Research proof index

For a multilinear t (each variable has degreeOf ≤ 1), substituting t into a univariate Q : L[X] via Polynomial.aeval yields a multivariate polynomial whose degree in each variable is bounded by Q.natDegree. Used by the structured sumcheck to bound the degree of Q(witness) in the round polynomial H = P · Q(t).

The per-variable / prismalinear degree-survival lemma: if a polynomial respects a per-variable degree bound b : Fin ℓ → ℕ, then fixing the first v variables to scalars produces a polynomial whose surviving Fin (ℓ-v) variables respect b restricted to their original suffix indices. Needed for SWIRL-style sumchecks where the multiplier has degree `|D...