that traders are log pricing that means they are quantum mechanical traders, they know they are trading large cap stocks forming a value added chain. As a distribution network, log gives the rank of the trade, are far down the tree a trade travels before it finds a match.
Te concept of Huffman coding creating generators that have aggregate ratio algebras, one distribution network can be made homomorphic with anther, it the pit boss is willing to carry approximation risk. It is a transformation that turns the N-graph coloring problem into an approximate version of a whiteming process on a finite index space, I am pretty sure.
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