Aw, crap, you're exactly right. I hit it when I made the topic, but then I went back to edit the topic (ironically, to add the moderation note) and didn't realize I needed to hit the button again. So ... Hmm, we've already got some nontechnical crap in this thread and I can't delete the post. I guess I'm going to lock the thread so it doesn't contribute to the flaming that people can't seem to resist. Besides, both of the people who've responded on-topic have pointed out the problem; miners would have an incentive to publish bogus blocks in order to force their competitors to waste time. So, really, the discussion is over. It floated as an idea, and it got a proper rebuttal.
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Nodes getting just the blocks could then easily verify that a block chain has grown from the genesis block and see how much proof-of-work it contains, allowing them to pick valid longest-chains without tracking the bulk of transactions.
The bandwidth requirement is still the same and the CPU overhead is slightly higher due to more hashing. A full node has to do this otherwise a malicious miner could be producing malicious blocks or just adding in arbitrary hashes.
Yes, you're right about that. I was talking about a new node type somewhere between full and lightweight. It could verify the whole chain of blocks goes to the genesis block, and show that it has more PoW than a bogus chain could have. And it could verify the tx in whatever bundles it happens to download (because it's getting a payment or verifying that one it sent got into the bundle). But it wouldn't attempt to check the entire transaction record.
It would be a little less useless than the usual lightweight client, in having the ability to do "spot checking" of the transaction bundles, but not as good for security as a full node.
Anyway, thanks to me forgetting to hit the self-moderate button, and then 2code doing exactly the thing I intended to moderate against, I'm going to lock this topic. It was a bad idea anyway, as you've pointed out.