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[Cryptography] Lightning network

For the lightning network to change from a single consistent state of who owns what part of each gateway unspent transaction output to another single consistent state is equivalent to the well known hard problems of a reliable broadcast channel, the Byzantine generals problem, the two generals problem, and acid transactions on a distributed database.

So when I looked at the lightning documents for a lightning layer on top of bitcoin I expected to see discussion of smart contracts on the bitcoin layer or lightning network protocols on the lightning layer for resolving these hard problems and eventually reaching a resolution.  Not seeing them.

Instead what I do see is that the lightning network is safe because "misconduct" will result in you losing your bitcoins.

It will?  Who do you lose them to?  How is *misconduct* defined?  Who decides *misconduct*?  The guy who gets your bitcoins?  Do we have a central banker of the lightning network somewhere?

A gateway does a unilateral transaction between the parties on the lightning layer controlling the gateway unspent transaction output by generating a new transaction on the bitcoin layer breaking up the gateway between the parties, and the parties refrain from committing that transaction to the blockchain, and instead endless generate new transactions, which do not get played either, thereby changing what part of the gateway is owned by each party to the gateway.

Well, what happens if someone commits an out of date transaction to the blockchain?

Suppose Alice's gateway to Bob is blocked because she now owns the whole of that gateway unspent transaction output, and her gateway to Frankie is blocked because Frankie owns all of that gateway.

So she organizes a transaction that moves bitcoin from the Ann/Bob gateway to the Ann/Frankie gateway.  So what Alice intends is that Alice pays Bob, Bob pays Carol, Carol pays Dan, Dan pays Erin, Erin pays Frank, and Frank pays Alice.  Except that in the middle the transaction Carol and Erin ungracefully disconnect from the network, so that either Ann generated a bitcoin layer transaction giving bitcoin to Bob, but Frankie did not generate a bitcoin layer transaction to Ann, or the other way around.

What happens then?

Does the central banker decide that Carol and Erin were engaged in misconduct and confiscate their bitcoin?
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