Consider

The pressure of a flowing mass goes as area squared, and we want flow constrained.  We have:

(x+i)^2 - (x-i)^2 = constant

This is deterministic constrained flow, hyperbolic.

Now, as I suggest to the Money Market Theory blog, just take that equation and use it for credit allocation with one proviso. We risk adjust all depositors and borrowers to six bit arithmetic.  Otherwise the S/L operates as normal in sandbox (risk adjusted, equal looks at the trade book, asynchronous intervention by the market maker to keep within the constant).

Limiting the agents to six bits is equivalent to a rank 6 structured queue.  The rank of the queue will be set via risk equalization of agents.  The market making risk will arbitrage free and that means the round off error will be non-repeating. 

What is the most arbitrage free ratio? Phi, that L/S ratio generates the maximum liquidity for the agents, it maximizes L/S times delta L/S which maximizes the second derivative, liquidity. But we never reach Phi, we do not have the precision.  The fair trades two color channel follows this rule, the market maker always bouncing over and under the optimum ratio.