So when does the sandbox S/L fail?

Blackswans bankrupt it, especially pandemics as we see.

The pit boss if aced with  acollapse of lhe loan queue and a huge pile of sudden deposits. There is  no bipartite matching between the two that remains within the pit boss error bounds.   The rank of the queues suddenly drop,, they are very inaccurate.     The pit boss gets into an infinite loop, constantly waiting for new entries, but never finding a solution to let the betting proceed.

In essence the map cannot be maintained.  Interest flow becomes too low to carry the burden of the map. The S/L kind of evaporates.

In this case loans are rising faster than deposits.  The Fed should be collecting interest by inserting it own savings. Bring the imbalance of 2020 back to the imbalance of 2025. The Fed needs a surplus in its market making account.   But we can see that after the sudden stop the two queues are composed of one humongous deposit and one humongous loan. Thisis a queue length of one.

There is no way the fed can find any structure, in the two color the primary goal is remove relative skew. There is no skew.

 The Fed could continually execute an interest swap from loans to deposits and keep them balanced.   That is a requant here, the place for the Fed to do that was a year ago when the divergence was observed. The Fed does not have a risk equalized set of traders, a requant lgrantss a bunch of arbitrage moments.   Some of the deposits in that last spike will get much more interest then thay expected. The Fed is way off equilibrium for a currency banker. It takes energy to close in on the optimum, if one gets too far off the cost is too high to return.

As a Turing machine our pit boss dos not resolve the graph into a spanning tree without loops.  In this cased the pit boss sees no step that yields a better match, they have the same skew. It sees the absence of skew and thus accepts more congestion, and retries, never coming to a conclusion.   Neither side willing to change the bet, the deposits and loans always agreeing, the validator does not see any message response..

The Fed gets no bandwidth, remember the pit boss get a bit at the lower rung of Markov.  Butr, given that transactions are minimized in the system, and any Fed exchange is a transaction, the Fed will have none. it is gone, not bankrupt, just retired.

That new proof is getting me to think, I need to read more of it. But in sandbox we can see failure modes, we can see instances where the pit boss contract fails,  make sure that is an adiabatic process.

I think we will find that risk equalized groups agree on boundary conditions, that sort of defines the stable pit.  A long time ago I went into this, each trader has to take the same size steps around the boundary in a no arbitrage pit. That and round robin access to the trade board.