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`prove` builds a `Witness` (input openings, digits, multiplicities, blinding and masks) and calls `prove_witness`, which runs the protocol and takes the alpha-dependent reciprocals as a closure. The soundness tests alter a `Witness` and run the production prover, replacing the duplicated cheating prover and the test-only p_s coefficients. Inputs off the (G, H_0)-plane are a witness field, entering the error polynomial as n_hat_V at T^3.
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… a test-only field
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Stacked on #1118. Proofs are unchanged.
provebuilds aWitnessand callsprove_witness, which runs the protocol. The soundness tests now alter aWitnessand run the production prover instead of a duplicated cheating prover.