Some new math related to sandbox

Graced With Knowledge, Mathematicians Seek to Understand 

A landmark proof in computer science has also solved an important problem called the Connes embedding conjecture. Mathematicians are working to understand it.

The Comnes conjecture was disproved. I read the introduction, the proof is actually a book and rapidly becoming a textbook.

Let me put the Comnes conjecture in terms of a sandbax standard two color S/L.  We can view the S/L at a matching that finds a bipartite match between the deposit queue and the loan queue. That is, the pit boss can find matching between all loans and all deposits within a bounded error. The Colmnes conjecture says that if we decrease the bounded error then the match between deposits and loans will be an adiabatic change, one node exchange at a time as the generator rank increases. The pit boss will not go into a loop. What we call a Comnes fail is a requant, an alteration of the generators by more than one node at a time, like the US economy is doing now.

The new proof says this may not always be true. They use bipartite matching of messages with a verifier.  The deposits attempt to send one message, and loans attempt to send the answers, the verifies adjusts both messages so their is response in loan for every question in deposits, an information coding model over a duplex channel.

Well there is a large class of problems for which Comnes is true, and the class matching problems where it is not true is unknown.  It seems the sandbox is dealing with cutting edge mathematics.  Whether we have a loop in the matching process depends on whether the pit boss captures an entire sequence.  And we impose a condition, risk equalization that should prevent pit boss from missing part of a complete sequence.  My assumption is that the pit boss error bound improves as deposits and loans adopt a longer depreciation cycle. This is a sub class fof sequences that assume players know and compensate to make Comnes true for the two queuse. I can see the proof outlines, the trading bots should always have a moment to retract a bet not yet processed and force the system to be Comnes compliant. And we can impose that condition on the pit boss contract.

But this is a lot of work for me, as usual, and I am a slacker. We can make Comnes true always via contract, then the pit boss can automatically reduce the error bound and report the new value as the complete sequence grows.  But for us, Comnes is always about making sure all traders get in their bets.  If one player finds an arbitrage places a bet, but the pit boss misses the bet, then the pit boss will loop.

This is also quite relevant to Coinbase matching algorithm as well as a number of trading pits out their now. I would hope their techies read the Quanta story.  The problem shows up for coinbase when they are hit with a sudden shock and not all then traders have automatic adjustments.  The Colmnes conjecture fails, and this has happened in bitcoin.  But it is always a problem when traders do not have correct bounded trading algorithms that spot and adjust to arbitrage.