Succinct Validation of a Sparse Linear Solve

Suppose you pose the following problem to me: solve a large sparse linear system Ax=b , where A and b are public and x is unknown. Can I convince you that I have a good x without sending the whole vector? The answer turns out to be yes. I can solve the system by any method I like and send a proof whose validator uses only a few megabytes of memory, even when the solution has millions of entries.…