Zero Hedge brings it up. How much liquidity should a bot retain? Generally Phi if the market is adapting perfectly. So for any two period model, a currency value may grow by G^2 and shrink by S^2, so G^2- S^2 = Phi. That gives the market enough liquidity to pass the 'map' around as circumstances change.
Here is my thinking, take it or leave it.
1) All the moves we see in the markets are one period moves designed to stabilize a two period plan. This includes the bots. If that were not the case then the market would blow up.
2) When a currency is gaining value then the market is doing the tanh function and the tanh flow constraints apply. Tanh gives you the down move over the up move and it should be less than one. The probability of that trade pair is given by (1/2)* tanh'', taken as positive. The most likely trades are Pi/4 down and Phi*Pi/4 up. But the bot should track the probability curve and bet to make that valid.
3) When a currency is losing value then the market is doing the coth function, and the most probable trades are around 1/2 up and sqrt(5)/2 down. Butuse the (1/2)* coth'' curve, taken positive, for the most probable trades.
4) There is twice the market activity up then there is down, I think. This is the boson uo and fermion down thing.
5) I am not sure how to scale these to real currency values. Phi should be the signal to noise power ratio, if this market is adapting. Measure that SNR in units of the currency and you can scale all this.
Frequency falls as the hyperbolic angle drops, is my latest contorted thinking, but I still am a bit disoriented about mapping the hyperbolics to real markets. But, once the no arbitrage bots protect everyone's trade, then high frequency spoofing will not work. Zero Hedge wants the world to go back to fundamentals, the no arbitrage bots do that because the recognize only new information.
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