Binomials as a miner fee optimization

 Transactions that happen frequently have low fees. Fees go as log.

A transaction queue in one partition of the block chain at lowest entropy is the place to make the best miners fee. Lowest entropy carries an unbid hedge.

If there are natural partitions it is due to the market uncertainty, no miner has the latest block chain. 

Consider the lower rung of a vertical partition. Call this bearer cash. It is locked cash in the sense that its chain can only have some small finite depth.  It is time limited.  Whenever a bearer cash is exchanged, one or both parties submit this to the miners queue. The miner who validates the entire chain, up to the locked node gets  a finders fee since this chain must ultimately unlock and revert, there is an additional miners fee to be had.  The miner makes change and reissues the bearer cash with the miner signature embedded. 

The exchange is registered up to the locked account, and the miner has a claim to the next fee up since locked accounts are finite.  The block chain miners become proof of stake.

Compound lock up? Sure why not.  The miner who invest in the bottom of the chain accumulates a lot like a yield curve.  The count limit, how many times can we turn over bearer cash.  Each bearer exchange creates another miner with a stake, and generally adds one stake to the previous miner. 

The account locked prepays for the unlock.  So the account holder is paying for some limited number of cash exchanges in advance.  The miners also service the block chain parts that do not have locked in partitions, and fee sharing happens there too.   So the umber of cash transactions desired should be a bound value. There should be a natural partition set once cash lock out is allowed.  

When a lock out happens, the unlock fee is saved for the bidding miner. All parties guaranteed the bearer cash clears.