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minor improvements to chapter "Comparison with Bitcoin" part 4 (#207)

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- bitcoin, not Bitcoin
- minor fixes
- etc
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@ -662,19 +662,20 @@ This must hold true for every single channel that the payment is routed through.
The lowest capacity of a channel set the upper limit of the full route through this channel.
Hence, capacity and connectivity are crucial resources in the Lightning network.
==== Using the Blockchain as a Ledger vs Using the Blockchain as a Court system
==== Using the Blockchain as a Ledger vs Using the Blockchain as a Court System
On the Bitcoin Network, every transaction is eventually recorded in a block on the blockchain.
The blockchain thus forms of a complete history of every transaction since Bitcoin's creation, and a way to fully audit every bitcoin in existence.
The blockchain thus forms a complete history of every transaction since Bitcoin's creation, and a way to fully audit every bitcoin in existence.
Once a transaction is included in the blockchain it is final.
Thus no disputes can arise and it is unambiguous how much bitcoin is controlled by a particular address at a particular point in the blockchain.
(The only possible dispute is if the blockchain forks into two or more different blockchains)
Thus, no disputes can arise and it is unambiguous how much bitcoin is controlled by a particular address at a particular point in the blockchain.
(The only possible dispute is if the blockchain forks into two or more different blockchains.)
On the Lightning Network, the balance in a channel at a particular time is known only to the two channel partners, and is only made visible to the rest of the network when the channel is closed.
When the channel is closed, the final balance of the channel is submitted to the Bitcoin blockchain, and each partner receives their share of the bitcoin in that channel.
For instance: if the opening balance was 1 BTC to Alice, and Alice made a payment of 0.3 BTC to Bob, then the final balance of the channel is 0.7 BTC to Alice and 0.3 BTC to Bob.
If Alice tries to cheat by submitting the opening state of the channel to the Bitcoin blockchain, with 1 BTC to Alice and 0 BTC to Bob, then Bob can retaliate by submitting the true final state of the channel, as well as penalty transaction that gives him all Bitcoin in the channel.
In this context, the Bitcoin blockchain acts as a court system; recording the initial and final balances of each channel, and approving penalties if one of the parties tries to cheat.
For instance, if the opening balance was 1 BTC paid by Alice, and Alice made a payment of 0.3 BTC to Bob, then the final balance of the channel is 0.7 BTC for Alice and 0.3 BTC for Bob.
If Alice tries to cheat by submitting the opening state of the channel to the Bitcoin blockchain, with 1 BTC for Alice and 0 BTC for Bob, then Bob can retaliate by submitting the true final state of the channel, as well as create a penalty transaction that gives him all bitcoin in the channel.
For the Lightning network, the Bitcoin blockchain acts as a court system.
Like an arbitrer Bitcoin records the initial and final balances of each channel, and approves penalties if one of the parties tries to cheat.
==== Offline vs Online, Asynchronous vs Synchronous

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