Bridge between L1 (Ethereum) and L2 (cheapETH)

We have two chains (lol two chainz: https://www.youtube.com/watch?v=4dfSrP1CbeQ)

The ETH chain and the cheapETH chain. We can assume the ETH chain has ~1000x more value than the cheapETH chain.

In order to move value between chains, we need a trusted way to get the state of each chain on to the other chain.

L1 -> L2 Bridge:

L1 (ETH) is secured by proof of work. Generating a fake proof of work chain is very expensive.

How it works:

1. Deploy contract on L2 with a checkpoint hash of an ETH block. You can manually audit this, the same way you would audit the contract address.

2. Anyone can submit future block headers of the main chain, the contract validates that they are correct and have the right difficultly. 

3. If someone submits a longer chain, the contract follows that chain. (block reorg)

Think like we are running a "light node" on cheapETH itself. I don't know how doable this is, but it would be nice if it worked. The key part is that the cheapETH contract must be able to validate the difficult operation.

If this can't be reasonably written on the Ethereum platform, we could have a special contract address on cheapETH which contains the mainETH state hash, but I hope it doesn't come to that.