Research proof index

Relative unique decoding radius for RS code with arbitrary finite index type ι.

The polynomials corresponding to Reed-Solomon codewords are of degree smaller than deg.

Perfect completeness for large-field reduction (Sumcheck ++ FinalSum)

Completeness of the round consistency check. Given a polynomial f, challenge γ, and n-th roots of unity ω, when f is honestly evaluated at the scaled points {ω i * s₀}, the round consistency check succeeds with the value (foldNth n f γ).eval (s₀^n). This establishes that the Lagrange interpolant through the evaluation points matches the n-wa...

For a nonzero multivariate polynomial f of total degree at most d, evaluated over a product of finite subsets of a field F, each of cardinality at least m, the number of roots is at most d / m multiplied by the side of the product set.

The pure verifier's underlying non-oracle verifier returns the statement together with the sampled challenge (read off the transcript), with the oracle statements passed through.