How banker bot handles term length, gains and losses

The hyperbolic banker bot equation is:

savings^2-loans^2 = 1

where savings and loans are grow rates in the balances. Banker bot is a spread sheet, and the equation is a projected a net loss over the next two periods.
What is a period?
It is left undefined in unit of time; but in units of spectrum, it is two banker bot transactions, and a transaction is the event where banker bot sets saving and loans rates, again unspecified as to term period. Banker bot is hunting for the economic bandwidth, operating in the spectral domain.

In other words, banker bot is challenging the member banks to determine the term periods for the posted rates. The rates are like adjustable term loans and deposits. Once the rates are posted we get the following dynamics. The longer the member banks wait, the cheaper the periodic rate for its loan on balance and the expensiver the periodic rate its savings on balance. Eventually member banks will pull their savings, or increase their borrowing; as the term length grows.  At that point, banker bot sees that the flow constraint is out of balance by some small value.  How small is that value? Banker bot has to pay a few humans to manage the member bankers and rent a building. So banker bot actually makes a bet by posting balances, it uses its own system to fund its own humans. Its unit of error is what it needs to make sure rent and salaries are paid.

I can only guess what banker bot aim to do.  It will attempt to take enough of its posted losses so its expenses are paid.  Beyond that I have not though out whether its humans are paid by commission of by month.   That is a determination to be made by experimenting.

So, David Beckworth, this is helicopter money done right, so I have this ongoing bet. I think you are going to adopt the helicopter as the standard vehicle for currency banking.

So, you see, banker bot is all about finding the Schramm-Loenner index of diffusion, the bandwidth of the member banks, including itself.