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The Basics of Folding Schemes
The main trick is something that we see very often in the proof systems. The random linear combination of different things. So what the folding scheme does is it has the prover commit to these cross terms or the error vector first, and then the verifier sends a challenge That's going to be used for the random linear combination. Then the prover can combine the two witness vectors and also the two error vectors using this cross term.