If we assume each agent is running a triple entry accounting system. Then, if the general distribution tree is a factorial, of dimension three, there exists a transformation into three matched binomials. It should be maximum entropy, it should be unique and preserve serialization.
We are assuming optimum portfolio balancing from the canonical trade format. Owner, clerk and customer. Each agent allocating serial trade space share according to -iLog(i), three 'i's sums to one. The trade selection based on the binomial that look more like a fair coin flip, I think it works out to.
My statement here the Huffman tree for each of three entropy generators has a transformation into an equivalent binomial. The the full factorial problem is reduced to balancing the three binomials by allocation of trade space. This is equivalent to altering coin weighting and toss share. There should always be a unique entropy maximizing selection of the next binomial, in the reduced model.
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