So my task is thus to show that the math of optimal fitness requires anarchy to be contained and limited.
I accept your challenge.

When I referred to the harvesting of entropy what I meant was that life requires entropy to exist, but critically such entropy must be limited and contained. Entropy/mutation must not be allowed to exceed the error threshold. Error threshold was developed from Quasispecies Theory by Eigen and Schuster to describe the dynamics of replicating nucleic acid under the influence of mutation and selection.

If replication was without entropy no mutants would arise and evolution would cease. On the other hand, evolution would also be impossible if the entropy/error rate of replication were too high (only a few mutation produce an improvement, but most will lead to deterioration). Error threshold allows us to quantify the resulting minimal replication accuracy (ie maximal mutation/entropy rate) that still maintains adaptation.

This can be shown analytically at its clearest in an extreme form of a fitness landscape which contains a single peak of fitness x > 1 with all other variations having a fitness of 1. With an infinite population there is a phase transition at a particular error rate p (the mutation rate at each loci in a genetic sequence). In Eigen and Schuster (1979), this critical error rate is determined analytically to be p = ln(x)/L (where L is the chromosome length). When this mutation/entropy rate is exceeded the proportion of the infinite population on the fitness peak drops to chance levels.

This can be thought of intuitively as a balance between exploitation and exploration in genetic search. In the limit of zero entropy/mutation successive generations of selection remove all variety from the population and the population converges to a single point. If the entropy/mutation rates are too excessive the evolutionary process degenerates into random search with no exploitation of the information acquired in preceding generations.

Thus the optimum entropy rate should maximize the search done through mutation subject to the constraint of not losing information already gained.
Any optimal entropy rate must lie between the two extremes, but its precise position will depend on several factors especially the structure of the fitness landscape.

It is also worth noting that at least with genetic algorithms natural selection tends to reduce the mutation/entropy rates on rugged landscapes (but not on smooth ones) so as to avoid the production of harmful mutations, even though this short-term benefit limits adaptation over the long term.


I agree and would argue that this applies to anarchism as well


Fair enough. In the interest of winding down this discussion I will concede that while the argument above demonstrates that entropy must be controlled/limited/harvested to achieve optimal fitness this does not mean we do not need anonymity now or that anonymity will push us over the error threshold for civilization at large. It appears far more likely that we are well below the optimum entropy rate currently and that an anonymous cryptocurrency will take us closer to an optimal state.

As you said anonymity is inevitable regardless of what you do.
Like minded individuals are already working to similar ends http://zerocoin.org/media/pdf/ZerocoinOakland.pdf
Should you lack the time for a response to this post I will not take offence
    
References:
Eigen, M., & Schuster, P. (1979). The Hypercycle: A Principle of Natural Self-Organization. Springer-Verlag.
Ochoa G., Harvey I, Buxton, H. Optimal Mutation Rates and Selection Pressure in Genetic Algorithms. Proc. Genetic and Evolutionary Computation Conference 2000
Clune J, Misevic D, Ofria C, Lenski RE, Elena SF, Sanjuán R. Natural Selection Fails to Optimize Mutation Rates for Long-Term Adaptation on Rugged Fitness Landscapes. PLOS September 26, 2008