Consider a whale at the top of the Btc chain

 He wants to shard his pile of bitcoins. All ne needs is a proof of work extension to existing block chain. He then published this extension, which is compatible to current block chain.

The proof is a contract, I agree to use this extended miner to manage the ocked account and the extended miner returns the money after a time out, to the master chain. I am legally bound, I do not need any other miners. The public knows that amount and can find the loced bitcoins in the block chain trailings.

Great I legally link my contract to a short chain Btc cash, everyone is safe except for congestion risk on my short chain. I have the equivalent of a Btc S/L, and can make Btc change. But if have a residual pile on the master chain and if any recipient of my short cash wants to put it on main chain, fine, I swap for a fee, and return the customers stable Btc back to the short chain.   And visa versa when the swap main chain Btc for stable short chain. 

I keep a transaction limit so short chain has a finite rank. I will add a make change function to my short chain.  

I am making a payment system and by passing huge chunks of main chain work, making the top of the main chain relatively less valued. I need absolutely nothing except a few lines of code in the miners algorithm. And I legally treat those few lines as a legal obligation.   Almost all he other miners would be forced to compete.

A mechant who accept my stable Btc may have an account at my Btc bank. They can run their own miners code to register the exchange.  My chain is short. When users exceed their count, theirstabe coins fold and I wrap up their chain, making me that payee,erasing your history, but making me a payee to you of the residual. Accounts balance, the chain is short, proof of stake is all I need. If my time limit is up on themain chain, no problemo, I just put another chunk of Btc on shard.

We should let the shard timeout go a year, enough to cover one season.  I will set my block chain so folks mostly balance n a quarterly basis.

Anyone who hols stable Btc but is not my account holder can go to the public entry and do an exit, getting the coin back on main lock. ll very simple, all a maximally efficient stable Btc.