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Edited appa_whitepaper.adoc with Atlas code editor

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@ -78,11 +78,11 @@ image::images/mbc3_aain04.png["disk"]
A block header with no transactions would be about 80 bytes. If we suppose blocks are generated every 10 minutes, +80 bytes * 6 * 24 * 365 = 4.2MB+ per year. With computer systems typically selling with 2GB of RAM as of 2008, and Moore's Law predicting current growth of 1.2GB per year, storage should not be a problem even if the block headers must be kept in memory.
==== Simplified Payment Verification
It is ((("payment verification", "in Bitcoin whitepaper", secondary-sortas="Bitcoin whitepaper", id="payment-verify")))((("verifying payment", "in Bitcoin whitepaper", secondary-sortas="Bitcoin whitepaper", id="verify-payment")))possible to verify payments without running a full network node. A user only needs to keep a copy of the block headers of the longest proof-of-work chain, which he can get by querying network nodes until he's convinced he has the longest chain, and obtain the Merkle branch linking the transaction to the block it's timestamped in. He can't check the transaction for himself, but by linking it to a place in the chain, he can see that a network node has accepted it, and blocks added after it further confirm the network has accepted it.
It is ((("payment verification", "in Bitcoin whitepaper", secondary-sortas="Bitcoin whitepaper", id="payment-verify")))((("verifying", "payment", "in Bitcoin whitepaper", tertiary-sortas="Bitcoin whitepaper", id="verify-payment")))possible to verify payments without running a full network node. A user only needs to keep a copy of the block headers of the longest proof-of-work chain, which he can get by querying network nodes until he's convinced he has the longest chain, and obtain the Merkle branch linking the transaction to the block it's timestamped in. He can't check the transaction for himself, but by linking it to a place in the chain, he can see that a network node has accepted it, and blocks added after it further confirm the network has accepted it.
image::images/mbc3_aain05.png["spv"]
As such, the verification is reliable as long as honest nodes control the network, but is more vulnerable if the network is overpowered by an attacker. While network nodes can verify transactions for themselves, the simplified method can be fooled by an attacker's fabricated transactions for as long as the attacker can continue to overpower the network. One strategy to protect against this would be to accept alerts from network nodes when they detect an invalid block, prompting the user's software to download the full block and alerted transactions to confirm the inconsistency. Businesses that receive frequent payments will probably still want to run their own nodes for more independent security and quicker ((("payment verification", "in Bitcoin whitepaper", secondary-sortas="Bitcoin whitepaper", startref="payment-verify")))((("verifying payment", "in Bitcoin whitepaper", secondary-sortas="Bitcoin whitepaper", startref="verify-payment")))verification.
As such, the verification is reliable as long as honest nodes control the network, but is more vulnerable if the network is overpowered by an attacker. While network nodes can verify transactions for themselves, the simplified method can be fooled by an attacker's fabricated transactions for as long as the attacker can continue to overpower the network. One strategy to protect against this would be to accept alerts from network nodes when they detect an invalid block, prompting the user's software to download the full block and alerted transactions to confirm the inconsistency. Businesses that receive frequent payments will probably still want to run their own nodes for more independent security and quicker ((("payment verification", "in Bitcoin whitepaper", secondary-sortas="Bitcoin whitepaper", startref="payment-verify")))((("verifying", "payment", "in Bitcoin whitepaper", tertiary-sortas="Bitcoin whitepaper", startref="verify-payment")))verification.
==== Combining and Splitting Value
Although ((("transactions", "inputs", "in Bitcoin whitepaper", secondary-sortas="Bitcoin whitepaper")))((("transactions", "outputs", "in Bitcoin whitepaper", secondary-sortas="Bitcoin whitepaper")))((("inputs", "in Bitcoin whitepaper", secondary-sortas="Bitcoin whitepaper")))((("outputs", "in Bitcoin whitepaper", secondary-sortas="Bitcoin whitepaper")))it would be possible to handle coins individually, it would be unwieldy to make a separate transaction for every cent in a transfer. To allow value to be split and combined, transactions contain multiple inputs and outputs. Normally there will be either a single input from a larger previous transaction or multiple inputs combining smaller amounts, and at most two outputs: one for the payment, and one returning the change, if any, back to the sender.