Wording "at anytime" to "at any time" #459

ch12.asciidoc

@@ -17,7 +17,7 @@ No Double-Spend:: The most fundamental guarantee of bitcoin's decentralized cons
 
 Immutability:: Once a transaction is recorded in the blockchain and sufficient work has been added with subsequent blocks, the transaction's data becomes immutable. Immutability is underwritten by energy, as rewriting the blockchain requires the expenditure of energy to produce Proof-of-Work. The energy required and therefore the degree of immutability increases with the amount of work committed on top of the block containing a transaction.
 
-Neutrality:: The decentralized bitcoin network propagates valid transactions regardless of the origin or content of those transactions. This means that anyone can create a valid transaction with sufficient fees and trust they will be able to transmit that transaction and have it included in the blockchain at anytime.
+Neutrality:: The decentralized bitcoin network propagates valid transactions regardless of the origin or content of those transactions. This means that anyone can create a valid transaction with sufficient fees and trust they will be able to transmit that transaction and have it included in the blockchain at any time.
 
 Secure Timestamping:: The consensus rules reject any block whose timestamp is too far in the past or future. This ensures that timestamps on blocks can be trusted. The timestamp on a block implies an unspent-before guarantee for the inputs of all included transactions.
 
@@ -311,7 +311,7 @@ The first form of unidirectional payment channel was demonstrated as a prototype
 
 Timelocks are not the only way to invalidate prior commitment transactions. In the next sections we will see how a revocation key can be used to achieve the same result. Timelocks are effective but they have two distinct disadvantages. By establishing a maximum timelock when the channel is first opened, they limit the lifetime of the channel. Worse, they force channel implementations to strike a balance between allowing long-lived channels and forcing one of the participants to wait a very long time for a refund in case of premature closure. For example, if you allow the channel to remain open for 30 days, by setting the refund timelock to 30 days, if one of the parties disappears immediately the other party must wait 30 days for a refund. The more distant the endpoint, the more distant the refund.
 
-The second problem is that since each subsequent commitment transaction must decrement the timelock, there is an explicit limit on the number of commitment transactions that can be exchanged between the parties. For example, a 30-day channel, setting a timelock of 4320 blocks into the future, can only accommodate 4320 intermediate commitment transactions before it must be closed. There is a danger in setting the timelock commitment transaction interval at 1 block. By setting the timelock interval between commitment transactions to 1 block, a developer is creating a very high burden for the channel participants who have to be vigilant, remain online and watching, and be ready to transmit the right commitment transaction at anytime.
+The second problem is that since each subsequent commitment transaction must decrement the timelock, there is an explicit limit on the number of commitment transactions that can be exchanged between the parties. For example, a 30-day channel, setting a timelock of 4320 blocks into the future, can only accommodate 4320 intermediate commitment transactions before it must be closed. There is a danger in setting the timelock commitment transaction interval at 1 block. By setting the timelock interval between commitment transactions to 1 block, a developer is creating a very high burden for the channel participants who have to be vigilant, remain online and watching, and be ready to transmit the right commitment transaction at any time.
 
 Now that we understand how timelocks can be used to invalidate prior commitments, we can see the difference between closing the channel cooperatively and closing it unilaterally by broadcasting a commitment transaction. All commitment transactions are timelocked, therefore broadcasting a commitment transaction will always involve waiting until the timelock has expired. But if the two parties agree on what the final balance is and know they both hold commitment transactions that will eventually make that balance a reality, they can construct a settlement transaction without a timelock representing that same balance. In a cooperative close, either party takes the most recent commitment transaction and builds a settlement transaction that is identical in every way except that it omits the timelock. Both parties can sign this settlement transaction knowing there is no way to cheat and get a more favorable balance. By cooperatively signing and transmitting the settlement transaction they can close the channel and redeem their balance immediately. Worst case, one of the parties can be petty, refuse to cooperate, and force the other party to do a unilateral close with the most recent commitment transaction. But if they do that, they have to wait for their funds too.((("", startref="PSCtrust12")))