Great idea

It is crypto overlaid on crypto: Republic miners work to match your order so that you can tell Ethereum miners to transfer your ether to your counterparty while she tells Bitcoin miners to transfer her Bitcoins to you. The distributed matching engine is separate from the two different distributed settlement ledgers.

Matt Levine talking about Republic Protocol.

Take the standard S&L pit as we know it, but skip 'mark to market' and give the pit boss a known protocol to search one structured queue for a match to a particular trade, then complete the order.

Good idea.  Think of the current standard S&L doing generator algebra as the Fast Fourier of trading. Then the Republic protocol is the individual integrator version. The result is that observations of the market and trade in the market happen simultaneously for the two traders, but they bear a bigger matching error and suffer more timeouts.

After the one trade finds the other, the two structured queues are left in a stable updated state, representing the fact that the last two traders had the most up to date match and thus leave the queues priced for optimal congestion.

Matching times will be longer, but we do not care because they are matching trades from a set of large values. I consider Republic Protocol a great company, welcome to the sandbox.

As part of  pipeline control

Dark pool is the spectre based pipeline control system, 100% dark pool and can support the global economy.  Pits, what we have been calling N-colored pricers are batch processors.  They have a different rule set than finite protocols. But both Republic and the batch processors have to queue up somewhere, they queue on the blockchain the batchers queue on the generator. In both cases we need a call out of pipeline control to a different security context, escrow routers don't queue up.

In my map, I have standard trading protocols running in the pipeline. A Republic Pricer is exactly like a call to a notary while a batch pricer is a call to the pit boss.