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I received the below as reply-one and am forwarding with permission:
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Hi Jeremy,
This is a presentation I did in 2016 on SPV as "Satoshi's scaling solution".
There are no new types of proofs, just old fashioned proofs-of-coin and proofs-of-spend. My approach was to try to envision what the whole network would need to look like.
A common objection to SPV was that full nodes would be "overloaded", so I introduced spv-serving light nodes with different services.
A key idea (which is not stated explicitly in the slides) is for a node to advertise interest in a set of tx hash stems for which it would provide proof services, and for which it wanted to be relayed transactions. The set would contain stems of varying lengths that could be as short as 1 hex character or as long as some max.
Wallets would do this same registration to cause transactions to be routed to themselves. Nearly all of those stems would be randomly introduced for privacy.
Bloom filters are mentioned as part of a transaction repeater service but that was for compatibility with existing SPV wallets of the time. The main idea was to achieve scaling and privacy by the registration scheme.
Hope it's useful in some way!
Cheers,
Tom Harding