Fibonacci ratio showed his mark

There’s a new volatility ‘witching hour’ puzzling stock traders

Consider bid to offer in volume, extracting the ratio of two queues, the in and out at balance.  We require the difference in variances to be 1, define that as tradebook error.

The ratio of 'sigma' or typical queue size must obey a ratio property, which I magically claim has a special result, ratio times  rate of ratio has a maximum when it is  .618.  It is a real result  of the market acting like an adaptable rational approximation theory. Phi is the solution to hyperbolic second derivative is make. It is the solution most elastic; meaning the ratio is accurate, pricing works.

The missing connection is that number theory is about finite algorithms and how they utilize index space.  And that becomes a a queuing problem on recursive protocols.  

It is there, queuing on interacting protocols makes a statistical flow problem, leading to queuing on networks and generators having algebras.  A high school kid will formulize it. 

But there is a close relationship between a generator derived from compressive pricing of sequences and  a bunch of short over the counter protocols discovering themselves. The same price menu should result via complexity proofs. And complexity and window size should be consistently divergent. We go from discovered sequences to an optimally interleaved pricing events.

In this case, there is a point when brokers have to record their numbers for the close. That is the most active trading period and a maximum on the second derivative of that ratio.